Implement a function that takes aÂ **square**Â 2D array (#Â columns = #Â rows = n) and rotates it by 90 degrees. Do not create a separate 2D array for the rotation, it rotates in the 2D array.

Example:

```
int a1[][] = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}};
Â // rotate(a1, 3) should return:
// [[7, 4, 1],
// [8, 5, 2],
// [9, 6, 3]]
```

Example:

```
Â int a2[][] = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};
Â // rotate(a2, 4) should return:
// [[13, 9, 5, 1],
// [14, 10, 6, 2],
// [15, 11, 7, 3],
// [16, 12, 8, 4]]
```

To understand this problem, we need to analyzeÂ what is really going on in the rotation.

**a.**Â each element in the rotationÂ is changing position with 3 other elements in the 2D array: a->b, b->c, c->d, d->a

[?, a, ?, ?] [?, ?, ?, b] [d, ?, ?, ?] [?, ?, c, ?]

If a={i,j}, then b={j,n-1-i}, c={n-1-i, n-1-j},d={n-1-j,i}

**b.**Â In each rotation happens in aÂ “ring” (example, a1, a2, a2, b1, b2 ….d2, d2), we only swap the positions ofÂ n-2Â elements in the first row. We do not swape n-1th element again because it is a duplicate (We swapped a1 with b1, and b1 does not need to be swappedÂ again. So we only swap a1, a2, a3. ).

[a1, a2, a3, b1] [d3, ??, ??, b2] [d2, ??, ??, b3] [d1, c3, c2, c1]

So the outer loop should beÂ **for (int i=0; i < n-1; i++)**:

**c.**Â We swap the positions from the outside ring (1’s) to the inner rings (2’s). Each time the iteration decrements by 2 elements. At **ith** row, we swap from **ith** element to **n-2-**i th elements.

[1, 1, 1, 1] [1, 2, 2, 1] [1, 2, 2, 1] [1, 1, 1, 1]

So the inner loop isÂ **for (int j=i; j<n-1-i; j++)**

Put everything together:

public static int[][] rotate(int[][] a, int n) { for (int i=0; i< n-1; i++){ for (int j=i; j<n-1-i; j++){ int temp = a[i][j]; a[i][j] = a[n-1-j][i]; a[n-1-j][i] = a[n-1-i][n-1-j]; a[n-1-i][n-1-j] = a[j][n-1-i]; a[j][n-1-i] = temp; } } return a; } }