数组旋转的反转算法

编写一个函数rotate(arr[], d, n) 将大小为 n 的 arr[] 旋转 d 个元素。
例子 ：

Input :  arr[] = [1, 2, 3, 4, 5, 6, 7]
         d = 2
Output : arr[] = [3, 4, 5, 6, 7, 1, 2] 

将上述数组旋转 2 次将生成数组

本文讨论了将数组旋转 d 个元素的前 3 种方法。
方法4（反转算法）：
算法 ：

rotate(arr[], d, n)
  reverse(arr[], 1, d) ;
  reverse(arr[], d + 1, n);
  reverse(arr[], 1, n);

令 AB 是输入数组的两部分，其中 A = arr[0..d-1] 和 B = arr[d..n-1]。该算法的思想是：

• 将 A 倒转得到 ArB，其中 Ar 是 A 的倒数。
• 将 B 倒转得到 ArBr，其中 Br 是 B 的倒数。
• 反转所有得到 (ArBr) r = BA。

例子 ：
设数组为 arr[] = [1, 2, 3, 4, 5, 6, 7], d =2 and n = 7
A = [1, 2] 和 B = [3, 4, 5, 6, 7]

• 反向A，我们得到ArB = [2, 1, 3, 4, 5, 6, 7]
• 逆向 B，我们得到 ArBr = [2, 1, 7, 6, 5, 4, 3]
• 反转所有，我们得到 (ArBr)r = [3, 4, 5, 6, 7, 1, 2]

以下是上述方法的实现：

C++

// C++ program for reversal algorithm
// of array rotation
#include 
using namespace std;
 
/*Function to reverse arr[] from index start to end*/
void reverseArray(int arr[], int start, int end)
{
    while (start < end) {
        int temp = arr[start];
        arr[start] = arr[end];
        arr[end] = temp;
        start++;
        end--;
    }
}
 
/* Function to left rotate arr[] of size n by d */
void leftRotate(int arr[], int d, int n)
{
    if (d == 0)
        return;
    // in case the rotating factor is
    // greater than array length
    d = d % n;
 
    reverseArray(arr, 0, d - 1);
    reverseArray(arr, d, n - 1);
    reverseArray(arr, 0, n - 1);
}
 
// Function to print an array
void printArray(int arr[], int size)
{
    for (int i = 0; i < size; i++)
        cout << arr[i] << " ";
}
 
/* Driver program to test above functions */
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int d = 2;
 
    // Function calling
    leftRotate(arr, d, n);
    printArray(arr, n);
 
    return 0;
}

C

// C/C++ program for reversal algorithm of array rotation
#include 
 
/*Utility function to print an array */
void printArray(int arr[], int size);
 
/* Utility function to reverse arr[] from start to end */
void reverseArray(int arr[], int start, int end);
 
/* Function to left rotate arr[] of size n by d */
void leftRotate(int arr[], int d, int n)
{
 
    if (d == 0)
        return;
    // in case the rotating factor is
    // greater than array length
    d = d % n;
 
    reverseArray(arr, 0, d - 1);
    reverseArray(arr, d, n - 1);
    reverseArray(arr, 0, n - 1);
}
 
/*UTILITY FUNCTIONS*/
/* function to print an array */
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        printf("%d ", arr[i]);
}
 
/*Function to reverse arr[] from index start to end*/
void reverseArray(int arr[], int start, int end)
{
    int temp;
    while (start < end) {
        temp = arr[start];
        arr[start] = arr[end];
        arr[end] = temp;
        start++;
        end--;
    }
}
 
/* Driver program to test above functions */
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int d = 2;
 
    leftRotate(arr, d, n);
    printArray(arr, n);
    return 0;
}

Java

// Java program for reversal algorithm of array rotation
import java.io.*;
 
class LeftRotate {
    /* Function to left rotate arr[] of size n by d */
    static void leftRotate(int arr[], int d)
    {
 
        if (d == 0)
            return;
 
        int n = arr.length;
        // in case the rotating factor is
        // greater than array length
        d = d % n;
        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
    }
 
    /*Function to reverse arr[] from index start to end*/
    static void reverseArray(int arr[], int start, int end)
    {
        int temp;
        while (start < end) {
            temp = arr[start];
            arr[start] = arr[end];
            arr[end] = temp;
            start++;
            end--;
        }
    }
 
    /*UTILITY FUNCTIONS*/
    /* function to print an array */
    static void printArray(int arr[])
    {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
    }
 
    /* Driver program to test above functions */
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
        int n = arr.length;
        int d = 2;
 
        leftRotate(arr, d); // Rotate array by d
        printArray(arr);
    }
}
/*This code is contributed by Devesh Agrawal*/

Python3

# Python program for reversal algorithm of array rotation
 
# Function to reverse arr[] from index start to end
 
 
def reverseArray(arr, start, end):
    while (start < end):
        temp = arr[start]
        arr[start] = arr[end]
        arr[end] = temp
        start += 1
        end = end-1
 
# Function to left rotate arr[] of size n by d
 
 
def leftRotate(arr, d):
 
    if d == 0:
        return
    n = len(arr)
    # in case the rotating factor is
    # greater than array length
    d = d % n
    reverseArray(arr, 0, d-1)
    reverseArray(arr, d, n-1)
    reverseArray(arr, 0, n-1)
 
# Function to print an array
 
 
def printArray(arr):
    for i in range(0, len(arr)):
        print (arr[i],end=' ')
 
 
# Driver function to test above functions
arr = [1, 2, 3, 4, 5, 6, 7]
n = len(arr)
d = 2
 
leftRotate(arr, d)  # Rotate array by 2
printArray(arr)
 
# This code is contributed by Devesh Agrawal

C#

// C# program for reversal algorithm
// of array rotation
using System;
 
class GFG {
    /* Function to left rotate arr[]
    of size n by d */
    static void leftRotate(int[] arr, int d)
    {
 
        if (d == 0)
            return;
        int n = arr.Length;
          // in case the rotating factor is
        // greater than array length
        d = d % n;
        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
    }
 
    /* Function to reverse arr[] from
    index start to end*/
    static void reverseArray(int[] arr, int start,
                             int end)
    {
        int temp;
        while (start < end) {
            temp = arr[start];
            arr[start] = arr[end];
            arr[end] = temp;
            start++;
            end--;
        }
    }
 
    /*UTILITY FUNCTIONS*/
    /* function to print an array */
    static void printArray(int[] arr)
    {
        for (int i = 0; i < arr.Length; i++)
            Console.Write(arr[i] + " ");
    }
 
    // Driver code
    public static void Main()
    {
        int[] arr = { 1, 2, 3, 4, 5, 6, 7 };
        int n = arr.Length;
        int d = 2;
 
        leftRotate(arr, d); // Rotate array by 2
        printArray(arr);
    }
}
 
// This code is contributed by Sam007

Javascript

      // JavaScript program for reversal algorithm
      // of array rotation
 
      /*Function to reverse arr[] from index start to end*/
      function reverseArray(arr, start, end) {
        while (start < end) {
          var temp = arr[start];
          arr[start] = arr[end];
          arr[end] = temp;
          start++;
          end--;
        }
      }
 
      /* Function to left rotate arr[] of size n by d */
      function leftRotate(arr, d, n) {
        if (d == 0) return;
        // in case the rotating factor is
        // greater than array length
        d = d % n;
 
        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
      }
 
      // Function to print an array
      function printArray(arr, size)
      {
        for (var i = 0; i < size; i++) document.write(arr[i] + " ");
      }
 
      /* Driver program to test above functions */
 
      var arr = [1, 2, 3, 4, 5, 6, 7];
      var n = arr.length;
      var d = 2;
 
      // Function calling
      leftRotate(arr, d, n);
      printArray(arr, n);
       
      // This code is contributed by rdtank.
    

输出 ：

3 4 5 6 7 1 2

时间复杂度： O(n)

辅助空间：O(1)