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“C Language Beginner’s Essential Knowledge Points Note Series 100 Articles“

The following notes finally enter the practical series, which is also the most important and difficult part of C language. Keep it up! Youngsters!

33. Comprehensive Summary of Techniques for Using Two-Dimensional and Multi-Dimensional Arrays, Hurry Up and Collect!

1. Basic Concept of Two-Dimensional Arrays

A two-dimensional array is an “array of arrays” and can be viewed as a table composed of rows and columns:

data_type array_name[rows][columns];

Memory Layout Characteristics

• • Stored in row-major order
• • Total size = number of rows × number of columns × sizeof(element type)
• • Each element is accessed using two subscripts:<span>arr[row][col]</span>

2. Various Ways to Declare and Initialize Two-Dimensional Arrays

1. Basic Declaration

int matrix[3][4];  // A 3-row 4-column integer array, similar to a mathematical matrix

2. Complete Initialization

int arr[2][3] = {
    {1, 2, 3},
    {4, 5, 6}
};

3. Partial Initialization

int arr[3][4] = {
    {1},          // First row: 1,0,0,0
    {0, 2},       // Second row: 0,2,0,0
    {0, 0, 3}     // Third row: 0,0,3,0
};

4. Omitted Row Count Initialization

int arr[][3] = {  // Row count is automatically inferred as 2
    {1,2,3},
    {4,5,6}
};

3. Accessing and Traversing Two-Dimensional Arrays

1. Basic Access

int val = matrix[1][2];  // Get the element at row 2, column 3
matrix[0][1] = 10;       // Modify the element at row 1, column 2

2. Nested Loop Traversal

for (int i = 0; i < 3; i++) {         // Row loop
    for (int j = 0; j < 4; j++) {     // Column loop
        printf("%d ", matrix[i][j]);
    }
    printf("\n");
}

3. Memory Order Access Optimization

// It is recommended to access the elements of the two-dimensional array in row-major order for higher efficiency
for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 4; j++) {
        process(matrix[i][j]);
    }
}

4. Memory Model of Two-Dimensional Arrays

1. Memory Arrangement Example

int arr[2][3] = {{1,2,3}, {4,5,6}};

Memory layout (contiguous storage):

1 2 3 4 5 6

2. How to Calculate Memory Addresses

printf("arr[0][0]: %p\n", &arr[0][0]);
printf("arr[0][1]: %p\n", &arr[0][1]);
printf("arr[1][0]: %p\n", &arr[1][0]);

5. Two-Dimensional Arrays and Pointers

1. Array Name Conversion

int arr[3][4];
int (*p)[4] = arr;  // Pointer to an array containing 4 ints

2. Pointer Access Method

for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 4; j++) {
        printf("%d ", *(*(arr + i) + j));
    }
}

6. Concept of Multi-Dimensional Arrays

1. Three-Dimensional Array Example

int cube[2][3][4];  // 2 layers, 3 rows, 4 columns, can be considered a rectangular prism

2. Initialization and Access

int cube[2][3][4] = {
    { {1,2,3,4}, {5,6,7,8}, {9,10,11,12} },
    { {13,14,15,16}, {17,18,19,20}, {21,22,23,24} }
};

printf("%d", cube[1][2][3]);  // 24

7. Arrays as Function Parameters

1. Passing Two-Dimensional Arrays

void printMatrix(int mat[][4], int rows) {
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < 4; j++) {
            printf("%d ", mat[i][j]);
        }
        printf("\n");
    }
}

2. Must Specify Column Count

// Error! Must specify the size of the second dimension
void func(int mat[][]);  

// Correct
void func(int mat[][4]);

8. Implementation of Dynamic Two-Dimensional Arrays

1. Pointer Array Method

int **mat = malloc(rows * sizeof(int*));
for (int i = 0; i < rows; i++) {
    mat[i] = malloc(cols * sizeof(int));
}

2. Contiguous Memory Method

int *mat = malloc(rows * cols * sizeof(int));
// Accessing mat[i][j]: mat[i*cols + j]

9. Common Errors

1. Out-of-Bounds Access

int arr[2][3];
arr[2][0] = 5;  // Row out of bounds!

Correction:

if (row < 2 && col < 3) {
    arr[row][col] = value;
}

2. Mismatched Number of Initialized Elements

int arr[2][3] = {1,2,3,4,5,6,7};  // Error! Too many elements

Correction:

int arr[2][3] = {{1,2,3}, {4,5,6}};

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