Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Make all elements zero by decreasing any two elements by one at a time

  • Last Updated : 25 May, 2021

Given an array arr[], the task is to check whether it is possible to make all the elements of the array zero by the given operation. In a single operation, any two elements arr[i] and arr[j] can be decremented by one at the same time. 
Examples: 
 

Input: arr[] = {1, 2, 1, 2, 2} 
Output: Yes 
Decrement the 1st and the 2nd element, arr[] = {0, 1, 1, 2, 2} 
Decrement the 2nd and the 3rd element, arr[] = {0, 0, 0, 2, 2} 
Decrement the 4th and the 5th element, arr[] = {0, 0, 0, 1, 1} 
Decrement the 4th and the 5th element, arr[] = {0, 0, 0, 0, 0}
Input: arr[] = {1, 2, 3, 4, 5} 
Output: No 
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

 



Approach: The given array can be only be made zero if it holds the following conditions true: 
 

  1. The sum of the elements of the array must be even.
  2. The largest elements must be less than or equal to ⌊sum / 2⌋ where sum is the sum of the other elements.

Below is the implementation of the above approach: 
 

CPP




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that returns true if all
// the array elements can be made
// 0 with the given operation
bool checkZeroArray(int* arr, int n)
{
 
    // Find the maximum element
    // and the sum
    int sum = 0, maximum = INT_MIN;
    for (int i = 0; i < n; i++) {
        sum = sum + arr[i];
        maximum = max(maximum, arr[i]);
    }
 
    // Check the required condition
    if (sum % 2 == 0 && maximum <= sum / 2)
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 1, 2, 2 };
    int n = sizeof(arr) / sizeof(int);
 
    if (checkZeroArray(arr, n))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java




// Java implementation of the above approach
public class GFG
{
     
    // Function that returns true if all
    // the array elements can be made
    // 0 with the given operation
    static boolean checkZeroArray(int []arr, int n)
    {
     
        // Find the maximum element
        // and the sum
        int sum = 0, maximum = Integer.MIN_VALUE;
         
        for (int i = 0; i < n; i++)
        {
            sum = sum + arr[i];
            maximum = Math.max(maximum, arr[i]);
        }
     
        // Check the required condition
        if (sum % 2 == 0 && maximum <= sum / 2)
            return true;
     
        return false;
    }
     
    // Driver code
    public static void main (String[] args)
    {
        int arr[] = { 1, 2, 1, 2, 2 };
        int n = arr.length;
     
        if (checkZeroArray(arr, n) == true)
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
 
// This code is contributed by AnkitRai01

Python




# Python3 implementation of the approach
 
# Function that returns true if all
# the array elements can be made
# 0 with the given operation
def checkZeroArray(arr,n):
 
    # Find the maximum element
    # and the sum
    sum = 0
    maximum = -10**9
    for i in range(n):
        sum = sum + arr[i]
        maximum = max(maximum, arr[i])
 
    # Check the required condition
    if (sum % 2 == 0 and maximum <= sum // 2):
        return True
 
    return False
 
# Driver code
 
arr = [1, 2, 1, 2, 2]
n = len(arr)
 
if (checkZeroArray(arr, n)):
    print("Yes")
else:
    print("No")
 
# This code is contributed by mohit kumar 29

C#




// C# implementation of the above approach
using System;
 
class GFG
{
     
    // Function that returns true if all
    // the array elements can be made
    // 0 with the given operation
    static bool checkZeroArray(int []arr, int n)
    {
     
        // Find the maximum element
        // and the sum
        int sum = 0, maximum = int.MinValue;
         
        for (int i = 0; i < n; i++)
        {
            sum = sum + arr[i];
            maximum = Math.Max(maximum, arr[i]);
        }
     
        // Check the required condition
        if (sum % 2 == 0 && maximum <= sum / 2)
            return true;
     
        return false;
    }
     
    // Driver code
    public static void Main ()
    {
        int []arr = { 1, 2, 1, 2, 2 };
        int n = arr.Length;
     
        if (checkZeroArray(arr, n) == true)
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
 
// This code is contributed by AnkitRai01

Javascript




<script>
 
// JavaScript implementation of the above approach
     
    // Function that returns true if all
    // the array elements can be made
    // 0 with the given operation
    function checkZeroArray(arr,n)
    {
        // Find the maximum element
        // and the sum
        let sum = 0, maximum = Number.MIN_VALUE;
           
        for (let i = 0; i < n; i++)
        {
            sum = sum + arr[i];
            maximum = Math.max(maximum, arr[i]);
        }
       
        // Check the required condition
        if (sum % 2 == 0 && maximum <= sum / 2)
            return true;
       
        return false;
    }
     
    // Driver code
    let arr=[1, 2, 1, 2, 2 ];
    let n = arr.length;
    if (checkZeroArray(arr, n) == true)
        document.write("Yes");
    else
        document.write("No");
       
 
 
// This code is contributed by unknown2108
 
</script>
Output: 
Yes

 




My Personal Notes arrow_drop_up
Recommended Articles
Page :