Find K numbers with sum equal to N and sum of their squares maximized

Given two integers N and K, the task is to find K numbers(A₁, A₂, …, A_K) such that ?_i=1^KA_i is equal to N and ?_i=1^KA_i² is maximum.
Examples:

Input: N = 3, K = 2 
Output: 1 2 
Explanation: The two numbers are 1 and 2 as their sum is equal to N and 1² + 2² is maximum.
Input: N = 10, K = 3 
Output: 1 8 1 

Approach: The idea is to take number 1, K – 1 times and number N – K + 1 once. The sum of these numbers is equal to N and sum of squares of these numbers is always maximum. For any two non-negative numbers a and b, (a² + b²) is always less than 1 + (a + b – 1)².
Below is the implementation of the above approach:

C++

// C++ program to find K numbers
// with sum equal to N and the
// sum of their squares maximized
#include <bits/stdc++.h>
using namespace std;

// Function that prints the
// required K numbers
void printKNumbers(int N, int K)
{
    // Print 1, K-1 times
    for (int i = 0; i < K - 1; i++)
        cout << 1 << " ";

    // Print (N-K+1)
    cout << (N - K + 1);
}

// Driver Code
int main()
{
    int N = 10, K = 3;

    printKNumbers(N, K);

    return 0;
}

Java

// Java program to find K numbers
// with sum equal to N and the
// sum of their squares maximized
class GFG{

// Function that prints the
// required K numbers
static void printKNumbers(int N, int K)
{
    // Print 1, K-1 times
    for(int i = 0; i < K - 1; i++)
        System.out.print(1 + " ");

    // Print (N - K + 1)
    System.out.print(N - K + 1);
}

// Driver Code
public static void main(String[] args)
{
    int N = 10, K = 3;
    printKNumbers(N, K);
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program to find K numbers
# with a sum equal to N and the
# sum of their squares maximized

# Function that prints the
# required K numbers
def printKNumbers(N, K):

    # Print 1, K-1 times
    for i in range(K - 1):
        print(1, end = ' ')

    # Print (N-K+1)
    print(N - K + 1)

# Driver code
if __name__=='__main__':

    (N, K) = (10, 3)

    printKNumbers(N, K)

# This code is contributed by rutvik_56

C#

// C# program to find K numbers
// with sum equal to N and the
// sum of their squares maximized
using System;

class GFG{

// Function that prints the
// required K numbers
static void printKNumbers(int N, int K)
{

    // Print 1, K-1 times
    for(int i = 0; i < K - 1; i++)
        Console.Write(1 + " ");

    // Print (N - K + 1)
    Console.Write(N - K + 1);
}

// Driver code
public static void Main(String[] args)
{
    int N = 10, K = 3;

    printKNumbers(N, K);
}
}

// This code is contributed by shivanisinghss2110

Javascript

<script>

    // Javascript program to find K numbers
    // with sum equal to N and the
    // sum of their squares maximized

    // Function that prints the
    // required K numbers
    function printKNumbers(N, K)
    {
        // Print 1, K-1 times
        for (let i = 0; i < K - 1; i++)
            document.write(1 + " ");

        // Print (N-K+1)
        document.write(N - K + 1);
    }

     let N = 10, K = 3;

    printKNumbers(N, K);

</script>

Output:

1 1 8

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