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Make all array elements even by replacing adjacent pair of array elements with their sum
  • Last Updated : 22 Feb, 2021

Given an array arr[] of size N, the task is to make all array elements even by replacing a pair of adjacent elements with their sum.

Examples:

Input: arr[] = { 2, 4, 5, 11, 6 }
Output: 1
Explanation:
Replacing a pair (arr[2], arr[3]) with their sum ( = 5 + 11 = 16) modifies arr[] to { 2, 4, 16, 16, 6 } 
Since all array elements are even, the required output is 1.

Input: arr[] = { 1, 2, 4, 3, 11 } 
Output: 3
Explanation: 
Replacing the pair (arr[3], arr[4]) and replacing them with their sum ( = 3 + 11 = 14) modifies arr[] to { 1, 2, 4, 14, 14 }
Replacing the pair (arr[0], arr[1]) and replacing them with their sum ( = 1 + 2 = 3) modifies arr[] to { 3, 3, 4, 14, 14 }
Replacing the pair (arr[0], arr[1]) with their sum ( = 3 + 3 = 6) modifies arr[] to { 6, 6, 4, 14, 14 }. 
Therefore, the required output is 3.

Approach: The idea is to use the fact that the sum of two odd numbers generates an even number. Follow the steps below to solve the problem:



  1. Initialize two integers, say res, to count the number of replacements, and odd_continuous_segment, to count the number of continuous odd numbers
  2. Traverse the array and check the following conditions for every array element:
    1. If arr[i] is odd, then increment the count of odd_continuous_segment by 1
    2. Otherwise, if odd_continuous_segment is odd, then increment res by odd_continuous_segment/2. Otherwise, increment res by odd_continuous_segment / 2 + 2 and assign odd_continuous_segment to 0.
  3. Check if odd_continuous_segment is odd. If found to be true, then increment res by odd_continuous_segment / 2. Otherwise increment res by (odd_continuous_segment / 2 + 2)
  4. Finally, print the obtained value of res

Below is the implementation of the above approach:

C++

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// C++ program to implement
// the above approach
 
#include <iostream>
using namespace std;
 
// Function to find minimum count of operations
// required to make all array elements even
int make_array_element_even(int arr[], int N)
{
    // Stores minimum count of replacements
    // to make all array elements even
    int res = 0;
 
    // Stores the count of odd
    // continuous numbers
    int odd_cont_seg = 0;
 
    // Traverse the array
    for (int i = 0; i < N; i++) {
 
        // If arr[i] is an odd number
        if (arr[i] % 2 == 1) {
 
            // Update odd_cont_seg
            odd_cont_seg++;
        }
        else {
 
            if (odd_cont_seg > 0) {
 
                // If odd_cont_seg is even
                if (odd_cont_seg % 2 == 0) {
 
                    // Update res
                    res += odd_cont_seg / 2;
                }
 
                else {
 
                    // Update res
                    res += (odd_cont_seg / 2) + 2;
                }
 
                // Reset odd_cont_seg = 0
                odd_cont_seg = 0;
            }
        }
    }
 
    // If odd_cont_seg exceeds 0
    if (odd_cont_seg > 0) {
 
        // If odd_cont_seg is even
        if (odd_cont_seg % 2 == 0) {
 
            // Update res
            res += odd_cont_seg / 2;
        }
 
        else {
 
            // Update res
            res += odd_cont_seg / 2 + 2;
        }
    }
 
    // Print the result
    return res;
}
 
// Drivers Code
int main()
{
    int arr[] = { 2, 4, 5, 11, 6 };
    int N = sizeof(arr) / sizeof(arr[0]);
    cout << make_array_element_even(arr, N);
 
    return 0;
}

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Java

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// Java program to implement
// the above approach
import java.util.*;
class GFG{
 
  // Function to find minimum count of operations
  // required to make all array elements even
  static int make_array_element_even(int arr[], int N)
  {
 
    // Stores minimum count of replacements
    // to make all array elements even
    int res = 0;
 
    // Stores the count of odd
    // continuous numbers
    int odd_cont_seg = 0;
 
    // Traverse the array
    for (int i = 0; i < N; i++)
    {
 
      // If arr[i] is an odd number
      if (arr[i] % 2 == 1)
      {
 
        // Update odd_cont_seg
        odd_cont_seg++;
      }
      else
      {
        if (odd_cont_seg > 0)
        {
 
          // If odd_cont_seg is even
          if (odd_cont_seg % 2 == 0)
          {
 
            // Update res
            res += odd_cont_seg / 2;
          }
 
          else
          {
 
            // Update res
            res += (odd_cont_seg / 2) + 2;
          }
 
          // Reset odd_cont_seg = 0
          odd_cont_seg = 0;
        }
      }
    }
 
    // If odd_cont_seg exceeds 0
    if (odd_cont_seg > 0)
    {
 
      // If odd_cont_seg is even
      if (odd_cont_seg % 2 == 0)
      {
 
        // Update res
        res += odd_cont_seg / 2;
      }
 
      else
      {
 
        // Update res
        res += odd_cont_seg / 2 + 2;
      }
    }
 
    // Print the result
    return res;
  }
 
  // Drivers Code
  public static void main(String[] args)
  {
    int arr[] = { 2, 4, 5, 11, 6 };
    int N = arr.length;
    System.out.print(make_array_element_even(arr, N));
  }
}
 
// This code is contributed by shikhasingrajput

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C#

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// C# program to implement
// the above approach
using System;
public class GFG
{
 
  // Function to find minimum count of operations
  // required to make all array elements even
  static int make_array_element_even(int []arr, int N)
  {
 
    // Stores minimum count of replacements
    // to make all array elements even
    int res = 0;
 
    // Stores the count of odd
    // continuous numbers
    int odd_cont_seg = 0;
 
    // Traverse the array
    for (int i = 0; i < N; i++)
    {
 
      // If arr[i] is an odd number
      if (arr[i] % 2 == 1)
      {
 
        // Update odd_cont_seg
        odd_cont_seg++;
      }
      else
      {
        if (odd_cont_seg > 0)
        {
 
          // If odd_cont_seg is even
          if (odd_cont_seg % 2 == 0)
          {
 
            // Update res
            res += odd_cont_seg / 2;
          }
 
          else
          {
 
            // Update res
            res += (odd_cont_seg / 2) + 2;
          }
 
          // Reset odd_cont_seg = 0
          odd_cont_seg = 0;
        }
      }
    }
 
    // If odd_cont_seg exceeds 0
    if (odd_cont_seg > 0)
    {
 
      // If odd_cont_seg is even
      if (odd_cont_seg % 2 == 0)
      {
 
        // Update res
        res += odd_cont_seg / 2;
      }
 
      else
      {
 
        // Update res
        res += odd_cont_seg / 2 + 2;
      }
    }
 
    // Print the result
    return res;
  }
 
  // Drivers Code
  public static void Main(String[] args)
  {
    int []arr = { 2, 4, 5, 11, 6 };
    int N = arr.Length;
    Console.Write(make_array_element_even(arr, N));
  }
}
 
// This code is contributed by 29AjayKumar

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Output: 

1

 

Time complexity: O(N)
Auxiliary space: O(1)

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