"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { blockquote: "blockquote", code: "code", h3: "h3", li: "li", ol: "ol", p: "p", pre: "pre", span: "span", strong: "strong", table: "table", tbody: "tbody", td: "td", th: "th", thead: "thead", tr: "tr", ul: "ul", ..._provideComponents(), ...props.components }, {Answer, Assessment, CodeBlock, ContentAttribution, DefinitionEntry, DefinitionGroup, English, Explanation, Hinglish, ImportantQA, KeyPoints, MCQ, Practical, Prompt, QAQuestion, SubTopicHeader, Theory, TopicOverview} = _components; if (!Answer) _missingMdxReference("Answer", true); if (!Assessment) _missingMdxReference("Assessment", true); if (!CodeBlock) _missingMdxReference("CodeBlock", true); if (!ContentAttribution) _missingMdxReference("ContentAttribution", true); if (!DefinitionEntry) _missingMdxReference("DefinitionEntry", true); if (!DefinitionGroup) _missingMdxReference("DefinitionGroup", true); if (!English) _missingMdxReference("English", true); if (!Explanation) _missingMdxReference("Explanation", true); if (!Hinglish) _missingMdxReference("Hinglish", true); if (!ImportantQA) _missingMdxReference("ImportantQA", true); if (!KeyPoints) _missingMdxReference("KeyPoints", true); if (!MCQ) _missingMdxReference("MCQ", true); if (!Practical) _missingMdxReference("Practical", true); if (!Prompt) _missingMdxReference("Prompt", true); if (!QAQuestion) _missingMdxReference("QAQuestion", true); if (!SubTopicHeader) _missingMdxReference("SubTopicHeader", true); if (!Theory) _missingMdxReference("Theory", true); if (!TopicOverview) _missingMdxReference("TopicOverview", true); return _jsxs(_Fragment, { children: [_jsxs(Theory, { children: [_jsx(SubTopicHeader, { id: "3.1", title: "Characteristics of an Array, One Dimensional & Two Dimensional Arrays, Multi-Dimensional Arrays" }), _jsxs(TopicOverview, { title: "Understanding Arrays in C", topicId: "3.1", readingTime: "8 min read", difficulty: "Medium", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["Arrays are one of the most fundamental data structures in C programming. Imagine you need to store marks of 100 students — declaring 100 separate variables like ", _jsx(_components.code, { children: "mark1" }), ", ", _jsx(_components.code, { children: "mark2" }), ", ..., ", _jsx(_components.code, { children: "mark100" }), " would be extremely tedious and impractical. Arrays solve this problem by providing a way to store multiple values of the ", _jsx(_components.strong, { children: "same data type" }), " under a single name, accessible using an index. In this subtopic, we will explore what arrays are, their key characteristics, and how one-dimensional, two-dimensional, and multi-dimensional arrays work in C."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Arrays C programming mein sabse fundamental data structures mein se ek hain. Socho agar tumhe 100 students ke marks store karne ho — toh 100 alag-alag variables declare karna jaise ", _jsx(_components.code, { children: "mark1" }), ", ", _jsx(_components.code, { children: "mark2" }), ", ..., ", _jsx(_components.code, { children: "mark100" }), " bahut mushkil aur impractical hoga. Arrays is problem ko solve karte hain — yeh ek aisa tarika dete hain jisme tum ", _jsx(_components.strong, { children: "same data type" }), " ke multiple values ko ek single name ke under store kar sakte ho, aur unhe index use karke access kar sakte ho. Is subtopic mein hum dekhenge arrays kya hain, unki key characteristics kya hain, aur C mein one-dimensional, two-dimensional, aur multi-dimensional arrays kaise kaam karte hain."] }) })] }), _jsxs(DefinitionGroup, { children: [_jsxs(DefinitionEntry, { term: "Array", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["An array is a collection of elements of the ", _jsx(_components.strong, { children: "same data type" }), " stored in ", _jsx(_components.strong, { children: "contiguous (adjacent) memory locations" }), " under a single variable name. Each element can be accessed individually using its position number, called an ", _jsx(_components.strong, { children: "index" }), ". For example, ", _jsx(_components.code, { children: "int marks[5]" }), " creates an array that can hold 5 integer values — ", _jsx(_components.code, { children: "marks[0]" }), ", ", _jsx(_components.code, { children: "marks[1]" }), ", ", _jsx(_components.code, { children: "marks[2]" }), ", ", _jsx(_components.code, { children: "marks[3]" }), ", and ", _jsx(_components.code, { children: "marks[4]" }), "."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Array ek aisi collection hai jisme ", _jsx(_components.strong, { children: "same data type" }), " ke elements ", _jsx(_components.strong, { children: "contiguous (bagal-bagal) memory locations" }), " mein ek single variable name ke under store hote hain. Har element ko uski position number — jise ", _jsx(_components.strong, { children: "index" }), " kehte hain — se access kiya ja sakta hai. For example, ", _jsx(_components.code, { children: "int marks[5]" }), " ek array banata hai jo 5 integer values store kar sakta hai — ", _jsx(_components.code, { children: "marks[0]" }), ", ", _jsx(_components.code, { children: "marks[1]" }), ", ", _jsx(_components.code, { children: "marks[2]" }), ", ", _jsx(_components.code, { children: "marks[3]" }), ", aur ", _jsx(_components.code, { children: "marks[4]" }), "."] }) })] }), _jsxs(DefinitionEntry, { term: "Index (Subscript)", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["An index (also called a subscript) is the position number used to access a specific element in an array. In C, array indexing always starts from ", _jsx(_components.strong, { children: "0" }), " — so the first element is at index 0, the second at index 1, and so on. If an array has ", _jsx(_components.code, { children: "n" }), " elements, the valid indices range from ", _jsx(_components.code, { children: "0" }), " to ", _jsx(_components.code, { children: "n-1" }), "."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Index (jise subscript bhi kehte hain) wo position number hai jo array ke kisi specific element ko access karne ke liye use hota hai. C mein array indexing hamesha ", _jsx(_components.strong, { children: "0" }), " se start hoti hai — toh pehla element index 0 par hota hai, doosra index 1 par, aur aise chalta rehta hai. Agar array mein ", _jsx(_components.code, { children: "n" }), " elements hain, toh valid indices ", _jsx(_components.code, { children: "0" }), " se ", _jsx(_components.code, { children: "n-1" }), " tak hote hain."] }) })] }), _jsxs(DefinitionEntry, { term: "Contiguous Memory", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["Contiguous memory means that all elements of an array are stored in ", _jsx(_components.strong, { children: "adjacent (back-to-back) memory addresses" }), " with no gaps between them. This is what makes arrays efficient — the compiler can quickly calculate the address of any element using the base address and index, without searching through the entire memory."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Contiguous memory ka matlab hai ki array ke saare elements ", _jsx(_components.strong, { children: "adjacent (bagal-bagal) memory addresses" }), " mein bina kisi gap ke store hote hain. Yahi cheez arrays ko efficient banati hai — compiler base address aur index use karke kisi bhi element ka address jaldi se calculate kar sakta hai, poori memory ko search kiye bina."] }) })] }), _jsxs(DefinitionEntry, { term: "Base Address", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["The base address is the memory address of the ", _jsx(_components.strong, { children: "first element" }), " (index 0) of an array. Once the compiler knows the base address and the size of each element, it can compute the address of any element using the formula: ", _jsx(_components.code, { children: "address(arr[i]) = base_address + i * sizeof(element)" }), "."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Base address array ke ", _jsx(_components.strong, { children: "pehle element" }), " (index 0) ka memory address hota hai. Jab compiler ko base address aur har element ka size pata hota hai, toh woh kisi bhi element ka address is formula se compute kar sakta hai: ", _jsx(_components.code, { children: "address(arr[i]) = base_address + i * sizeof(element)" }), "."] }) })] }), _jsxs(DefinitionEntry, { term: "One-Dimensional Array", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["A one-dimensional array (1D array) is the simplest form of an array — it stores elements in a ", _jsx(_components.strong, { children: "single linear row" }), ". Think of it like a row of lockers, each with a number. Declaration example: ", _jsx(_components.code, { children: "int arr[5];" }), " creates a 1D array of 5 integers."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["One-dimensional array (1D array) array ka sabse simple form hai — yeh elements ko ek ", _jsx(_components.strong, { children: "single linear row" }), " mein store karta hai. Isko ek row of lockers jaiso samjho, jisme har locker ka ek number hai. Declaration example: ", _jsx(_components.code, { children: "int arr[5];" }), " ek 5 integers ka 1D array banata hai."] }) })] }), _jsxs(DefinitionEntry, { term: "Two-Dimensional Array", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["A two-dimensional array (2D array) is essentially an ", _jsx(_components.strong, { children: "array of arrays" }), " — it organizes data in a ", _jsx(_components.strong, { children: "grid or table format" }), " with rows and columns. It is perfect for representing matrices, chess boards, spreadsheets, or any tabular data. Declaration example: ", _jsx(_components.code, { children: "int arr[3][4];" }), " creates a 2D array with 3 rows and 4 columns (12 elements total)."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Two-dimensional array (2D array) basically ", _jsx(_components.strong, { children: "array of arrays" }), " hai — yeh data ko ", _jsx(_components.strong, { children: "grid ya table format" }), " mein rows aur columns mein organize karta hai. Yeh matrices, chess boards, spreadsheets, ya koi bhi tabular data represent karne ke liye perfect hai. Declaration example: ", _jsx(_components.code, { children: "int arr[3][4];" }), " ek 2D array banata hai jisme 3 rows aur 4 columns hain (total 12 elements)."] }) })] }), _jsxs(DefinitionEntry, { term: "Multi-Dimensional Array", children: [_jsx(English, { children: _jsxs(_components.p, { children: ["Multi-dimensional arrays extend the concept beyond two dimensions. A three-dimensional array adds a ", _jsx(_components.strong, { children: "depth" }), " dimension to the rows and columns, creating a cube-like data structure. In C, you can have arrays with more dimensions, though practically 3D is the most common beyond 2D. Declaration example: ", _jsx(_components.code, { children: "int arr[2][3][4];" }), " creates a 3D array."] }) }), _jsx(Hinglish, { children: _jsxs(_components.p, { children: ["Multi-dimensional arrays concept ko two dimensions se aage le jaate hain. Three-dimensional array rows aur columns ke saath ek ", _jsx(_components.strong, { children: "depth" }), " dimension add karta hai, jo ek cube jaisa data structure banata hai. C mein tumhein aur bhi dimensions ke arrays mil sakte hain, lekin practically 3D sabse common hai 2D ke baad. Declaration example: ", _jsx(_components.code, { children: "int arr[2][3][4];" }), " ek 3D array banata hai."] }) })] })] }), _jsxs(Explanation, { children: [_jsxs(English, { children: [_jsx(_components.h3, { children: "🔍 Characteristics of an Array" }), _jsx(_components.p, { children: "Arrays have several important characteristics that define how they work in C:" }), _jsxs(_components.ol, { children: ["\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Homogeneous Collection" }), " — All elements in an array must be of the ", _jsx(_components.strong, { children: "same data type" }), ". You cannot store an ", _jsx(_components.code, { children: "int" }), " and a ", _jsx(_components.code, { children: "float" }), " together in the same array."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Fixed Size" }), " — Once declared, the size of an array ", _jsx(_components.strong, { children: "cannot be changed" }), " during program execution. ", _jsx(_components.code, { children: "int arr[10]" }), " will always hold exactly 10 integers."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Contiguous Memory Allocation" }), " — All elements sit next to each other in memory — no gaps, no jumping around."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Zero-Based Indexing" }), " — The first element is always at index ", _jsx(_components.code, { children: "0" }), ", not ", _jsx(_components.code, { children: "1" }), ". This is a common source of bugs for beginners!"] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Direct Access via Index" }), " — Any element can be accessed directly in ", _jsx(_components.strong, { children: "O(1) time" }), " using its index — no need to traverse from the beginning."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Array Name as Pointer" }), " — The name of an array acts as a ", _jsx(_components.strong, { children: "constant pointer" }), " to the first element. So ", _jsx(_components.code, { children: "arr" }), " is equivalent to ", _jsx(_components.code, { children: "&arr[0]" }), "."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Elements are Mutable" }), " — You can change (assign new values to) any element after declaration."] }), "\n"] }), _jsx(_components.h3, { children: "🧮 One-Dimensional Array — Deep Dive" }), _jsx(_components.p, { children: "A 1D array is like a shelf with numbered compartments. Here's how it looks in memory:" }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Index: [0] [1] [2] [3] [4]\r\nValue: 10 25 30 15 40\r\nAddress: 1000 1004 1008 1012 1016 (assuming int = 4 bytes)\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration and Initialization:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "// Declaration only\r\nint marks[5];\r\n\r\n// Declaration + Initialization\r\nint marks[5] = {10, 25, 30, 15, 40};\r\n\r\n// Partial Initialization (remaining elements become 0)\r\nint marks[5] = {10, 25}; // Result: {10, 25, 0, 0, 0}\r\n\r\n// Shorthand (compiler automatically determines size)\r\nint marks[] = {10, 25, 30, 15, 40}; // size = 5\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Accessing Elements:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "marks[0] = 10; // First element\r\nmarks[2] = 30; // Third element (index 2)\r\nprintf(\"%d\", marks[3]); // Prints the 4th element\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Traversal using a Loop:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "for (int i = 0; i < 5; i++) {\r\n printf(\"marks[%d] = %d\\n\", i, marks[i]);\r\n}\n" }) }), _jsx(_components.h3, { children: "📊 Two-Dimensional Array — Deep Dive" }), _jsx(_components.p, { children: "A 2D array is like a spreadsheet — it has rows and columns. Think of it as a table where you need both a row number and a column number to pinpoint a value." }), _jsx(_components.pre, { children: _jsx(_components.code, { children: " Col 0 Col 1 Col 2 Col 3\r\nRow 0: [10] [20] [30] [40]\r\nRow 1: [50] [60] [70] [80]\r\nRow 2: [90] [100] [110] [120]\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration and Initialization:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "// Declaration\r\nint matrix[3][4];\r\n\r\n// Declaration + Initialization\r\nint matrix[3][4] = {\r\n {10, 20, 30, 40}, // Row 0\r\n {50, 60, 70, 80}, // Row 1\r\n {90, 100, 110, 120} // Row 2\r\n};\r\n\r\n// Flattened initialization (still fills row-by-row)\r\nint matrix[3][4] = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120};\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Accessing Elements:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "matrix[1][2] = 70; // Row 1, Column 2\r\nprintf(\"%d\", matrix[0][3]); // Prints 40 (Row 0, Column 3)\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Nested Loop Traversal:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "for (int i = 0; i < 3; i++) { // Row loop\r\n for (int j = 0; j < 4; j++) { // Column loop\r\n printf(\"%d\\t\", matrix[i][j]);\r\n }\r\n printf(\"\\n\");\r\n}\n" }) }), _jsx(_components.h3, { children: "🧊 Multi-Dimensional Arrays — The Concept" }), _jsxs(_components.p, { children: ["Multi-dimensional arrays go beyond rows and columns. A ", _jsx(_components.strong, { children: "3D array" }), " adds a depth layer — imagine a stack of spreadsheets."] }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "int cube[2][3][4]; // 2 layers, 3 rows per layer, 4 columns per row\n" }) }), _jsxs(_components.p, { children: ["This creates ", _jsx(_components.code, { children: "2 × 3 × 4 = 24" }), " integer elements. You can visualize it as:"] }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Layer 0: Layer 1:\r\n Col0 Col1 Col2 Col3 Col0 Col1 Col2 Col3\r\nRow0: [ 1] [ 2] [ 3] [ 4] Row0: [ 13] [ 14] [ 15] [ 16]\r\nRow1: [ 5] [ 6] [ 7] [ 8] Row1: [ 17] [ 18] [ 19] [ 20]\r\nRow2: [ 9] [ 10] [ 11] [ 12] Row2: [ 21] [ 22] [ 23] [ 24]\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Access:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "cube[1][2][3] = 24; // Layer 1, Row 2, Column 3\n" }) }), _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.strong, { children: "Note:" }), " In practice, C supports arrays up to any number of dimensions, but going beyond 3D becomes very hard to visualize and manage. Most real-world applications stop at 2D or 3D."] }), "\n"] }), _jsx(_components.h3, { children: "🧠 Memory Layout of 2D Arrays (Row-Major Order)" }), _jsxs(_components.p, { children: ["C stores 2D arrays in ", _jsx(_components.strong, { children: "row-major order" }), " — meaning row 0 is stored first, then row 1, then row 2, all in a single continuous block:"] }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Memory: [10][20][30][40][50][60][70][80][90][100][110][120]\r\n ↑ Row 0 ↑ Row 1 ↑ Row 2\n" }) }), _jsxs(_components.p, { children: ["The formula to find the address of ", _jsx(_components.code, { children: "matrix[i][j]" }), ":"] }), _jsx(_components.p, { children: _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Address" }) }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "ma" }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "r" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mclose", children: "]" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: "])" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Base Address" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "cols" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "sizeof(element)" }) })] })] }) }) }), _jsxs(_components.p, { children: ["For ", _jsx(_components.code, { children: "matrix[1][2]" }), " with base address 1000, 4 columns, and ", _jsx(_components.code, { children: "int" }), " = 4 bytes:"] }), _jsx(_components.p, { children: _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Address" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "1000" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "4" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord", children: "2" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "4" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "1000" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "24" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "1024" })] })] }) }) }), _jsx(_components.h3, { children: "⚠️ Common Mistakes to Avoid" }), _jsxs(_components.table, { children: [_jsx(_components.thead, { children: _jsxs(_components.tr, { children: [_jsx(_components.th, { children: "Mistake" }), _jsx(_components.th, { children: "Problem" })] }) }), _jsxs(_components.tbody, { children: [_jsxs(_components.tr, { children: [_jsxs(_components.td, { children: ["Accessing ", _jsx(_components.code, { children: "arr[5]" }), " when size is 5"] }), _jsx(_components.td, { children: "Index out of bounds! Valid indices are 0–4" })] }), _jsxs(_components.tr, { children: [_jsx(_components.td, { children: "Forgetting array size in declaration without initialization" }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "int arr[];" }), " is invalid — compiler can't determine size"] })] }), _jsxs(_components.tr, { children: [_jsxs(_components.td, { children: ["Using ", _jsx(_components.code, { children: "=" }), " to copy arrays"] }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "arr1 = arr2;" }), " doesn't work — arrays are not assignable"] })] }), _jsxs(_components.tr, { children: [_jsx(_components.td, { children: "Confusing rows and columns in 2D arrays" }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "arr[rows][cols]" }), " — remember: rows first, columns second"] })] })] })] })] }), _jsxs(Hinglish, { children: [_jsx(_components.h3, { children: "🔍 Characteristics of an Array" }), _jsx(_components.p, { children: "Arrays ke kai important characteristics hain jo define karte hain ki yeh C mein kaise kaam karte hain:" }), _jsxs(_components.ol, { children: ["\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Homogeneous Collection" }), " — Array ke saare elements ", _jsx(_components.strong, { children: "same data type" }), " ke hone chahiye. Tum ek ", _jsx(_components.code, { children: "int" }), " aur ", _jsx(_components.code, { children: "float" }), " ko same array mein store nahi kar sakte."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Fixed Size" }), " — Ek baar declare karne ke baad, array ka size ", _jsx(_components.strong, { children: "program execution ke dauran change nahi ho sakta" }), ". ", _jsx(_components.code, { children: "int arr[10]" }), " hamesha exactly 10 integers hi hold karega."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Contiguous Memory Allocation" }), " — Saare elements memory mein ek-doosre ke bagal mein hote hain — koi gap nahi, koi jumping nahi."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Zero-Based Indexing" }), " — Pehla element hamesha index ", _jsx(_components.code, { children: "0" }), " par hota hai, ", _jsx(_components.code, { children: "1" }), " par nahi. Yeh beginners ke liye bugs ka common source hai!"] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Direct Access via Index" }), " — Kisi bhi element ko ", _jsx(_components.strong, { children: "O(1) time" }), " mein directly uske index se access kiya ja sakta hai — beginning se traverse karne ki zaroorat nahi."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Array Name as Pointer" }), " — Array ka naam ek ", _jsx(_components.strong, { children: "constant pointer" }), " ki tarah kaam karta hai jo pehle element ko point karta hai. Toh ", _jsx(_components.code, { children: "arr" }), ", ", _jsx(_components.code, { children: "&arr[0]" }), " ke equivalent hai."] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.strong, { children: "Elements are Mutable" }), " — Declare karne ke baad kisi bhi element ki value change (assign new values) kar sakte ho."] }), "\n"] }), _jsx(_components.h3, { children: "🧮 One-Dimensional Array — Deep Dive" }), _jsx(_components.p, { children: "1D array ek shelf jaisa hai jisme numbered compartments hain. Memory mein aisa dikhta hai:" }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Index: [0] [1] [2] [3] [4]\r\nValue: 10 25 30 15 40\r\nAddress: 1000 1004 1008 1012 1016 (assuming int = 4 bytes)\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration aur Initialization:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "// Sirf Declaration\r\nint marks[5];\r\n\r\n// Declaration + Initialization\r\nint marks[5] = {10, 25, 30, 15, 40};\r\n\r\n// Partial Initialization (baaki elements 0 ho jaate hain)\r\nint marks[5] = {10, 25}; // Result: {10, 25, 0, 0, 0}\r\n\r\n// Shorthand (compiler khud size determine karta hai)\r\nint marks[] = {10, 25, 30, 15, 40}; // size = 5\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Elements Access Karna:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "marks[0] = 10; // Pehla element\r\nmarks[2] = 30; // Teesra element (index 2)\r\nprintf(\"%d\", marks[3]); // Chautha element print karta hai\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Loop se Traversal:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "for (int i = 0; i < 5; i++) {\r\n printf(\"marks[%d] = %d\\n\", i, marks[i]);\r\n}\n" }) }), _jsx(_components.h3, { children: "📊 Two-Dimensional Array — Deep Dive" }), _jsx(_components.p, { children: "2D array ek spreadsheet jaisa hai — isme rows aur columns hain. Isko ek table samjho jisme kisi value ko point karne ke liye row number aur column number dono chahiye." }), _jsx(_components.pre, { children: _jsx(_components.code, { children: " Col 0 Col 1 Col 2 Col 3\r\nRow 0: [10] [20] [30] [40]\r\nRow 1: [50] [60] [70] [80]\r\nRow 2: [90] [100] [110] [120]\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration aur Initialization:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "// Declaration\r\nint matrix[3][4];\r\n\r\n// Declaration + Initialization\r\nint matrix[3][4] = {\r\n {10, 20, 30, 40}, // Row 0\r\n {50, 60, 70, 80}, // Row 1\r\n {90, 100, 110, 120} // Row 2\r\n};\r\n\r\n// Flattened initialization (phir bhi row-by-row fill hota hai)\r\nint matrix[3][4] = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120};\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Elements Access Karna:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "matrix[1][2] = 70; // Row 1, Column 2\r\nprintf(\"%d\", matrix[0][3]); // 40 print karta hai (Row 0, Column 3)\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Nested Loop se Traversal:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "for (int i = 0; i < 3; i++) { // Row loop\r\n for (int j = 0; j < 4; j++) { // Column loop\r\n printf(\"%d\\t\", matrix[i][j]);\r\n }\r\n printf(\"\\n\");\r\n}\n" }) }), _jsx(_components.h3, { children: "🧊 Multi-Dimensional Arrays — The Concept" }), _jsxs(_components.p, { children: ["Multi-dimensional arrays rows aur columns se aage badhte hain. ", _jsx(_components.strong, { children: "3D array" }), " ek depth layer add karta hai — isko ek stack of spreadsheets samjho."] }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Declaration:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "int cube[2][3][4]; // 2 layers, har layer mein 3 rows, har row mein 4 columns\n" }) }), _jsxs(_components.p, { children: ["Yeh ", _jsx(_components.code, { children: "2 × 3 × 4 = 24" }), " integer elements create karta hai. Isko aise visualize kar sakte ho:"] }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Layer 0: Layer 1:\r\n Col0 Col1 Col2 Col3 Col0 Col1 Col2 Col3\r\nRow0: [ 1] [ 2] [ 3] [ 4] Row0: [ 13] [ 14] [ 15] [ 16]\r\nRow1: [ 5] [ 6] [ 7] [ 8] Row1: [ 17] [ 18] [ 19] [ 20]\r\nRow2: [ 9] [ 10] [ 11] [ 12] Row2: [ 21] [ 22] [ 23] [ 24]\n" }) }), _jsx(_components.p, { children: _jsx(_components.strong, { children: "Access:" }) }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c", children: "cube[1][2][3] = 24; // Layer 1, Row 2, Column 3\n" }) }), _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.strong, { children: "Note:" }), " Practically C mein kisi bhi number of dimensions ke arrays support hote hain, lekin 3D se zyada dimensions visualize aur manage karna bahut mushkil ho jaata hai. Zyada tar real-world applications 2D ya 3D tak hi ruke hain."] }), "\n"] }), _jsx(_components.h3, { children: "🧠 2D Arrays ka Memory Layout (Row-Major Order)" }), _jsxs(_components.p, { children: ["C 2D arrays ko ", _jsx(_components.strong, { children: "row-major order" }), " mein store karta hai — matlab pehle row 0 store hoti hai, phir row 1, phir row 2, sab ek single continuous block mein:"] }), _jsx(_components.pre, { children: _jsx(_components.code, { children: "Memory: [10][20][30][40][50][60][70][80][90][100][110][120]\r\n ↑ Row 0 ↑ Row 1 ↑ Row 2\n" }) }), _jsxs(_components.p, { children: [_jsx(_components.code, { children: "matrix[i][j]" }), " ka address find karne ka formula:"] }), _jsx(_components.p, { children: _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Address" }) }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "ma" }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "r" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mclose", children: "]" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: "])" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Base Address" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "cols" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "sizeof(element)" }) })] })] }) }) }), _jsxs(_components.p, { children: [_jsx(_components.code, { children: "matrix[1][2)" }), " ke liye, base address 1000, 4 columns, aur ", _jsx(_components.code, { children: "int" }), " = 4 bytes:"] }), _jsx(_components.p, { children: _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Address" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "1000" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "4" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord", children: "2" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "4" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "1000" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "24" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "1024" })] })] }) }) }), _jsx(_components.h3, { children: "⚠️ Common Mistakes jo Avoid Karne Chahiye" }), _jsxs(_components.table, { children: [_jsx(_components.thead, { children: _jsxs(_components.tr, { children: [_jsx(_components.th, { children: "Mistake" }), _jsx(_components.th, { children: "Problem" })] }) }), _jsxs(_components.tbody, { children: [_jsxs(_components.tr, { children: [_jsxs(_components.td, { children: ["Size 5 hone par ", _jsx(_components.code, { children: "arr[5]" }), " access karna"] }), _jsx(_components.td, { children: "Index out of bounds! Valid indices 0–4 hain" })] }), _jsxs(_components.tr, { children: [_jsx(_components.td, { children: "Bina initialization ke array size bhool jaana" }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "int arr[];" }), " invalid hai — compiler size determine nahi kar paata"] })] }), _jsxs(_components.tr, { children: [_jsxs(_components.td, { children: ["Array copy karne ke liye ", _jsx(_components.code, { children: "=" }), " use karna"] }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "arr1 = arr2;" }), " kaam nahi karta — arrays assignable nahi hote"] })] }), _jsxs(_components.tr, { children: [_jsx(_components.td, { children: "2D arrays mein rows aur columns confusion" }), _jsxs(_components.td, { children: [_jsx(_components.code, { children: "arr[rows][cols]" }), " — yaad rakhno: pehle rows, phir columns"] })] })] })] })] }), _jsx(_components.h3, { children: "📐 Visualizing Array Concepts" }), _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-mermaid", children: "flowchart TD\r\n A[\"Array Concept in C\"] --> B[\"1D Array
int arr[5];
→ Linear row of elements\"]\r\n A --> C[\"2D Array
int arr[3][4];
→ Grid / Table (rows × cols)\"]\r\n A --> D[\"Multi-Dimensional Array
int arr[2][3][4];
→ Cube / Stack of grids\"]\r\n \r\n B --> B1[\"Single index: arr[i]\"]\r\n C --> C1[\"Two indices: arr[i][j]\"]\r\n D --> D1[\"Three indices: arr[i][j][k]\"]\r\n \r\n B1 --> E[\"Contiguous Memory
Base + i × sizeof(int)\"]\r\n C1 --> F[\"Row-Major Order
Base + (i × cols + j) × sizeof(int)\"]\r\n D1 --> G[\"Layer-Major Order
Base + (i×rows×cols + j×cols + k) × sizeof(int)\"]\n" }) }), _jsx(CodeBlock, { language: "c", children: `#include int main() { // --- 1D Array Example --- int marks[5] = {85, 90, 78, 92, 88}; printf("= 1D Array =\n"); for (int i = 0; i < 5; i++) { printf("marks[%d] = %d\\n", i, marks[i]); } // --- 2D Array Example --- int matrix[3][4] = { {10, 20, 30, 40}, {50, 60, 70, 80}, {90, 100, 110, 120} }; printf("\\n= 2D Array =\n"); for (int i = 0; i < 3; i++) { for (int j = 0; j < 4; j++) { printf("%d\\t", matrix[i][j]); } printf("\\n"); } // --- 3D Array Example --- int cube[2][2][2] = { {{1, 2}, {3, 4}}, {{5, 6}, {7, 8}} }; printf("\\n= 3D Array =\n"); for (int i = 0; i < 2; i++) { printf("Layer %d:\\n", i); for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { printf("cube[%d][%d][%d] = %d\\n", i, j, k, cube[i][j][k]); } } } return 0; }` }), _jsx(KeyPoints, { children: _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["An array stores multiple elements of the ", _jsx(_components.strong, { children: "same data type" }), " in ", _jsx(_components.strong, { children: "contiguous memory locations" }), "."] }), "\n", _jsxs(_components.li, { children: ["Array indexing in C starts from ", _jsx(_components.strong, { children: "0" }), " — last valid index is ", _jsx(_components.code, { children: "size - 1" }), "."] }), "\n", _jsxs(_components.li, { children: ["A ", _jsx(_components.strong, { children: "1D array" }), " is a linear list; a ", _jsx(_components.strong, { children: "2D array" }), " is a grid (rows × columns); a ", _jsx(_components.strong, { children: "3D array" }), " adds a depth layer."] }), "\n", _jsxs(_components.li, { children: ["C stores 2D arrays in ", _jsx(_components.strong, { children: "row-major order" }), " — all elements of row 0 come first, then row 1, and so on."] }), "\n", _jsxs(_components.li, { children: ["The array name acts as a ", _jsx(_components.strong, { children: "constant pointer" }), " to the first element (", _jsx(_components.code, { children: "arr" }), " == ", _jsx(_components.code, { children: "&arr[0]" }), ")."] }), "\n", _jsxs(_components.li, { children: ["Array size is ", _jsx(_components.strong, { children: "fixed at compile time" }), " — you cannot resize it during execution."] }), "\n", _jsxs(_components.li, { children: ["Always be careful about ", _jsx(_components.strong, { children: "index out of bounds" }), " errors — accessing beyond the declared size leads to undefined behavior."] }), "\n"] }) })] })] }), "\n", _jsx(Practical, { children: _jsxs(ImportantQA, { children: [_jsxs(QAQuestion, { marks: 2, children: [_jsx(Prompt, { children: "Define an array and state any four characteristics of an array." }), _jsx(Answer, { children: _jsxs(_components.p, { children: ["An ", _jsx(_components.strong, { children: "array" }), " is a collection of similar data elements stored at contiguous memory locations, accessible using a common name and individual indices. ### 📝 Key Characteristics of an Array: 1. ", _jsx(_components.strong, { children: "Homogeneous Elements:" }), " All elements in an array must be of the same data type (e.g., all ", _jsx(_components.code, { children: "int" }), ", all ", _jsx(_components.code, { children: "float" }), ", etc.). 2. ", _jsx(_components.strong, { children: "Contiguous Memory:" }), " Array elements are stored in consecutive memory locations, which allows efficient access and traversal. 3. ", _jsx(_components.strong, { children: "Index-Based Access:" }), " Each element is accessed using its ", _jsx(_components.strong, { children: "index" }), " (position number). In C, indexing starts from ", _jsx(_components.code, { children: "0" }), ". 4. ", _jsx(_components.strong, { children: "Fixed Size:" }), " Once declared, the size of an array cannot be changed during program execution. The size must be a ", _jsx(_components.strong, { children: "constant expression" }), ". 5. ", _jsx(_components.strong, { children: "Random Access:" }), " Any element can be accessed directly in constant time ", _jsx(_components.span, { className: "katex", children: _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "O" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) }) }), " using its index, without traversing the previous elements. The first element is at index ", _jsx(_components.code, { children: "0" }), " and the last element is at index ", _jsx(_components.code, { children: "size - 1" }), ". For example, an array of size 5 has indices 0, 1, 2, 3, 4."] }) })] }), _jsxs(QAQuestion, { marks: 4, children: [_jsx(Prompt, { children: "Explain one-dimensional and two-dimensional arrays in C with their declaration syntax and a suitable example for each." }), _jsx(Answer, { children: _jsxs(_components.h3, { children: ["🎯 One-Dimensional Array A ", _jsx(_components.strong, { children: "one-dimensional (1D) array" }), " is a linear collection of elements. It stores a single row of data. ", _jsx(_components.strong, { children: "Declaration Syntax:" }), " ", _jsx(_components.code, { children: "data_type array_name[size];" }), " ", _jsx(_components.strong, { children: "Example:" }), " ", `int marks[5]; // Declares an array of 5 integers marks[0] = 90; // Assigning value to first element marks[1] = 85; // Assigning value to second element // Declaration with initialization int marks[5] = {90, 85, 78, 92, 88}; // Accessing elements printf("%d", marks[2]); // Output: 78`, " ", _jsx(_components.strong, { children: "Memory Layout (1D):" }), " ", _jsx(_components.code, { children: "Index: [0] [1] [2] [3] [4] Value: 90 85 78 92 88 Address: 1000 1004 1008 1012 1016 (assuming int = 4 bytes)" }), " --- ### 🎯 Two-Dimensional Array A ", _jsx(_components.strong, { children: "two-dimensional (2D) array" }), " is an array of arrays. It is visualized as a ", _jsx(_components.strong, { children: "table" }), " with rows and columns. ", _jsx(_components.strong, { children: "Declaration Syntax:" }), " ", _jsx(_components.code, { children: "data_type array_name[rows][columns];" }), " ", _jsx(_components.strong, { children: "Example:" }), " ", `// Declaration and initialization of a 2x3 matrix int matrix[2][3] = { {1, 2, 3}, {4, 5, 6} }; // Accessing element in row 1, column 2 printf("%d", matrix[1][2]); // Output: 6 // Traversing entire 2D array for (int i = 0; i < 2; i++) { for (int j = 0; j < 3; j++) { printf("%d ", matrix[i][j]); } printf("\\n"); }`, " ", _jsx(_components.strong, { children: "Memory Layout (2D - Row-Major Order):" }), " C stores 2D arrays in ", _jsx(_components.strong, { children: "row-major order" }), " (all elements of row 0 first, then row 1, and so on): ", _jsx(_components.code, { children: "matrix[0][0]=1, matrix[0][1]=2, matrix[0][2]=3, matrix[1][0]=4, matrix[1][1]=5, matrix[1][2]=6" }), " | Array Type | Dimensions | Access Pattern | Use Case | |---|---|---|---| | ", _jsx(_components.strong, { children: "1D Array" }), " | ", _jsx(_components.code, { children: "arr[size]" }), " | ", _jsx(_components.code, { children: "arr[index]" }), " | Linear data like marks list | | ", _jsx(_components.strong, { children: "2D Array" }), " | ", _jsx(_components.code, { children: "arr[rows][cols]" }), " | ", _jsx(_components.code, { children: "arr[i][j]" }), " | Tabular data like matrix | In a 2D array ", _jsx(_components.code, { children: "matrix[R][C]" }), ", the total number of elements = ", _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0077em" }, children: "R" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "C" })] })] }) }), ", and valid indices range from ", _jsx(_components.code, { children: "matrix[0][0]" }), " to ", _jsx(_components.code, { children: "matrix[R-1][C-1]" }), "."] }) })] }), _jsxs(QAQuestion, { marks: 6, children: [_jsx(Prompt, { children: "Explain the concept of multi-dimensional arrays in C. Include the declaration syntax, memory allocation method, and write a C program to demonstrate a three-dimensional array with initialization and traversal." }), _jsx(Answer, { children: _jsxs(_components.h3, { children: ["🎯 Concept of Multi-Dimensional Arrays A ", _jsx(_components.strong, { children: "multi-dimensional array" }), " is an array with more than two dimensions. In C, there is ", _jsx(_components.strong, { children: "no upper limit" }), " on the number of dimensions, though practically 2D and 3D arrays are most commonly used. A multi-dimensional array can be thought of as an ", _jsx(_components.strong, { children: "array of arrays of arrays..." }), " (nested structure). ", _jsx(_components.strong, { children: "General Declaration Syntax:" }), " ", _jsx(_components.code, { children: "data_type array_name[dim1][dim2][dim3]...[dimN];" }), " For a ", _jsx(_components.strong, { children: "3D array:" }), " ", _jsx(_components.code, { children: "data_type array_name[size1][size2][size3];" }), " --- ### 🧠 Memory Allocation - Row-Major Order C allocates all multi-dimensional arrays in a ", _jsx(_components.strong, { children: "single contiguous block of memory" }), " using ", _jsx(_components.strong, { children: "row-major order" }), " (last index varies fastest). For a 3D array ", _jsx(_components.code, { children: "arr[D1][D2][D3]" }), ", the total number of elements is: ", _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Total Elements" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "2" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "3" })] })] }) }), " The ", _jsx(_components.strong, { children: "address of element" }), " ", _jsx(_components.code, { children: "arr[i][j][k]" }), " can be calculated as: ", _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Address" }) }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "a" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "r" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "r" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mclose", children: "]" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: "]" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0315em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: "])" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "Base Address" }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "i" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "2" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "3" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.854em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0572em" }, children: "j" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "D" }), _jsx(_components.span, { className: "mord", children: "3" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0315em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6679em" } }), _jsx(_components.span, { className: "mord text", children: _jsx(_components.span, { className: "mord", children: "size" }) })] })] }) }), " Where ", _jsx(_components.code, { children: "size" }), " is the size of each element in bytes. ", _jsx(_components.strong, { children: "Visualizing Memory (Row-Major):" }), " For a 3D array ", _jsx(_components.code, { children: "arr[2][2][2]" }), ", the elements are stored sequentially in memory as: ", _jsx(_components.code, { children: "arr[0][0][0], arr[0][0][1], arr[0][1][0], arr[0][1][1], arr[1][0][0], arr[1][0][1], arr[1][1][0], arr[1][1][1]" }), " Think of it as ", _jsx(_components.strong, { children: "2 layers" }), ", each layer having a ", _jsx(_components.strong, { children: "2x2 matrix" }), ": ", _jsx(_components.code, { children: "Layer 0 (i=0): Layer 1 (i=1): ┌─────────────────┐ ┌─────────────────┐ │ [0][0] [0][1] │ │ [0][0] [0][1] │ │ 1 2 │ │ 5 6 │ │ │ │ │ │ [1][0] [1][1] │ │ [1][0] [1][1] │ │ 3 4 │ │ 7 8 │ └─────────────────┘ └─────────────────┘" }), " --- ### 📝 C Program: 3D Array Demonstration ", `#include int main() { // Declaration and initialization of a 3D array (2x2x2) int arr[2][2][2] = { { // Layer 0 {1, 2}, {3, 4} }, { // Layer 1 {5, 6}, {7, 8} } }; // Total elements int total = 2 * 2 * 2; printf("Total elements in 3D array: %d\\n\\n", total); // Traversal using three nested for loops printf("Traversing 3D Array:\\n"); for (int i = 0; i < 2; i++) { printf("Layer %d:\\n", i); for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { printf(" arr[%d][%d][%d] = %d\\n", i, j, k, arr[i][j][k]); } } printf("\\n"); } // Accessing a specific element printf("Element at arr[1][0][1] = %d\\n", arr[1][0][1]); return 0; }`, " ", _jsx(_components.strong, { children: "Output:" }), " ", _jsx(_components.code, { children: "Total elements in 3D array: 8 Traversing 3D Array: Layer 0: arr[0][0][0] = 1 arr[0][0][1] = 2 arr[0][1][0] = 3 arr[0][1][1] = 4 Layer 1: arr[1][0][0] = 5 arr[1][0][1] = 6 arr[1][1][0] = 7 arr[1][1][1] = 8 Element at arr[1][0][1] = 6" }), " --- ### 📊 Comparison: 1D, 2D, and 3D Arrays | Feature | 1D Array | 2D Array | 3D Array | |---|---|---|---| | ", _jsx(_components.strong, { children: "Declaration" }), " | ", _jsx(_components.code, { children: "arr[s1]" }), " | ", _jsx(_components.code, { children: "arr[s1][s2]" }), " | ", _jsx(_components.code, { children: "arr[s1][s2][s3]" }), " | | ", _jsx(_components.strong, { children: "Visualization" }), " | Single row | Table (rows & columns) | Cube (layers, rows, columns) | | ", _jsx(_components.strong, { children: "Total Elements" }), " | ", _jsx(_components.span, { className: "katex", children: _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "mord", children: "1" })] }) }) }), " | ", _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "mord", children: "2" })] })] }) }), " | ", _jsx(_components.span, { className: "katex", children: _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { 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_jsx(_components.strong, { children: "undefined behavior" }), " (memory errors). - In practice, arrays beyond 3D dimensions are rarely used because they become very difficult to visualize and manage."] }) })] })] }) }), "\n", _jsxs(Assessment, { topicId: "3.1", children: [_jsx(MCQ, { questions: [{ "id": "78e73756-0076-4c41-85c6-624b291a8cf1", "q": "What is a key characteristic of arrays in C?", "options": ["Elements can be of different data types", "Elements are stored in random memory locations", "Elements are stored in contiguous memory locations", "Array size can be changed after declaration"], "answer": 2, "hint": "Arrays store elements in contiguous memory locations.", "explanation": "One key characteristic of arrays in C is that all elements are stored in contiguous (adjacent) memory locations, which allows efficient indexing using an offset from the base address." }, { "id": "7851b910-3e97-4da1-a49d-167b073e0073", "q": "What is the index of the first element in a C array?", "options": ["0", "1", "-1", "Depends on compiler"], "answer": 0, "hint": "Array indexing in C always starts from zero.", "explanation": "In C, array indexing always starts from 0. 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The correct syntax is int arr[3][4], representing a table with 3 rows and 4 columns." }, { "id": "3d928ef0-f167-4d34-91df-30d6f97044bf", "q": "What is the total number of elements in the declaration int arr[3][4];?", "options": ["7", "3", "12", "16"], "answer": 2, "hint": "The total number of elements is the product of all dimension sizes.", "explanation": "For a two-dimensional array declared as int arr[3][4], the total number of elements is calculated by multiplying the dimensions: 3 multiplied by 4 equals 12 elements." }, { "id": "10ca5ca4-ac32-4ed2-8921-62c849f668c2", "q": "Which of the following is true about array size in C?", "options": ["It must be a constant expression at compile time", "It can be changed at runtime using a special function", "It defaults to 100 if not specified", "It can only be an even number"], "answer": 0, "hint": "Static arrays in C require the size to be known before the program runs.", "explanation": "In C, the size of a static array must be a constant expression known at compile time. It cannot be a variable that changes at runtime (unless using variable-length arrays in C99)." }, { "id": "103bc215-57a1-4a76-8ed4-e5c784717b6f", "q": "In C, a two-dimensional array is stored in memory in which order by default?", "options": ["Column-major order", "Row-major order", "Random order", "Diagonal order"], "answer": 1, "hint": "Think about how the compiler lays out a 2D array in linear memory.", "explanation": "Two-dimensional arrays in C are stored in row-major order by default, meaning elements of the first row are stored first in memory, followed by elements of the second row, and so on." }, { "id": "70517303-a8e9-44a7-ba32-871d14010c5f", "q": "Which of the following is NOT a characteristic of a C array?", "options": ["Homogeneous data type", "Fixed size after declaration", "Elements of different data types", "Contiguous memory allocation"], "answer": 2, "hint": "All elements in a C array must share the same data type.", "explanation": "Arrays in C are homogeneous collections, meaning all elements must be of the same data type. Having elements of different data types is NOT a characteristic of C arrays." }, { "id": "10f158bf-a737-415f-ab1a-804050c0dd42", "q": "What is the correct way to declare a three-dimensional array in C?", "options": ["int arr[2,3,4];", "int arr[2][3,4];", "int arr(2)(3)(4);", "int arr[2][3][4];"], "answer": 3, "hint": "Multi-dimensional arrays use one set of square brackets per dimension.", "explanation": "A three-dimensional array in C uses three sets of square brackets, one for each dimension. 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