Minimum sum after subtracting multiples of k from the elements of the array

Given an integer K and an integer array arr, the task is to find the minimum possible sum of all the elements of the array after they are reduced by subtracting a multiple of K from each element (the result must be positive and every element of the array must be equal after this reduction). If the array cannot be reduced then print -1. Note that an element may or may not be reduced in the final state of the array.

Examples:

Input: arr[] = {2, 3, 4, 5}, K = 1
Output: 4
Subtract 1 form 2, arr[] = {1, 3, 4, 5}
Subtract 2 from 3, arr[] = {1, 1, 4, 5}
Subtract 3 from 4, arr[] = {1, 1, 1, 5}
Subtract 4 from 5 to make arr[] = {1, 1, 1, 1}, thus giving minimum possible sum as 4.

Input: arr[] = {5, 6, 7}, K = 2
Output: -1



Approach: First, the array needs to be sorted as the problem can be solved using greedy approach.

  • Sort the array, if arr[0] < 0 then print -1 as every element needs to be ≥ 0.
  • If K == 0 then no element can be reduced further. So in order to have an answer every element of the array must be equal. So the sum of elements is n * arr[0] else print -1.
  • Now for the rest of the elements, run a loop from 1 to n and check whether ((arr[i] – arr[0]) % K) == 0 i.e. arr[i] can be reduced to arr[0].
  • If above condition fails for any element, print -1.
  • Else if k == 1 then the answer is n i.e. every element will get reduced to 1.
  • Else the answer is n * (a[0] % k).

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// function to calculate minimum sum after transformation
int min_sum(int n, int k, int a[])
{
  
    sort(a, a + n);
  
    if (a[0] < 0) 
        return -1;
      
  
    // no element can be reduced further
    if (k == 0) {
  
        // if all the elements of the array
        // are identical
        if (a[0] == a[n - 1])
            return (n * a[0]);
        else
            return -1;
    }
    else {
        int f = 0;
        for (int i = 1; i < n; i++) {
  
            int p = a[i] - a[0];
  
            // check if a[i] can be reduced to a[0]
            if (p % k == 0)
                continue;
            else {
                f = 1;
                break;
            }
        }
  
        // one of the elements cannot be reduced
        // to be equal to the other elements
        if (f)
            return -1;
        else {
  
            // if k = 1 then all elements can be reduced to 1
            if (k == 1)
                return n;
            else
                return (n * (a[0] % k));
        }
    }
}
  
// Driver code
int main()
{
    int arr[] = { 2, 3, 4, 5 };
    int K = 1;
    int N = sizeof(arr) / sizeof(arr[0]);
    cout << min_sum(N, K, arr);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program of the above approach
  
import java.io.*;
import java.util.*;
class GFG {
      
// function to calculate minimum sum after transformation
static int min_sum(int n, int k, int a[])
{
  
    Arrays.sort(a);
  
    if (a[0] < 0
        return -1;
      
  
    // no element can be reduced further
    if (k == 0) {
  
        // if all the elements of the array
        // are identical
        if (a[0] == a[n - 1])
            return (n * a[0]);
        else
            return -1;
    }
    else {
        int f = 0;
        for (int i = 1; i < n; i++) {
  
            int p = a[i] - a[0];
  
            // check if a[i] can be reduced to a[0]
            if (p % k == 0)
                continue;
            else {
                f = 1;
                break;
            }
        }
  
        // one of the elements cannot be reduced
        // to be equal to the other elements
        if (f>0)
            return -1;
        else {
  
            // if k = 1 then all elements can be reduced to 1
            if (k == 1)
                return n;
            else
                return (n * (a[0] % k));
        }
    }
}
  
// Driver code
  
  
    public static void main (String[] args) {
            int arr[] = { 2, 3, 4, 5 };
    int K = 1;
    int N = arr.length;
    System.out.println(min_sum(N, K, arr));
    }
}
// This code is contributed by shs..

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program of the above approach
using System;
  
class GFG 
{
      
// function to calculate minimum 
// sum after transformation
static int min_sum(int n, int k, int[] a)
{
  
    Array.Sort(a);
  
    if (a[0] < 0) 
        return -1;
  
    // no element can be reduced further
    if (k == 0)
    {
  
        // if all the elements of the array
        // are identical
        if (a[0] == a[n - 1])
            return (n * a[0]);
        else
            return -1;
    }
    else 
    {
        int f = 0;
        for (int i = 1; i < n; i++) 
        {
            int p = a[i] - a[0];
  
            // check if a[i] can be 
            // reduced to a[0]
            if (p % k == 0)
                continue;
            else 
            {
                f = 1;
                break;
            }
        }
  
        // one of the elements cannot be reduced
        // to be equal to the other elements
        if (f > 0)
            return -1;
        else
        {
  
            // if k = 1 then all elements can 
            // be reduced to 1
            if (k == 1)
                return n;
            else
                return (n * (a[0] % k));
        }
    }
}
  
// Driver code
public static void Main ()
{
    int[] arr = new int[] { 2, 3, 4, 5 };
    int K = 1;
    int N = arr.Length;
    Console.WriteLine(min_sum(N, K, arr));
}
}
  
// This code is contributed by mits

chevron_right


PHP

Output:

4

Time Complexity : O(n Log n)

Further Optimizations :
Instead of sorting the array, we can find minimum element in O(n) time. We can check all elements are same or not also in O(n) time.



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

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.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.