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The **Spiral Matrix** problem takes as an input a 2-Dimensional array of $N$ rows and $M$ columns and prints the elements of this matrix in spiral order.

The spiral begins at the top left corner of the input matrix and prints the elements it encounters while looping towards the center of this matrix in a clockwise manner.

The algorithm works as follows:

- First, four variables containing the indices for the corner points of the array are initialized.
- The algorithm starts from the top left corner of the array and traverses the first row from left to right. Once it traverses this whole row, it no longer needs to revisit it; hence, it increments the top corner index.
- Once complete, it now traverses the rightmost column top to bottom. Again, once this completes, there is no need to revisit this rightmost column; hence, it decrements the right corner index.
- Next, the algorithm traverses the bottommost row and decrements bottom corner index after doing so.
- Lastly, the algorithm now traverses the leftmost column, incrementing the left corner index after doing so.

This continues until the left index gets greater than the right index, and the top index gets greater than the bottom index.

The following code implements the spiral matrix algorithm in Java.

import java.io.*; class MAIN { public static void spiralMatrixPrint(int[][] arr) { int rows = arr.length; int cols = arr[0].length; // Defining the boundaries of the matrix. int top = 0, bottom = rows - 1, left = 0, right = cols - 1; // Defining the direction in which the array is to be traversed. int dir = 1; while (top <= bottom && left <= right) { if (dir == 1) { // moving left->right for (int i = left; i <= right; ++i) { System.out.print(arr[top][i] + " "); } // Since we have traversed the whole first // row, move down to the next row. ++top; dir = 2; } else if (dir == 2) { // moving top->bottom for (int i = top; i <= bottom; ++i) { System.out.print(arr[i][right]+ " "); } // Since we have traversed the whole last // column, move left to the previous column. --right; dir = 3; } else if (dir == 3) { // moving right->left for (int i = right; i >= left; --i) { System.out.print(arr[bottom][i]+ " "); } // Since we have traversed the whole last // row, move up to the previous row. --bottom; dir = 4; } else if (dir == 4) { // moving bottom->up for (int i = bottom; i >= top; --i) { System.out.print(arr[i][left]+ " "); } // Since we have traversed the whole first // col, move right to the next column. ++left; dir = 1; } } } public static void main(String[] args) { // Driver code // Change the following array to test // on some other input int a[][] = { {1,2,3,4}, {5,6,7,8}, {9,10,11,12}}; spiralMatrixPrint(a); } }

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