algorithm - Print two-dimensional array in spiral order

Question

How do I print a 5×5 two-dimensional array in spiral order?

Is there any formula so that I can print an array of any size in spiral order?

Answer 1

The idea is to treat the matrix as a series of layers, top-right layers and bottom-left layers. To print the matrix spirally we can peel layers from these matrix, print the peeled part and recursively call the print on the left over part. The recursion terminates when we don't have any more layers to print.

Input matrix:

1 2 3 4 
5 6 7 8
9 0 1 2   
3 4 5 6 
7 8 9 1

After peeling top-right layer:

 1 2 3 4 
       8
5 6 7  2
9 0 1  6   
3 4 5  1 
7 8 9

After peeling bottom-left layer from sub-matrix:

   6 7
5  0 1   
9  4 5
3 
7 8 9 

After peeling top-right layer from sub-matrix:

    6 7
      1   
   0  5
   4

After peeling bottom-left layer from sub-matrix:

  0
  4

Recursion terminates.

---

C functions:

// function to print the top-right peel of the matrix and 
// recursively call the print bottom-left on the submatrix.
void printTopRight(int a[][COL], int x1, int y1, int x2, int y2) {
    int i = 0, j = 0;

    // print values in the row.
    for(i = x1; i<=x2; i++) {
        printf("%d ", a[y1][i]);
    }

    // print values in the column.
    for(j = y1 + 1; j <= y2; j++)         {
        printf("%d ", a[j][x2]);
    }

    // see if more layers need to be printed.
    if(x2-x1 > 0) {
        // if yes recursively call the function to 
        // print the bottom left of the sub matrix.
        printBottomLeft(a, x1, y1 + 1, x2-1, y2);
    }
}

// function to print the bottom-left peel of the matrix and 
// recursively call the print top-right on the submatrix.
void printBottomLeft(int a[][COL], int x1, int y1, int x2, int y2) {
    int i = 0, j = 0;

    // print the values in the row in reverse order.
    for(i = x2; i>=x1; i--) {
        printf("%d ", a[y2][i]);
    }

    // print the values in the col in reverse order.
    for(j = y2 - 1; j >= y1; j--) {
        printf("%d ", a[j][x1]);
    }

    // see if more layers need to be printed.
    if(x2-x1 > 0) {
        // if yes recursively call the function to 
        // print the top right of the sub matrix.
        printTopRight(a, x1+1, y1, x2, y2-1);
    }
}

void printSpiral(int arr[][COL]) {
    printTopRight(arr,0,0,COL-1,ROW-1);
    printf("
");
}