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Data Structures

## Rotate Matrix Elements

Given a matrix, clockwise rotate elements in it.

Examples:

Input
1    2    3
4    5    6
7    8    9
Output:
4    1    2
7    5    3
8    9    6
For 4*4 matrix
Input:
1    2    3    4
5    6    7    8
9    10   11   12
13   14   15   16
Output:
5    1    2    3
9    10   6    4
13   11   7    8
14   15   16   12


The idea is to use loops similar to the program for printing a matrix in spiral form. One by one rotate all rings of elements, starting from the outermost. To rotate a ring, we need to do following.
1) Move elements of top row.
2) Move elements of last column.
3) Move elements of bottom row.
4) Move elements of first column.
Repeat above steps for inner ring while there is an inner ring.

// C++ program to rotate a matrix

#include <bits/stdc++.h>
#define R 4
#define C 4
using namespace std;

// A function to rotate a matrix mat[][] of size R x C.
// Initially, m = R and n = C
void rotatematrix(int m, int n, int mat[R][C])
{
int row = 0, col = 0;
int prev, curr;

/*
row - Staring row index
m - ending row index
col - starting column index
n - ending column index
i - iterator
*/
while (row < m && col < n)
{

if (row + 1 == m || col + 1 == n)
break;

// Store the first element of next row, this
// element will replace first element of current
// row
prev = mat[row + 1][col];

/* Move elements of first row from the remaining rows */
for (int i = col; i < n; i++)
{
curr = mat[row][i];
mat[row][i] = prev;
prev = curr;
}
row++;

/* Move elements of last column from the remaining columns */
for (int i = row; i < m; i++)
{
curr = mat[i][n-1];
mat[i][n-1] = prev;
prev = curr;
}
n--;

/* Move elements of last row from the remaining rows */
if (row < m)
{
for (int i = n-1; i >= col; i--)
{
curr = mat[m-1][i];
mat[m-1][i] = prev;
prev = curr;
}
}
m--;

/* Move elements of first column from the remaining rows */
if (col < n)
{
for (int i = m-1; i >= row; i--)
{
curr = mat[i][col];
mat[i][col] = prev;
prev = curr;
}
}
col++;
}

// Print rotated matrix
for (int i=0; i<R; i++)
{
for (int j=0; j<C; j++)
cout << mat[i][j] << " ";
cout << endl;
}
}

/* Driver program to test above functions */
int main()
{
// Test Case 1
int a[R][C] = { {1,  2,  3,  4},
{5,  6,  7,  8},
{9,  10, 11, 12},
{13, 14, 15, 16}  };

// Tese Case 2
/* int a[R][C] = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
*/  rotatematrix(R, C, a);
return 0;
}


# Python program to rotate a matrix

# Function to rotate a matrix
def rotateMatrix(mat):

if not len(mat):
return

"""
top : starting row index
bottom : ending row index
left : starting column index
right : ending column index
"""

top = 0
bottom = len(mat)-1

left = 0
right = len(mat[0])-1

while left < right and top < bottom:

# Store the first element of next row,
# this element will replace first element of
# current row
prev = mat[top+1][left]

# Move elements of top row one step right
for i in range(left, right+1):
curr = mat[top][i]
mat[top][i] = prev
prev = curr

top += 1

# Move elements of rightmost column one step downwards
for i in range(top, bottom+1):
curr = mat[i][right]
mat[i][right] = prev
prev = curr

right -= 1

# Move elements of bottom row one step left
for i in range(right, left-1, -1):
curr = mat[bottom][i]
mat[bottom][i] = prev
prev = curr

bottom -= 1

# Move elements of leftmost column one step upwards
for i in range(bottom, top-1, -1):
curr = mat[i][left]
mat[i][left] = prev
prev = curr

left += 1

return mat

# Utility Function
def printMatrix(mat):
for row in mat:
print row

# Test case 1
matrix =[
[1,  2,  3,  4 ],
[5,  6,  7,  8 ],
[9,  10, 11, 12 ],
[13, 14, 15, 16 ]
]
# Test case 2
"""
matrix =[
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
"""

matrix = rotateMatrix(matrix)
# Print modified matrix
printMatrix(matrix)


Output:

5 1 2 3
9 10 6 4
13 11 7 8
14 15 16 12