What is a 2D Array?

A 2D array (two-dimensional array) is an array of arrays. It represents data in a table format with rows and columns, like a matrix or grid.

Declaration Syntax

data_type array_name[rows][columns];

Declaring and Initializing 2D Arrays

1. Declaration Then Assignment

#include <stdio.h> int main() { int matrix[3][4]; // 3 rows, 4 columns // Assign values matrix[0][0] = 1; matrix[0][1] = 2; matrix[0][2] = 3; matrix[0][3] = 4; matrix[1][0] = 5; matrix[1][1] = 6; matrix[1][2] = 7; matrix[1][3] = 8; matrix[2][0] = 9; matrix[2][1] = 10; matrix[2][2] = 11; matrix[2][3] = 12; printf("matrix[1][2] = %d\n", matrix[1][2]); // 7 return 0; }

2. Initialization at Declaration (Full)

#include <stdio.h> int main() { int matrix[3][4] = { {1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12} }; printf("matrix[0][0] = %d\n", matrix[0][0]); // 1 printf("matrix[2][3] = %d\n", matrix[2][3]); // 12 return 0; }

3. Omitting Row Size (Auto-Detection)

#include <stdio.h> int main() { // Column size MUST be specified int matrix[][3] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} }; // Compiler auto-detects 3 rows printf("Number of rows: %lu\n", sizeof(matrix)/sizeof(matrix[0])); // 3 for(int i = 0; i < 3; i++) { for(int j = 0; j < 3; j++) { printf("%d ", matrix[i][j]); } printf("\n"); } return 0; }

4. Partial Initialization (Remaining = 0)

#include <stdio.h> int main() { int matrix[3][3] = { {1, 2}, // {1, 2, 0} {4, 5, 6}, // {4, 5, 6} {7} // {7, 0, 0} }; for(int i = 0; i < 3; i++) { for(int j = 0; j < 3; j++) { printf("%d ", matrix[i][j]); } printf("\n"); } return 0; } /* Output: 1 2 0 4 5 6 7 0 0 */

5. Initialize All to Zero

int matrix[5][5] = {0}; // All 25 elements = 0 int matrix2[3][4] = {}; // All elements = 0 (C99+)

Accessing 2D Array Elements

#include <stdio.h> int main() { int matrix[2][3] = {{10, 20, 30}, {40, 50, 60}}; // Access individual elements printf("matrix[0][0] = %d\n", matrix[0][0]); // 10 (1st row, 1st col) printf("matrix[0][2] = %d\n", matrix[0][2]); // 30 (1st row, 3rd col) printf("matrix[1][1] = %d\n", matrix[1][1]); // 50 (2nd row, 2nd col) printf("matrix[1][2] = %d\n", matrix[1][2]); // 60 (2nd row, 3rd col) // Modify elements matrix[0][1] = 99; printf("Modified: matrix[0][1] = %d\n", matrix[0][1]); // 99 return 0; }

Traversing 2D Arrays (Nested Loops)

Standard Traversal (Row by Row)

#include <stdio.h> int main() { int matrix[3][4] = { {1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12} }; printf("Matrix (3 rows × 4 columns):\n"); for(int i = 0; i < 3; i++) { // Outer loop = rows for(int j = 0; j < 4; j++) { // Inner loop = columns printf("%3d ", matrix[i][j]); } printf("\n"); // New line after each row } return 0; }

User Input for 2D Array

#include <stdio.h> int main() { int rows, cols; printf("Enter number of rows: "); scanf("%d", &rows); printf("Enter number of columns: "); scanf("%d", &cols); int matrix[rows][cols]; // Variable Length Array (C99) // Input printf("\nEnter elements:\n"); for(int i = 0; i < rows; i++) { for(int j = 0; j < cols; j++) { printf("matrix[%d][%d] = ", i, j); scanf("%d", &matrix[i][j]); } } // Output printf("\nYour matrix:\n"); for(int i = 0; i < rows; i++) { for(int j = 0; j < cols; j++) { printf("%5d ", matrix[i][j]); } printf("\n"); } return 0; }

Common Operations on 2D Arrays

1. Sum of All Elements

#include <stdio.h> int main() { int matrix[2][3] = {{1, 2, 3}, {4, 5, 6}}; int sum = 0; for(int i = 0; i < 2; i++) { for(int j = 0; j < 3; j++) { sum += matrix[i][j]; } } printf("Sum of all elements: %d\n", sum); // 21 return 0; }

2. Row-wise Sum

#include <stdio.h> int main() { int matrix[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; for(int i = 0; i < 3; i++) { int row_sum = 0; for(int j = 0; j < 3; j++) { row_sum += matrix[i][j]; } printf("Row %d sum: %d\n", i, row_sum); } return 0; } /* Output: Row 0 sum: 6 Row 1 sum: 15 Row 2 sum: 24 */

3. Column-wise Sum

#include <stdio.h> int main() { int matrix[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; for(int j = 0; j < 3; j++) { int col_sum = 0; for(int i = 0; i < 3; i++) { col_sum += matrix[i][j]; } printf("Column %d sum: %d\n", j, col_sum); } return 0; } /* Output: Column 0 sum: 12 Column 1 sum: 15 Column 2 sum: 18 */

4. Find Maximum Element

#include <stdio.h> int main() { int matrix[3][4] = { {5, 8, 2, 11}, {9, 23, 4, 7}, {15, 3, 19, 6} }; int max = matrix[0][0]; int max_row = 0, max_col = 0; for(int i = 0; i < 3; i++) { for(int j = 0; j < 4; j++) { if(matrix[i][j] > max) { max = matrix[i][j]; max_row = i; max_col = j; } } } printf("Maximum element: %d\n", max); printf("Position: [%d][%d]\n", max_row, max_col); return 0; }

5. Transpose of a Matrix

#include <stdio.h> int main() { int original[2][3] = {{1, 2, 3}, {4, 5, 6}}; int transpose[3][2]; // Calculate transpose for(int i = 0; i < 2; i++) { for(int j = 0; j < 3; j++) { transpose[j][i] = original[i][j]; } } // Print original printf("Original matrix (2×3):\n"); for(int i = 0; i < 2; i++) { for(int j = 0; j < 3; j++) { printf("%d ", original[i][j]); } printf("\n"); } // Print transpose printf("\nTranspose matrix (3×2):\n"); for(int i = 0; i < 3; i++) { for(int j = 0; j < 2; j++) { printf("%d ", transpose[i][j]); } printf("\n"); } return 0; }

6. Matrix Addition

#include <stdio.h> int main() { int A[2][2] = {{1, 2}, {3, 4}}; int B[2][2] = {{5, 6}, {7, 8}}; int C[2][2]; // Addition for(int i = 0; i < 2; i++) { for(int j = 0; j < 2; j++) { C[i][j] = A[i][j] + B[i][j]; } } // Result printf("A + B =\n"); for(int i = 0; i < 2; i++) { for(int j = 0; j < 2; j++) { printf("%d ", C[i][j]); } printf("\n"); } return 0; } /* Output: A + B = 6 8 10 12 */

7. Matrix Multiplication

#include <stdio.h> int main() { int A[2][3] = {{1, 2, 3}, {4, 5, 6}}; int B[3][2] = {{7, 8}, {9, 10}, {11, 12}}; int result[2][2] = {0}; // Multiplication: A(2×3) × B(3×2) = C(2×2) for(int i = 0; i < 2; i++) { for(int j = 0; j < 2; j++) { for(int k = 0; k < 3; k++) { result[i][j] += A[i][k] * B[k][j]; } } } printf("Result of multiplication:\n"); for(int i = 0; i < 2; i++) { for(int j = 0; j < 2; j++) { printf("%d ", result[i][j]); } printf("\n"); } return 0; } /* Output: 58 64 139 154 */

2D Array Memory Representation

#include <stdio.h> int main() { int matrix[2][3] = {{1, 2, 3}, {4, 5, 6}}; printf("Memory addresses:\n"); for(int i = 0; i < 2; i++) { for(int j = 0; j < 3; j++) { printf("&matrix[%d][%d] = %p\n", i, j, &matrix[i][j]); } } printf("\nAll elements are stored contiguously in row-major order!\n"); return 0; }

3D Arrays (Quick Look)

#include <stdio.h> int main() { // 3D array: 2 layers × 3 rows × 4 columns int cube[2][3][4] = { { // Layer 0 {1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12} }, { // Layer 1 {13, 14, 15, 16}, {17, 18, 19, 20}, {21, 22, 23, 24} } }; printf("cube[1][2][3] = %d\n", cube[1][2][3]); // 24 return 0; }

Common Mistakes

Mistake	Wrong	Correct
Wrong index order	`matrix[col][row]`	`matrix[row][col]`
Missing column size	`int arr[][]`	`int arr[][3]`
Index out of bounds	`matrix[3][2]` (3×3)	`matrix[2][2]`
Wrong loop bounds	`for(i<=rows)`	`for(i<rows)`

Quick Reference

Operation	Syntax Example
Declare	`int arr[3][4];`
Initialize	`int arr[2][2] = {{1,2},{3,4}};`
Access	`arr[row][col]`
Row count	`sizeof(arr)/sizeof(arr[0])`
Column count	`sizeof(arr[0])/sizeof(arr[0][0])`

Key Points

Row-major order - Elements stored row by row in memory
Column size is mandatory when omitting row size
Index starts at 0 (rows: 0 to rows-1, cols: 0 to cols-1)
Use nested loops to traverse (outer for rows, inner for columns)
2D arrays are arrays of 1D arrays

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