Minimum number of colors required to color a Circular Array

Given a circular array arr[] containing N integers, the task is to find the minimum number of colours required to colour the array element such that two adjacent elements having different values must not be coloured the same.

Examples:

Input: arr[] = {1, 2, 1, 1, 2}
Output: 2
Explanation:
Minimum 2 type of colors are required.
We can distribute color as {r, g, r, r, g} such that no adjacent element having different value are colored same.

Input: arr[] = {1, 2, 3, 4}
Output: 2
Explanation:
Minimum 2 type of colors are required.
We can distribute color as {r, g, r, g}.

Approach: This problem can be solved using Greedy Approach.



  1. If all the values are same then only 1 color is required.
  2. If there are more than one distinct elements and the total number of elements are even then, 2 colors are required.
  3. If there are more than one distinct elements and the total number of elements are odd then, check:
    • If there exist adjacent elements having the same value, then 2 colors are required.
    • Else 3 colors are required.

Below is the implementation of the above approach:

C++

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// C++ implementation of above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function that finds minimum number of
// colors required
void colorRequired(int arr[], int n)
{
  
    // To check that if all the elements
    // are same or not
    bool all_same = true;
  
    // To check if only one adjacent exist
    bool one_adjacent_same = false;
  
    // Traverse the array
    for (int i = 0; i < n - 1; i++) {
  
        // If adjacent elements found
        // different means all are not
        // same
        if (arr[i] != arr[i + 1]) {
            all_same = false;
        }
  
        // If two adjacent elements found
        // to be same then make
        // one_adjacent_same true
        if (arr[i] == arr[i + 1]) {
            one_adjacent_same = true;
        }
    }
  
    // If all elements are same
    // then print 1
    if (all_same == true) {
        cout << 1 << endl;
        return;
    }
  
    // If total number of elements are
    // even or there exist two adjacent
    // elements that are same
    // then print 2
    if (n % 2 == 0
        || one_adjacent_same == true) {
        cout << 2 << endl;
        return;
    }
  
    // Else 3 type of colors
    // are required
    cout << 3 << endl;
}
  
// Driver Code
int main()
{
    int arr[] = { 1, 2, 1, 1, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    // Function call
    colorRequired(arr, n);
    return 0;
}

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Java

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// Java implementation of above approach
import java.util.*;
  
class GFG{
  
// Function that finds minimum number of
// colors required
static void colorRequired(int arr[], int n)
{
  
    // To check that if all the elements
    // are same or not
    boolean all_same = true;
  
    // To check if only one adjacent exist
    boolean one_adjacent_same = false;
  
    // Traverse the array
    for(int i = 0; i < n - 1; i++)
    {
         
       // If adjacent elements found
       // different means all are not
       // same
       if (arr[i] != arr[i + 1]) 
       {
           all_same = false;
       }
         
       // If two adjacent elements found
       // to be same then make
       // one_adjacent_same true
       if (arr[i] == arr[i + 1]) 
       {
           one_adjacent_same = true;
       }
    }
  
    // If all elements are same
    // then print 1
    if (all_same == true)
    {
        System.out.print(1 + "\n");
        return;
    }
  
    // If total number of elements are
    // even or there exist two adjacent
    // elements that are same
    // then print 2
    if (n % 2 == 0 || 
        one_adjacent_same == true)
    {
        System.out.print(2 + "\n");
        return;
    }
  
    // Else 3 type of colors
    // are required
    System.out.print(3 + "\n");
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 1, 2, 1, 1, 2 };
    int n = arr.length;
  
    // Function call
    colorRequired(arr, n);
}
}
  
// This code is contributed by Rohit_ranjan

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Python3

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# Python3 implementation of the above approach
  
# Function that finds minimum number 
# of colors required
def colorRequired(arr, n):
  
    # To check that if all the elements
    # are same or not
    all_same = True
  
    # To check if only one adjacent exist
    one_adjacent_same = False
  
    # Traverse the array
    for i in range(n - 1):
  
        # If adjacent elements found
        # different means all are not
        # same
        if(arr[i] != arr[i + 1]):
            all_same = False
  
        # If two adjacent elements 
        # found to be same then make
        # one_adjacent_same true
        if(arr[i] == arr[i + 1]):
            one_adjacent_same = True
  
    # If all elements are same
    # then print 1
    if(all_same == True):
        print(1)
        return
  
    # If total number of elements are
    # even or there exist two adjacent
    # elements that are same
    # then print 2
    if(n % 2 == 0 or one_adjacent_same == True):
        print(2)
        return
  
    # Else 3 type of colors
    # are required
    print(3)
  
# Driver Code
if __name__ == '__main__':
  
    arr = [ 1, 2, 1, 1, 2 ]
    n = len(arr)
  
    # Function call
    colorRequired(arr, n)
  
# This code is contributed by Shivam Singh

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C#

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// C# implementation of above approach
using System;
class GFG{
  
// Function that finds minimum number of
// colors required
static void colorRequired(int []arr, int n)
{
  
    // To check that if all the elements
    // are same or not
    bool all_same = true;
  
    // To check if only one adjacent exist
    bool one_adjacent_same = false;
  
    // Traverse the array
    for(int i = 0; i < n - 1; i++)
    {
          
        // If adjacent elements found
        // different means all are not
        // same
        if (arr[i] != arr[i + 1]) 
        {
            all_same = false;
        }
              
        // If two adjacent elements found
        // to be same then make
        // one_adjacent_same true
        if (arr[i] == arr[i + 1]) 
        {
            one_adjacent_same = true;
        }
    }
  
    // If all elements are same
    // then print 1
    if (all_same == true)
    {
        Console.Write(1 + "\n");
        return;
    }
  
    // If total number of elements are
    // even or there exist two adjacent
    // elements that are same
    // then print 2
    if (n % 2 == 0 || 
        one_adjacent_same == true)
    {
        Console.Write(2 + "\n");
        return;
    }
  
    // Else 3 type of colors
    // are required
    Console.Write(3 + "\n");
}
  
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 1, 2, 1, 1, 2 };
    int n = arr.Length;
  
    // Function call
    colorRequired(arr, n);
}
}
  
// This code is contributed by sapnasingh4991

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Output:

2

Time Complexity: O(N), where N is the number of elements.

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