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Make all the elements of array even with given operations

  • Last Updated : 31 May, 2021

Given an array arr[] of positive integers, find the minimum number of operations required to make all the array elements even where:  

  1. If there is an odd number, then, increment the element and the next adjacent element by 1.
  2. Each increment costs one operation.

Note: If there is any number in arr[] which is odd after all operations, then, print -1.

Examples: 

Input: arr[] = {2, 3, 4, 5, 6} 
Output:
Explanation: 
Add 1 to 3 (at 1st index) and add 1 to its adjacent element 4(2nd index). 
Now the array becomes {2, 4, 5, 5, 6}. 
Add 1 to 5 (at 2nd index) and add 1 to its adjacent element 5(3rd index). 
Now the array becomes {2, 4, 6, 6, 6}. 
The resultant array has all even numbers. 
The total number of operations for 4 increments is 4.

Input: arr[] = {5, 6} 
Output: -1 
Explanation: 
Adding 1 to 5(0th index), then we have to increment 1 to its adjacent element 6(1st index). 
Now the array becomes {6, 7}. 
And we have 1 odd number left after all possible increments. Therefore, we can’t make all array elements even.  

Approach: 
This problem can be solved using Greedy Approach. The following are the steps: 

  1. Traverse the given array arr[].
  2. If an odd element occurs, then increment that element by 1 to make it even and the next adjacent element by 1.
  3. Repeat the above step for all the odd elements for the given array arr[].
  4. If all the elements in arr[] are even, then print the number of operations.
  5. Else print -1.

Below is the implementation of the above approach: 

C++




// C++ program to make all array
// element even
#include "bits/stdc++.h"
using namespace std;
 
// Function to count the total
// number of operations needed to make
// all array element even
int countOperations(int arr[], int n)
{
    int count = 0;
 
    // Traverse the given array
    for (int i = 0; i < n - 1; i++) {
 
        // If an odd element occurs
        // then increment that element
        // and next adjacent element
        // by 1
        if (arr[i] & 1) {
            arr[i]++;
            arr[i + 1]++;
            count += 2;
        }
    }
 
    // Traverse the array if any odd
    // element occurs then return -1
    for (int i = 0; i < n; i++) {
        if (arr[i] & 1)
            return -1;
    }
 
    // Returns the count of operations
    return count;
}
 
int main()
{
    int arr[] = { 2, 3, 4, 5, 6 };
    int n = sizeof(arr) / sizeof(int);
    cout << countOperations(arr, n);
    return 0;
}

Java




// Java program to make all array
// element even
class GFG
{
 
// Function to count the total
// number of operations needed to make
// all array element even
static int countOperations(int arr[], int n)
{
    int count = 0;
 
    // Traverse the given array
    for (int i = 0; i < n - 1; i++)
    {
 
        // If an odd element occurs
        // then increment that element
        // and next adjacent element
        // by 1
        if (arr[i] % 2 == 1)
        {
            arr[i]++;
            arr[i + 1]++;
            count += 2;
        }
    }
 
    // Traverse the array if any odd
    // element occurs then return -1
    for (int i = 0; i < n; i++)
    {
        if (arr[i] % 2 == 1)
            return -1;
    }
 
    // Returns the count of operations
    return count;
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 2, 3, 4, 5, 6 };
    int n = arr.length;
    System.out.print(countOperations(arr, n));
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 program to make all array
# element even
 
# Function to count the total
# number of operations needed to make
# all array element even
def countOperations(arr, n) :
 
    count = 0;
 
    # Traverse the given array
    for i in range(n - 1) :
 
        # If an odd element occurs
        # then increment that element
        # and next adjacent element
        # by 1
        if (arr[i] & 1) :
            arr[i] += 1;
            arr[i + 1] += 1;
            count += 2;
 
    # Traverse the array if any odd
    # element occurs then return -1
    for i in range(n) :
        if (arr[i] & 1) :
            return -1;
 
    # Returns the count of operations
    return count;
 
if __name__ == "__main__" :
 
    arr = [ 2, 3, 4, 5, 6 ];
    n = len(arr);
    print(countOperations(arr, n));
     
    # This code is contributed by AnkitRai01

C#




// C# program to make all array
// element even
using System;
 
class GFG
{
 
// Function to count the total
// number of operations needed to make
// all array element even
static int countOperations(int []arr, int n)
{
    int count = 0;
 
    // Traverse the given array
    for (int i = 0; i < n - 1; i++)
    {
 
        // If an odd element occurs
        // then increment that element
        // and next adjacent element
        // by 1
        if (arr[i] % 2 == 1)
        {
            arr[i]++;
            arr[i + 1]++;
            count += 2;
        }
    }
 
    // Traverse the array if any odd
    // element occurs then return -1
    for (int i = 0; i < n; i++)
    {
        if (arr[i] % 2 == 1)
            return -1;
    }
 
    // Returns the count of operations
    return count;
}
 
// Driver code
public static void Main()
{
    int []arr = { 2, 3, 4, 5, 6 };
    int n = arr.Length;
    Console.Write(countOperations(arr, n));
}
}
 
// This code is contributed by AnkitRai01

Javascript




<script>
// Javascript program to make all array
// element even
 
// Function to count the total
// number of operations needed to make
// all array element even
function countOperations(arr, n)
{
    let count = 0;
 
    // Traverse the given array
    for (let i = 0; i < n - 1; i++) {
 
        // If an odd element occurs
        // then increment that element
        // and next adjacent element
        // by 1
        if (arr[i] & 1) {
            arr[i]++;
            arr[i + 1]++;
            count += 2;
        }
    }
 
    // Traverse the array if any odd
    // element occurs then return -1
    for (let i = 0; i < n; i++) {
        if (arr[i] & 1)
            return -1;
    }
 
    // Returns the count of operations
    return count;
}
 
 
let arr = [ 2, 3, 4, 5, 6 ];
let n = arr.length;
document.write(countOperations(arr, n));
 
// This code is contributed by _saurabh_jaiswal
</script>
Output: 
4

 

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


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