# 将矩阵旋转 180 度

> 原文： [https://www.geeksforgeeks.org/rotate-matrix-180-degree/](https://www.geeksforgeeks.org/rotate-matrix-180-degree/)

给定一个正方形矩阵，任务是我们在不使用任何额外空间的情况下将其沿逆时针方向旋转 180 度。
**范例：**

```
Input :  1  2  3
         4  5  6
         7  8  9
Output : 9 8 7 
         6 5 4 
         3 2 1

Input :  1 2 3 4 
         5 6 7 8 
         9 0 1 2 
         3 4 5 6 
Output : 6 5 4 3 
         2 1 0 9 
         8 7 6 5 
         4 3 2 1

```

**方法：1（仅打印旋转的矩阵）**
此问题的解决方案是将矩阵旋转 180 度，我们可以轻松地执行此步骤

```
Matrix =  a00 a01 a02
          a10 a11 a12
          a20 a21 a22

when we rotate it by 90 degree
then matrix is
Matrix = a02 a12 a22
         a01 a11 a21
         a00 a10 a20

when we rotate it by again 90 
degree then matrix is 
Matrix = a22 a21 a20
         a12 a11 a10
         a02 a01 a00 

```

**从上面的插图中我们可以简单地将矩阵旋转 180 度，然后必须以相反的方式打印给定的矩阵。**

## C++ 

```

// C++ program to rotate a matrix by 180 degrees 
#include <bits/stdc++.h> 
#define N 3 
using namespace std; 

// Function to Rotate the matrix by 180 degree 
void rotateMatrix(int mat[][N]) 
{ 
    // Simply print from last cell to first cell. 
    for (int i = N - 1; i >= 0; i--) { 
        for (int j = N - 1; j >= 0; j--) 
            printf("%d ", mat[i][j]); 

        printf("\n"); 
    } 
} 

// Driven code 
int main() 
{ 
    int mat[N][N] = { 
        { 1, 2, 3 }, 
        { 4, 5, 6 }, 
        { 7, 8, 9 } 
    }; 

    rotateMatrix(mat); 
    return 0; 
} 

```

## 爪哇

```

// Java program to rotate a 
// matrix by 180 degrees 
import java.util.*; 

class GFG { 
    static int N = 3; 

    // Function to Rotate the 
    // matrix by 180 degree 
    static void rotateMatrix(int mat[][]) 
    { 

        // Simply print from last 
        // cell to first cell. 
        for (int i = N - 1; i >= 0; i--) { 
            for (int j = N - 1; j >= 0; j--) 
                System.out.print(mat[i][j] + " "); 

            System.out.println(); 
        } 
    } 

    // Driver Code 
    public static void main(String[] args) 
    { 
        int[][] mat = { { 1, 2, 3 }, 
                        { 4, 5, 6 }, 
                        { 7, 8, 9 } }; 

        rotateMatrix(mat); 
    } 
} 

// This code is contributed by ChitraNayal 

```

## Python3

```

# Python3 program to  
# rotate a matrix by  
# 180 degrees 
N = 3; 

# Function to Rotate  
# the matrix by 180 degree 
def rotateMatrix(mat): 

    # Simply print from 
    # last cell to first cell. 
    i = N - 1;  
    while(i >= 0): 
        j = N - 1; 
        while(j >= 0): 
            print(mat[i][j], end = " "); 
            j = j - 1; 
        print(); 
        i = i - 1; 

# Driven code 
mat = [[1, 2, 3], 
       [ 4, 5, 6 ], 
       [ 7, 8, 9 ]]; 
rotateMatrix(mat); 

# This code is contributed  
# by mits 

```

## C# 

```

// C# program to rotate a 
// matrix by 180 degrees 
using System; 

class GFG { 
    static int N = 3; 

    // Function to Rotate the 
    // matrix by 180 degree 
    static void rotateMatrix(int[, ] mat) 
    { 
        // Simply print from last 
        // cell to first cell. 
        for (int i = N - 1; i >= 0; i--) { 
            for (int j = N - 1; j >= 0; j--) 
                Console.Write(mat[i, j] + " "); 

            Console.WriteLine(); 
        } 
    } 

    // Driver Code 
    static public void Main() 
    { 
        int[, ] mat = { { 1, 2, 3 }, 
                        { 4, 5, 6 }, 
                        { 7, 8, 9 } }; 

        rotateMatrix(mat); 
    } 
} 

// This code is contributed by aj_36 

```

## 的 PHP

```

<?php 
// PHP program to rotate  
// a matrix by 180 degree 
$N = 3; 

// Function to Rotate the 
// matrix by 180 degree 
function rotateMatrix($mat) 
{ 
    global $N; 

    // Simply print from  
    // last cell to first cell. 
    for ($i = $N - 1; $i >= 0; $i--)  
    { 
        for ($j = $N - 1; $j >= 0; $j--)  
            echo $mat[$i][$j], " "; 

    echo "\n"; 
    } 
} 

// Driver Code 
$mat = array(array(1, 2, 3), 
             array(4, 5, 6), 
             array(7, 8, 9)); 

rotateMatrix($mat); 

// This code is contributed by ajit 
?> 

```

**Output :**

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

```

**时间复杂度：** O（N * N）
**辅助空间：** O（1）

**方法：2（原位旋转）**
有四个步骤：
1-查找矩阵的转置。
2-转置的反向列。
3-查找矩阵的转置。
4-转置的反向列

```
Let the given matrix be
1  2  3  4
5  6  7  8
9  10 11 12
13 14 15 16

First we find transpose.
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16

Then we reverse elements of every column.
4 8 12 16
3 7 11 15
2 6 10 14
1 5  9 13

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

Then we reverse elements of every column again
16 15 14 13 
12 11 10 9 
8 7 6 5 
4 3 2 1

```

## C++

```

// C++ program for left rotation of matrix by 180 
#include <bits/stdc++.h> 
using namespace std; 

#define R 4 
#define C 4 

// Function to rotate the matrix by 180 degree 
void reverseColumns(int arr[R][C]) 
{ 
    for (int i = 0; i < C; i++) 
        for (int j = 0, k = C - 1; j < k; j++, k--) 
            swap(arr[j][i], arr[k][i]); 
} 

// Function for transpose of matrix 
void transpose(int arr[R][C]) 
{ 
    for (int i = 0; i < R; i++) 
        for (int j = i; j < C; j++) 
            swap(arr[i][j], arr[j][i]); 
} 

// Function for display the matrix 
void printMatrix(int arr[R][C]) 
{ 
    for (int i = 0; i < R; i++) { 
        for (int j = 0; j < C; j++) 
            cout << arr[i][j] << " "; 
        cout << '\n'; 
    } 
} 

// Function to anticlockwise rotate matrix 
// by 180 degree 
void rotate180(int arr[R][C]) 
{ 
    transpose(arr); 
    reverseColumns(arr); 
    transpose(arr); 
    reverseColumns(arr); 
} 

// Driven code 
int main() 
{ 
    int arr[R][C] = { { 1, 2, 3, 4 }, 
                      { 5, 6, 7, 8 }, 
                      { 9, 10, 11, 12 }, 
                      { 13, 14, 15, 16 } }; 
    rotate180(arr); 
    printMatrix(arr); 
    return 0; 
} 

```

## Java

```

// Java program for left 
// rotation of matrix by 180 
import java.util.*; 

class GFG { 
    static int R = 4, C = 4, t = 0; 

    // Function to rotate the 
    // matrix by 180 degree 
    static void reverseColumns(int arr[][]) 
    { 
        for (int i = 0; i < C; i++) { 
            for (int j = 0, k = C - 1; j < k; j++, k--) { 
                t = arr[j][i]; 
                arr[j][i] = arr[k][i]; 
                arr[k][i] = t; 
            } 
        } 
    } 

    // Function for transpose of matrix 
    static void transpose(int arr[][]) 
    { 
        for (int i = 0; i < R; i++) { 
            for (int j = i; j < C; j++) { 
                t = arr[i][j]; 
                arr[i][j] = arr[j][i]; 
                arr[j][i] = t; 
            } 
        } 
    } 

    // Function for display the matrix 
    static void printMatrix(int arr[][]) 
    { 
        for (int i = 0; i < R; i++) { 
            for (int j = 0; j < C; j++) 
                System.out.print(arr[i][j] + " "); 
            System.out.println(); 
        } 
    } 

    // Function to anticlockwise 
    // rotate matrix by 180 degree 
    static void rotate180(int arr[][]) 
    { 
        transpose(arr); 
        reverseColumns(arr); 
        transpose(arr); 
        reverseColumns(arr); 
    } 

    // Driver Code 
    public static void main(String[] args) 
    { 
        int[][] arr = { { 1, 2, 3, 4 }, 
                        { 5, 6, 7, 8 }, 
                        { 9, 10, 11, 12 }, 
                        { 13, 14, 15, 16 } }; 

        rotate180(arr); 
        printMatrix(arr); 
    } 
} 

// This code is contributed by ChitraNayal 

```

## C#

```

// C# program for left 
// rotation of matrix by 180 
using System; 

class GFG { 
    static int R = 4, C = 4, t = 0; 

    // Function to rotate the 
    // matrix by 180 degree 
    static void reverseColumns(int[, ] arr) 
    { 
        for (int i = 0; i < C; i++) { 
            for (int j = 0, k = C - 1; 
                 j < k; j++, k--) { 
                t = arr[j, i]; 
                arr[j, i] = arr[k, i]; 
                arr[k, i] = t; 
            } 
        } 
    } 

    // Function for transpose of matrix 
    static void transpose(int[, ] arr) 
    { 
        for (int i = 0; i < R; i++) { 
            for (int j = i; j < C; j++) { 
                t = arr[i, j]; 
                arr[i, j] = arr[j, i]; 
                arr[j, i] = t; 
            } 
        } 
    } 

    // Function for display the matrix 
    static void printMatrix(int[, ] arr) 
    { 
        for (int i = 0; i < R; i++) { 
            for (int j = 0; j < C; j++) 
                Console.Write(arr[i, j] + " "); 
            Console.WriteLine(); 
        } 
    } 

    // Function to anticlockwise 
    // rotate matrix by 180 degree 
    static void rotate180(int[, ] arr) 
    { 
        transpose(arr); 
        reverseColumns(arr); 
        transpose(arr); 
        reverseColumns(arr); 
    } 

    // Driver Code 
    static public void Main() 
    { 
        int[, ] arr = { { 1, 2, 3, 4 }, 
                        { 5, 6, 7, 8 }, 
                        { 9, 10, 11, 12 }, 
                        { 13, 14, 15, 16 } }; 

        rotate180(arr); 
        printMatrix(arr); 
    } 
} 

// This code is contributed by ajit 

```

## Python 3

```

# Python 3 program for left rotation of matrix by 180 

R = 4
C = 4

# Function to rotate the matrix by 180 degree 
def reverseColumns(arr): 
    for i in range(C): 
        j = 0
        k = C-1
        while j < k: 
            t = arr[j][i] 
            arr[j][i] = arr[k][i] 
            arr[k][i] = t 
            j += 1
            k -= 1

# Function for transpose of matrix 
def transpose(arr): 
    for i in range(R): 
        for j in range(i, C): 
            t = arr[i][j] 
            arr[i][j] = arr[j][i] 
            arr[j][i] = t 

# Function for display the matrix 
def printMatrix(arr): 
    for i in range(R): 
        for j in range(C): 
            print(arr[i][j], end = " "); 
        print(); 

# Function to anticlockwise rotate matrix 
# by 180 degree 
def rotate180(arr): 
    transpose(arr); 
    reverseColumns(arr); 
    transpose(arr); 
    reverseColumns(arr); 

# Driven code 
arr = [ [ 1, 2, 3, 4 ], 
        [ 5, 6, 7, 8 ], 
        [9, 10, 11, 12 ], 
        [13, 14, 15, 16 ] ]; 
rotate180(arr); 
printMatrix(arr); 

```

## PHP

```

<?php 
// PHP program for left rotation of matrix by 180 

$R = 4; 
$C = 4; 

// Function to rotate the matrix by 180 degree 
function reverseColumns(&$arr) 
{ 
    global $C; 
    for ($i = 0; $i < $C; $i++) 
    { 
        for ($j = 0, $k = $C - 1; $j < $k; $j++, $k--) 
        { 
              $t = $arr[$j][$i]; 
              $arr[$j][$i] = $arr[$k][$i]; 
              $arr[$k][$i] = $t; 
        } 
    }     
} 

// Function for transpose of matrix 
function transpose(&$arr) 
{ 
    global $R, $C; 
    for ($i = 0; $i < $R; $i++) 
    { 
        for ($j = $i; $j < $C; $j++) 
        { 
            $t = $arr[$i][$j]; 
            $arr[$i][$j] = $arr[$j][$i]; 
            $arr[$j][$i] = $t; 
        } 
    } 
} 

// Function for display the matrix 
function printMatrix(&$arr) 
{ 
    global $R, $C; 
    for ($i = 0; $i < $R; $i++) { 
        for ($j = 0; $j < $C; $j++) 
        { 
            echo $arr[$i][$j]." "; 
        } 
        echo "\n"; 
    } 
} 

// Function to anticlockwise rotate matrix 
// by 180 degree 
function rotate180(&$arr) 
{ 

    transpose($arr); 
    reverseColumns($arr); 
    transpose($arr); 
    reverseColumns($arr); 
} 

// Driven code 

$arr = array( array( 1, 2, 3, 4 ), 
                 array( 5, 6, 7, 8 ), 
                 array( 9, 10, 11, 12 ), 
                 array( 13, 14, 15, 16 ) ); 
rotate180($arr); 
printMatrix($arr); 
return 0; 
?> 

```

**Output :**

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

```

**时间复杂度：** O（R * C）
**辅助空间：** O（1）

在上面的代码中，矩阵的转置必须被找到两次，并且列必须被反转两次。
因此，我们可以有一个更好的解决方案。

**方法：3（位置交换）**

在这里，我们交换相应位置的值。

## Java

```

public class GFG { 
       /** 
     * Reverse Row at specified index in the matrix 
     * @param data matrix 
     * @param index row index 
     */
    private static void reverseRow(int[][] data, int index) { 
        int cols = data[index].length; 
        for (int i = 0; i < cols / 2; i++) { 
            int temp = data[index][i]; 
            data[index][i] = data[index][cols - i - 1]; 
            data[index][cols - i - 1] = temp; 
        } 
    } 

    /** 
     * Print Matrix data 
     * @param data matrix 
     */
    private static void printMatrix(int[][] data) { 
        for (int i = 0; i < data.length; i++) { 
            for (int j = 0; j < data[i].length; j++) { 
                System.out.print(data[i][j] + " "); 
            } 
            System.out.println(""); 
        } 
    } 

    /** 
     * Rotate Matrix by 180 degrees 
     * @param data matrix 
     */
    private static void rotateMatrix180(int[][] data) { 
        int rows = data.length; 
        int cols = data[0].length; 

        if (rows % 2 != 0) { 
            //If N is odd reverse the middle row in the matrix 
            reverseRow(data, data.length / 2); 
        } 

        //Swap the value of matrix [i][j] with [rows - i - 1][cols - j - 1] for half the rows size.  
        for (int i = 0; i <= (rows/2) - 1; i++) { 
            for (int j = 0; j < cols; j++) { 
                int temp = data[i][j]; 
                data[i][j] = data[rows - i - 1][cols - j - 1]; 
                data[rows - i - 1][cols - j - 1] = temp; 
            } 
        } 
    } 

    public static void main(String[] args) { 
        int[][] data = { 
                {1, 2, 3, 4, 5}, 
                {6, 7, 8, 9, 10}, 
                {11, 12, 13, 14, 15}, 
                {16, 17, 18, 19, 20}, 
                {21, 22, 23, 24, 25} 
        }; 

        //Rotate Matrix 
        rotateMatrix180(data); 

        //Print Matrix 
        printMatrix(data); 
    } 
} 

```

**输出：**

```
25 24 23 22 21 
20 19 18 17 16 
15 14 13 12 11 
10 9 8 7 6 
5 4 3 2 1 

```

**Time complexity :** O(R*C)
**Auxiliary Space :** O(1)

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