C++ Program to find juggling algorithm for array rotation

Juggling-Algorithm for array rotation

Here in this program we’ll be learning about Juggling Algorithm. Juggling-algorithm is one of the efficient algorithms used for array rotation. Now, let’s discuss about juggling-algorithm and a program to rotate an array using the juggling-algorithm.

Cpp Program to find juggling algorithm for array rotation


In this section we will learn about basic knowledge which we need to know before coding the above Program. So we must have knowledge of what is an array? 

What is an array?
An array is a data structure, it is collection of similar data elements which is stored at contiguous memory locations in which each data element can be accessed directly by only using its index number.
About C++ language:-
C++ Programming Object Oriented Programming C++ is a programming language developed by Bjarne Stroustrup in 1979 at Bell Labs. C++ is a cross-platform language that can be used to create high-performance applications. It is extension of C language. About C++ Programming it is Multi-paradigm Language – C++ supports at least seven different styles of programming. It is General Purpose Language – You can use C++ to develop games, desktop apps, operating systems, and so on and  Speed – Like C programming, the performance of optimized C++ code is exceptional. 
How to declare an array?
To declare an array in C, a programmer specifies the type of the elements and the number of elements required by an array as follows − This is called a single-dimensional array. The array Size must be an integer constant greater than zero and type can be any valid C data type. For example, to declare a 10-element array called balance of type double, use this statement − Here balance is a variable array which is sufficient to hold up to 10 double numbers

Algorithm :

  • In this method, divide the array into M sets, where M = GCD (n, k), and then rotate the elements in each set.
  • From the number of elements ( n ) of the array and number of rotations ( k ) to be made to the array, the GCD(n, k) number of blocks are made.
  • Then in each block, shifting will take place to the corresponding elements in the block.
  •  After all the elements in all the blocks are shifted, the array will be rotated for the given number of times.
  • Example: If we want to rotate the array Arr : {10, 20, 30, 40, 50, 60} by 2 positions :
  •  M = GCD(60, 20) = 20
  • Initial Array : 10  20  30  40  50  60  
  • First Set Moves : 50  20  10  40  30  60
  • Second Set Moves : 50   60  10  20  30  40    
Juggling algorithm for array rotation in Cpp
Juggling Algorithm (Array Rotation In Place)

C++ Program to find juggling algorithm for array rotation

#include <bits/stdc++.h>
using namespace std;
 int gcd(int a, int b) {
    if (b == 0)
        return a;
        return gcd(b, a % b);
void ArrayRotate(int A[], int n, int k) {
    int d = -1, i, temp, j;
    for (i = 0; i < gcd(n, k); i++) {
        j = i;
        temp = A[i];
        while (1) {
            d = (j + k) % n;
            if (d == i) break;
            A[j] = A[d];
            j = d;
        A[j] = temp;
void displayArray(int A[], int n) {
    int i;
    for (i = 0; i < n; i++) 
    cout<<" ";
int main() {
    int n = 9, i, k = 3;
    cout<<"The size of the Array: "<< n<<endl;
    int A[n] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
    cout<<"The Array elements";
    for (i = 0; i < n; i++) 
    cout<<A[i]<<" ";
    cout<<"\nThe value of k: "<<k<<endl;
    cout<<"Original array: ";
    displayArray(A, n);
    ArrayRotate(A, n, k);
    cout<<"\nArray after rotation: ";
    displayArray(A, n);
    return 0;


The size of the Array: 9
The Array elements1 2 3 4 5 6 7 8 9
The value of k: 3
Original array: 123456789
Array after rotation: 456789123