Given an array arr[] containing natural numbers from 1 to N, the task is to find the maximum number of elements that can be made equal after below operations:

1. Remove any pair of elements from the array and insert their sum to array.
2. Repeat the above operation any numbers of times to maximize the count of equal elements.

Examples:

Input:_ arr[] = {1, 2, 3, 4} _

Output:_ 2 _

Explanation:

_We can perform following operations: _

{1, 2, 3, 4} -> {3, 3, 4} -> 2 elements are equal

Input:_ arr[] = {1 2 3 4 5 6} _

Output:_ 3 _

Explanation:

{1, 2, 3, 4, 5, 6} -> {7, 2, 3, 4, 5} -> {7, 7, 3, 4} -> {7, 7, 37} -> 3 elements are equal

**Approach: **The key observation in the problem is that:

• If N is even, we can make a maximum count of equal elements by
• 
• If N is odd, we can make maximum count of equal elements by
• 

Therefore, the answer will always be 

Below is the implementation of the above approach:

• C++
• Python3

// C++ implementation of

// the above approach

#include <bits/stdc++.h>

**using** **namespace** std;

// Function to count maximum number

// of array elements equal

**int** countEqual(``**int** n)

{

**return** (n + 1) / 2;

}

// Driver Code

**int** main()

{

**int** arr[] = { 1, 2, 3, 4, 5, 6 };

**int** n = **sizeof**``(arr) / **sizeof**``(arr[0]);

// Function Call

cout << countEqual(n);

**return** 0;

}

Output:

3

Performance Analysis:

• **Time Complexity: **O(1)
• Auxiliary Space: O(1)

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#arrays #mathematical #school programming #natural numbers