Print matrix in antispiral form

In C programming, printing a matrix in antispiral form means traversing the matrix in a spiral order (clockwise from outside to inside) and then displaying the elements in reverse order. This creates an "antispiral" pattern where we start from the center and work outward.

Syntax

// Using array to store spiral elements
int spiral[n*n];
// Traverse in spiral order: right ? down ? left ? up
// Print in reverse order

Algorithm

The approach involves two main steps −

1. Spiral Traversal: Traverse the matrix in spiral order (right ? down ? left ? up) and store elements in an array
2. Reverse Print: Print the stored elements in reverse order to achieve antispiral effect

Example

Here's a complete implementation to print a 4x4 matrix in antispiral form −

#include <stdio.h>

int main() {
    int mat[4][4] = {{1, 2, 3, 4},
                     {5, 6, 7, 8},
                     {9, 10, 11, 12},
                     {13, 14, 15, 16}};
    
    int spiral[16];
    int index = 0;
    int top = 0, bottom = 3, left = 0, right = 3;
    
    printf("Original Matrix:<br>");
    for(int i = 0; i < 4; i++) {
        for(int j = 0; j < 4; j++) {
            printf("%d ", mat[i][j]);
        }
        printf("<br>");
    }
    
    // Spiral traversal
    while(top <= bottom && left <= right) {
        // Right direction
        for(int i = left; i <= right; i++) {
            spiral[index++] = mat[top][i];
        }
        top++;
        
        // Down direction
        for(int i = top; i <= bottom; i++) {
            spiral[index++] = mat[i][right];
        }
        right--;
        
        // Left direction
        if(top <= bottom) {
            for(int i = right; i >= left; i--) {
                spiral[index++] = mat[bottom][i];
            }
            bottom--;
        }
        
        // Up direction
        if(left <= right) {
            for(int i = bottom; i >= top; i--) {
                spiral[index++] = mat[i][left];
            }
            left++;
        }
    }
    
    // Print in reverse (antispiral)
    printf("Antispiral Form: ");
    for(int i = index - 1; i >= 0; i--) {
        printf("%d ", spiral[i]);
    }
    printf("<br>");
    
    return 0;
}

Original Matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
Antispiral Form: 10 11 7 6 5 9 13 14 15 16 12 8 4 3 2 1

How It Works

1. Boundary Setup: Initialize top, bottom, left, right boundaries
2. Spiral Traversal: Move right ? down ? left ? up, adjusting boundaries after each direction
3. Store Elements: Store each traversed element in the spiral array
4. Reverse Print: Print the spiral array from last index to first

Conclusion

The antispiral form of a matrix is achieved by performing spiral traversal and then reversing the order of elements. This technique demonstrates both spiral matrix traversal and array reversal concepts in C programming.