Make n using 1s and 2s with minimum number of terms multiple of k

Given two positive integer n and k. n can be represented as the sum of 1s and 2s in many ways, using multiple numbers of terms. The task is to find the minimum number of terms of 1s and 2s use to make the sum n and also number of terms must be multiple of k. Print “-1”, if no such number of terms exists.

Examples:

Input : n = 10, k = 2
Output : 6
10 can be represented as 2 + 2 + 2 + 2 + 1 + 1.
Number of terms used are 6 which is multiple of 2.

Input : n = 11, k = 4
Output : 8
10 can be represented as 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1
Number of terms used are 8 which is multiple of 4.

Observe, the maximum number of terms used to represent n as the sum of 1s and 2s is n, when 1 are added n number of times. Also, the minimum number of terms will be n/2 times of 2s and n%2 times 1s are added. So, iterate from minimum number of terms to maximum number of terms and check if there is any multiple of k.

// C++ program to find minimum multiple of k
// terms used to make sum n using 1s and 2s.
#include<bits/stdc++.h>
using namespace std;

// Return minimum multiple of k terms used to
// make sum n using 1s and 2s.
int minMultipleK(int n, int k)
{
    // Minimum number of terms required to make
    // sum n using 1s and 2s.
    int min = (n / 2) + (n % 2);

    // Iterate from Minimum to maximum to find
    // multiple of k. Maximum number of terns is
    // n (Sum of all 1s)
    for (int i = min; i <= n; i++)
        if (i % k == 0)
            return i;

    return -1;
}

// Driven Program
int main()
{
    int n = 10, k = 2;
    cout << minMultipleK(n, k) << endl;
    return 0;
}

Output:

6

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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