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

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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  `

Output:

```Yes
```

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