Circular array

3

An array is called circular if we consider first element as next of last element. Circular arrays are used to implement queue (Refer this and this).

An example problem :
Suppose n people are sitting in a circular table with names A, B, C, D,…. Given a name, we need to print all n people (in order) starting from given name.

For example, consider 6 people A B C D E F and given name as ‘D’. People sitting in circular manner starting from D are D E F A B C.

A simple solution is to create an auxiliary array of size 2*n and store in another array. For example for 6 people, we create below auxiliary array.
A B C D E F A B C D E F

Now for any given index, we simply print n elements starting from it. For example, we print following 6.
A B C D E F A B C D E F

Below is the implementation of the above approach.

C++

// CPP program to demonstrate use of circular 
// array using extra memory space
#include <bits/stdc++.h>
using namespace std;
void print(char a[], int n, int ind)
{
    // Create an auxiliary array of twice size.
    char b[(2 * n)];

    // Copy a[] to b[] two times 
    for (int i = 0; i < n; i++) 
        b[i] = b[n + i] = a[i];

    // print from ind-th index to (n+i)th index.
    for (int i = ind; i < n + ind; i++)
        cout << b[i] << " ";
}

// driver code 
int main()
{
    char a[] = { 'A', 'B', 'C', 'D', 'E', 'F' };
    int n = sizeof(a) / sizeof(a[0]);
    print(a, n, 3);
    return 0;
}

Java

// Java program to demonstrate use of circular 
// array using extra memory space
import java.util.*;
import java.lang.*;

public class GfG{
    
    public static void print(char a[], int n, 
                                  int ind){
    
        // Create an auxiliary array 
        // of twice size.
        char[] b = new char[(2 * n)];

        // Copy a[] to b[] two times 
        for (int i = 0; i < n; i++) 
            b[i] = b[n + i] = a[i];

        // print from ind-th index to 
        // (n+i)th index.
        for (int i = ind; i < n + ind; i++)
            System.out.print(b[i]+" ");
    }
    
    // driver function
    public static void main(String argc[]){
        char[] a = new char[]{ 'A', 'B', 'C', 
                             'D', 'E', 'F' };
        int n = 6;
        print(a, n, 3);
    }
}

/* This code is contributed by Sagar Shukla */

Python3

# Python3 program to demonstrate use of 
# circular array using extra memory space

def prints(a, n, ind):
    
    # Create an auxiliary array of twice size.
    b = [None]*2*n
    i = 0
    
    # Copy a[] to b[] two times 
    while i < n: 
        b[i] = b[n + i] = a[i]
        i = i + 1
    
    i = ind

    # print from ind-th index to (n+i)th index.
    while i < n + ind :
        print(b[i], end = " ");
        i = i + 1

# Driver Code
a = ['A', 'B', 'C', 'D', 'E', 'F']
n = len(a);
prints(a, n, 3);

#This code is contributed by rishabh_jain


Output:

D E F A B C 

This approach takes of O(n) time but takes extra space of order O(n)

An efficient solution is to deal with circular arrays using the same array. If a careful observation is run through the array, then after n-th index, the next index always starts from 0 so using mod operator, we can easily access the elements of the circular list, if we use (i)%n and run the loop from i-th index to n+i-th index . and apply mod we can do the traversal in a circular array within the given array without using any extra space.

C++

// CPP program to demonstrate the use of circular
// array without using extra memory space
#include <bits/stdc++.h>
using namespace std;

// function to print circular list starting
// from given index ind.
void print(char a[], int n, int ind)
{
    // print from ind-th index to (n+i)th index.
    for (int i = ind; i < n + ind; i++)
        cout << a[(i % n)] << " ";
}

// driver code to check the above function
int main()
{
    char a[] = { 'A', 'B', 'C', 'D', 'E', 'F' };
    int n = sizeof(a) / sizeof(a[0]);
    print(a, n, 3);
    return 0;
}

Java

// Java program to demonstrate use of circular 
// array using extra memory space
import java.util.*;
import java.lang.*;

public class GfG{
    
    // function to print circular list 
    // starting from given index ind.
    public static void print(char a[], int n, 
                                   int ind){
        
        // print from ind-th index to 
        // (n+i)th index.
        for (int i = ind; i < n + ind; i++)
            System.out.print(a[(i % n)] + " ");
    }
    
    // driver code to check the above function
    public static void main(String argc[]){
        char[] a = new char[]{ 'A', 'B', 'C', 
                             'D', 'E', 'F' };
        int n = 6;
        print(a, n, 3);
    }
}

/* This code is contributed by Sagar Shukla */

Python3

# Python3 program to demonstrate the use of 
# circular array without using extra memory space

# function to print circular list starting
# from given index ind.
def prints(a, n, ind):
    i = ind
    
    # print from ind-th index to (n+i)th index.
    while i < n + ind :
        print(a[(i % n)], end = " ")
        i = i + 1

# Driver Code
a = ['A', 'B', 'C', 'D', 'E', 'F']
n = len(a);
prints(a, n, 3);

# This code is contributed by rishabh_jain


Output:

D E F A B C 

This approach takes O(n) time and O(1) extra space.

More problems based on circular array :

Recent articles on circular array.


Check out this Author's contributed articles.

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