Write a function rotate(arr[], d, n) that rotates arr[] of size n by d elements.
Rotation of the above array by 2 will make an array
Algorithm :
Initialize A = arr[0..d-1] and B = arr[d..n-1]
1) Do following until size of A is equal to size of B
a) If A is shorter, divide B into Bl and Br such that Br is of same
length as A. Swap A and Br to change ABlBr into BrBlA. Now A
is at its final place, so recur on pieces of B.
b) If A is longer, divide A into Al and Ar such that Al is of same
length as B Swap Al and B to change AlArB into BArAl. Now B
is at its final place, so recur on pieces of A.
2) Finally when A and B are of equal size, block swap them.
Recursive Implementation:
C++
#include <bits/stdc++.h> using namespace std; #include <bits/stdc++.h> using namespace std; /*UTILITY FUNCTIONS*//* function to print an array */void printArray(int arr[], int size) { int i; for (i = 0; i < size; i++) cout << arr[i] << " "; cout << endl; } /*This function swaps d elements starting at index fi with d elements starting at index si */void swap(int arr[], int fi, int si, int d) { int i, temp; for (i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } void leftRotate(int arr[], int d, int n) { /* Return If number of elements to be rotated is zero or equal to array size */ if (d == 0 || d == n) return; /* If number of elements to be rotated is more than * array size*/ if (d > n) d = d % n; /*If number of elements to be rotated is exactly half of array size */ if (n - d == d) { swap(arr, 0, n - d, d); return; } /* If A is shorter*/ if (d < n - d) { swap(arr, 0, n - d, d); leftRotate(arr, d, n - d); } else /* If B is shorter*/ { swap(arr, 0, d, n - d); leftRotate(arr + n - d, 2 * d - n, d); /*This is tricky*/ } } // Driver Code int main() { int arr[] = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); return 0; } // This code is contributed by rathbhupendra |
C
#include<stdio.h> /*Prototype for utility functions */void printArray(int arr[], int size); void swap(int arr[], int fi, int si, int d); void leftRotate(int arr[], int d, int n) { /* Return If number of elements to be rotated is zero or equal to array size */ if(d == 0 || d == n) return; /*If number of elements to be rotated is exactly half of array size */ if(n-d == d) { swap(arr, 0, n-d, d); return; } /* If A is shorter*/ if(d < n-d) { swap(arr, 0, n-d, d); leftRotate(arr, d, n-d); } else /* If B is shorter*/ { swap(arr, 0, d, n-d); leftRotate(arr+n-d, 2*d-n, d); /*This is tricky*/ } } /*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]); printf("\n "); } /*This function swaps d elements starting at index fi with d elements starting at index si */void swap(int arr[], int fi, int si, int d) { int i, temp; for(i = 0; i<d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } /* Driver program to test above functions */int main() { int arr[] = {1, 2, 3, 4, 5, 6, 7}; leftRotate(arr, 2, 7); printArray(arr, 7); getchar(); return 0; } |
Java
import java.util.*; class GFG { // Wrapper over the recursive function leftRotateRec() // It left rotates arr[] by d. public static void leftRotate(int arr[], int d, int n) { leftRotateRec(arr, 0, d, n); } public static void leftRotateRec(int arr[], int i, int d, int n) { /* Return If number of elements to be rotated is zero or equal to array size */ if(d == 0 || d == n) return; /*If number of elements to be rotated is exactly half of array size */ if(n - d == d) { swap(arr, i, n - d + i, d); return; } /* If A is shorter*/ if(d < n - d) { swap(arr, i, n - d + i, d); leftRotateRec(arr, i, d, n - d); } else /* If B is shorter*/ { swap(arr, i, d, n - d); leftRotateRec(arr, n - d + i, 2 * d - n, d); /*This is tricky*/ } } /*UTILITY FUNCTIONS*//* function to print an array */public static void printArray(int arr[], int size) { int i; for(i = 0; i < size; i++) System.out.print(arr[i] + " "); System.out.println(); } /*This function swaps d elements starting at index fi with d elements starting at index si */public static void swap(int arr[], int fi, int si, int d) { int i, temp; for(i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } // Driver Code public static void main (String[] args) { int arr[] = {1, 2, 3, 4, 5, 6, 7}; leftRotate(arr, 2, 7); printArray(arr, 7); } } // This code is contributed by codeseeker |
Python3
# Wrapper over the recursive function leftRotateRec() # It left rotates arr by d. def leftRotate(arr, d, n): leftRotateRec(arr, 0, d, n); def leftRotateRec(arr, i, d, n): ''' * Return If number of elements to be rotated is zero or equal to array size ''' if (d == 0 or d == n): return; ''' * If number of elements to be rotated is exactly half of array size ''' if (n - d == d): swap(arr, i, n - d + i, d); return; ''' If A is shorter ''' if (d < n - d): swap(arr, i, n - d + i, d); leftRotateRec(arr, i, d, n - d); ''' If B is shorter ''' else: swap(arr, i, d, n - d); ''' This is tricky ''' leftRotateRec(arr, n - d + i, 2 * d - n, d); ''' UTILITY FUNCTIONS '''''' function to print an array '''def printArray(arr, size): for i in range(size): print(arr[i], end = " "); print(); ''' * This function swaps d elements starting at * index fi with d elements starting at index si '''def swap(arr, fi, si, d): for i in range(d): temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; # Driver Code if __name__ == '__main__': arr = [1, 2, 3, 4, 5, 6, 7]; leftRotate(arr, 2, 7); printArray(arr, 7); # This code is contributed by Rohit_ranjan |
C#
using System; class GFG{ // Wrapper over the recursive function // leftRotateRec() // It left rotates []arr by d. public static void leftRotate(int []arr, int d, int n) { leftRotateRec(arr, 0, d, n); } public static void leftRotateRec(int []arr, int i, int d, int n) { // Return If number of elements // to be rotated is zero or equal // to array size if(d == 0 || d == n) return; // If number of elements to be rotated // is exactly half of array size if(n - d == d) { swap(arr, i, n - d + i, d); return; } // If A is shorter if(d < n - d) { swap(arr, i, n - d + i, d); leftRotateRec(arr, i, d, n - d); } // If B is shorter else { swap(arr, i, d, n - d); // This is tricky leftRotateRec(arr, n - d + i, 2 * d - n, d); } } // UTILITY FUNCTIONS // Function to print an array public static void printArray(int []arr, int size) { int i; for(i = 0; i < size; i++) Console.Write(arr[i] + " "); Console.WriteLine(); } // This function swaps d elements // starting at index fi with d elements // starting at index si public static void swap(int []arr, int fi, int si, int d) { int i, temp; for(i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } // Driver Code public static void Main(String[] args) { int []arr = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); } } // This code is contributed by amal kumar choubey |
Javascript
<script> let leftRotate = (arr, d, n) =>{ /* Return If number of elements to be rotated is zero or equal to array size */ if(d == 0 || d == n) return; /*If number of elements to be rotated is exactly half of array size */ if(n - d == d) { arr = swap(arr, 0, n - d, d); return; } /* If A is shorter*/ if(d < n - d) { arr = swap(arr, 0, n - d, d); leftRotate(arr, d, n - d); } else{ /* If B is shorter*/ arr = swap(arr, 0, d, n - d); /*This is tricky*/ leftRotate(arr + n - d, 2 * d - n, d); } } /*UTILITY FUNCTIONS*//* function to print an array */let printArray = (arr, size) =>{ ans = '' for(let i = 0; i < size; i++) ans += arr[i]+" "; document.write(ans) } /*This function swaps d elements starting at index fi with d elements starting at index si */let swap = (arr, fi, si, d) =>{ for(let i = 0; i < d; i++) { let temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } return arr } // Driver Code arr = [1, 2, 3, 4, 5, 6, 7]; leftRotate(arr, 2, 7); printArray(arr, 7); </script> |
Output
3 4 5 6 7 1 2
Time Complexity: O(n)
Auxiliary Space: O(log n)
Iterative Implementation:
Here is an iterative implementation of the same algorithm. The same utility function swap() is used here.
C++
// C++ code for above implementation #include <bits/stdc++.h> using namespace std; /*UTILITY FUNCTIONS*//* function to print an array */void printArray(int arr[], int size) { int i; for (i = 0; i < size; i++) cout << arr[i] << " "; cout << endl; } /*This function swaps d elements starting at index fi with d elements starting at index si */void swap(int arr[], int fi, int si, int d) { int i, temp; for (i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } // This code is contributed by rathbhupendra void leftRotate(int arr[], int d, int n) { int i, j; if (d == 0 || d == n) return; /* If number of elements to be rotated is more than * array size*/ if (d > n) d = d % n; i = d; j = n - d; while (i != j) { if (i < j) /*A is shorter*/ { swap(arr, d - i, d + j - i, i); j -= i; } else /*B is shorter*/ { swap(arr, d - i, d, j); i -= j; } // printArray(arr, 7); } /*Finally, block swap A and B*/ swap(arr, d - i, d, i); } // Driver Code int main() { int arr[] = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); return 0; } // This code is contributed by Shivani |
C
// C code for above implementation #include <stdio.h> /*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]); printf("\n "); } /*This function swaps d elements starting at index fi with d elements starting at index si */void swap(int arr[], int fi, int si, int d) { int i, temp; for (i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } void leftRotate(int arr[], int d, int n) { int i, j; if (d == 0 || d == n) return; /* If number of elements to be rotated is more than * array size*/ if (d > n) d = d % n; i = d; j = n - d; while (i != j) { if (i < j) /*A is shorter*/ { swap(arr, d - i, d + j - i, i); j -= i; } else /*B is shorter*/ { swap(arr, d - i, d, j); i -= j; } // printArray(arr, 7); } /*Finally, block swap A and B*/ swap(arr, d - i, d, i); } /* Driver program to test above functions */int main() { int arr[] = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); getchar(); return 0; } |
Java
// Java code for above implementation import java.io.*; public class GFG { static void leftRotate(int arr[], int d, int n) { int i, j; if (d == 0 || d == n) return; /* If number of elements to be rotated is more than * array size*/ if (d > n) d = d % n; i = d; j = n - d; while (i != j) { if (i < j) /*A is shorter*/ { swap(arr, d - i, d + j - i, i); j -= i; } else /*B is shorter*/ { swap(arr, d - i, d, j); i -= j; } // printArray(arr, 7); } /*Finally, block swap A and B*/ swap(arr, d - i, d, i); } /*UTILITY FUNCTIONS*/ /* function to print an array */ public static void printArray(int arr[], int size) { int i; for (i = 0; i < size; i++) System.out.print(arr[i] + " "); System.out.println(); } /*This function swaps d elements starting at index fi with d elements starting at index si */ public static void swap(int arr[], int fi, int si, int d) { int i, temp; for (i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } // Driver Code public static void main(String[] args) { int arr[] = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); } } |
Python3
# Python3 code for above implementation # Wrapper over the recursive function leftRotateRec() # It left rotates arr by d. ''' UTILITY FUNCTIONS '''''' function to print an array ''' def printArray(arr, size): for i in range(size): print(arr[i], end=" ") print() ''' * This function swaps d elements starting at * index fi with d elements starting at index si ''' def swap(arr, fi, si, d): for i in range(d): temp = arr[fi + i] arr[fi + i] = arr[si + i] arr[si + i] = temp def leftRotate(arr, d, n): if(d == 0 or d == n): return i = d j = n - d while (i != j): if(i < j): # A is shorter swap(arr, d - i, d + j - i, i) j -= i else: # B is shorter swap(arr, d - i, d, j) i -= j swap(arr, d - i, d, i) # Driver Code if __name__ == '__main__': arr = [1, 2, 3, 4, 5, 6, 7] leftRotate(arr, 2, 7) printArray(arr, 7) |
C#
// C# code for above implementation using System; class GFG { // UTILITY FUNCTIONS // Function to print an array public static void printArray(int[] arr, int size) { int i; for (i = 0; i < size; i++) Console.Write(arr[i] + " "); Console.WriteLine(); } // This function swaps d elements // starting at index fi with d elements // starting at index si public static void swap(int[] arr, int fi, int si, int d) { int i, temp; for (i = 0; i < d; i++) { temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; } } static void leftRotate(int[] arr, int d, int n) { int i, j; if (d == 0 || d == n) return; /* If number of elements to be rotated is more than * array size*/ if (d > n) d = d % n; i = d; j = n - d; while (i != j) { if (i < j) /*A is shorter*/ { swap(arr, d - i, d + j - i, i); j -= i; } else /*B is shorter*/ { swap(arr, d - i, d, j); i -= j; } } /*Finally, block swap A and B*/ swap(arr, d - i, d, i); } // Driver Code public static void Main(String[] args) { int[] arr = { 1, 2, 3, 4, 5, 6, 7 }; leftRotate(arr, 2, 7); printArray(arr, 7); } } // This code is contributed by Rajput-Ji |
Javascript
<script> // JavaScript code for above implementation function leftRotate(arr, d, n) { if(d == 0 || d == n) return; let i = d; let j = n - d; while (i != j) { if(i < j) { // A is shorter arr = swap(arr, d - i, d + j - i, i); j -= i; } else{ // B is shorter arr = swap(arr, d - i, d, j); i -= j; } } arr = swap(arr, d - i, d, i); // This code is contributed by rohitsingh04052. } </script> |
Output
3 4 5 6 7 1 2
Time Complexity: O(n)
Auxiliary Space: O(1)
Please see the following posts for other methods of array rotation:
https://www.geeksforgeeks.org/array-rotation/
https://www.geeksforgeeks.org/program-for-array-rotation-continued-reversal-algorithm/
Please write comments if you find any bug in the above programs/algorithms or want to share any additional information about the block swap algorithm.
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