Minimize the maximum element in constructed Array with sum divisible by K

Last Updated : 27 Aug, 2021

Given two integers N and K, the task is to find the smallest value for maximum element of an array of size N consisting of positive integers whose sum of elements is divisible by K.

Examples:

Input: N = 4, K = 3
Output: 2
Explanation:
Let the array be [2, 2, 1, 1]. Here, sum of elements of this array is divisible by K=3, and maximum element is 2.

Input: N = 3, K = 5
Output: 2

Approach: To find the smallest maximum of an array of size N and having sum divisible by K, try to create an array with the minimum sum possible.

The minimum sum of N elements (each having a value greater than 0) that is divisible by K is:

sum = K * ceil(N/K)

Now, if the sum is divisible by N then the maximum element will be sum/N otherwise it is (sum/N + 1).

Below is the implementation of above approach.

C++

// C++ program for the above approach.

#include <iostream>
using namespace std;

// Function to find smallest maximum number
// in an array whose sum is divisible by K.
int smallestMaximum(int N, int K)
{
    // Minimum possible sum possible
    // for an array of size N such that its
    // sum is divisible by K
    int sum = ((N + K - 1) / K) * K;

    // If sum is not divisible by N
    if (sum % N != 0)
        return (sum / N) + 1;

    // If sum is divisible by N
    else
        return sum / N;
}

// Driver code.
int main()
{
    int N = 4;
    int K = 3;

    cout << smallestMaximum(N, K) << endl;
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.util.*;

class GFG{
    

// Function to find smallest maximum number
// in an array whose sum is divisible by K.
static int smallestMaximum(int N, int K)
{
    // Minimum possible sum possible
    // for an array of size N such that its
    // sum is divisible by K
    int sum = ((N + K - 1) / K) * K;

    // If sum is not divisible by N
    if (sum % N != 0)
        return (sum / N) + 1;

    // If sum is divisible by N
    else
        return sum / N;
}

// Driver code
public static void main(String args[])
{
    int N = 4;
    int K = 3;

    System.out.println(smallestMaximum(N, K));
}
}

// This code is contributed by code_hunt.

Python3

# python program for the above approach.
# Function to find smallest maximum number
# in an array whose sum is divisible by K.
def smallestMaximum(N,K):
  
    # Minimum possible sum possible
    # for an array of size N such that its
    # sum is divisible by K
    sum = ((N + K - 1) // K) * K

    # If sum is not divisible by N
    if (sum % N != 0):
        return (sum // N) + 1

    # If sum is divisible by N
    else:
        return sum // N

# Driver code.
if __name__ == "__main__":
    N = 4
    K = 3

    print(smallestMaximum(N, K))
    
# This code is contributed by anudeep23042002.

// C# program for the above approach.
using System;
using System.Collections.Generic;

class GFG{

// Function to find smallest maximum number
// in an array whose sum is divisible by K.
static int smallestMaximum(int N, int K)
{
    // Minimum possible sum possible
    // for an array of size N such that its
    // sum is divisible by K
    int sum = ((N + K - 1) / K) * K;

    // If sum is not divisible by N
    if (sum % N != 0)
        return (sum / N) + 1;

    // If sum is divisible by N
    else
        return sum / N;
}

// Driver code.
public static void Main()
{
    int N = 4;
    int K = 3;
    Console.Write(smallestMaximum(N, K));
}
}

// This code is contributed by SURENDRA_GANGWAR.

JavaScript

<script>
        // JavaScript Program to implement
        // the above approach

        // Function to find smallest maximum number
        // in an array whose sum is divisible by K.
        function smallestMaximum(N, K) 
        {
        
            // Minimum possible sum possible
            // for an array of size N such that its
            // sum is divisible by K
            let sum = Math.floor((N + K - 1) / K) * K;

            // If sum is not divisible by N
            if (sum % N != 0)
                return Math.floor(sum / N) + 1;

            // If sum is divisible by N
            else
                return Math.floor(sum / N);
        }

        // Driver code.

        let N = 4;
        let K = 3;

        document.write(smallestMaximum(N, K));

// This code is contributed by Potta Lokesh
    </script>

Output:

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

Minimize the maximum element in constructed Array with sum divisible by K

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