# Minimize sum of smallest elements from K subsequences of length L

• Last Updated : 12 May, 2021

Given an array arr[] of size N, the task is to find the minimum possible sum by extracting the smallest element from any K subsequences from arr[] of length L such that each of the subsequences have no shared element. If it is not possible to get the required sum, print -1.

Examples:

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Input: arr[] = {2, 15, 5, 1, 35, 16, 67, 10}, K = 3, L = 2
Output:
Explanation:
Three subsequences of length 2 can be {1, 35}, {2, 15}, {5, 16}
Minimum element of {1, 35} is 1.
Minimum element of {2, 15} is 2.
Minimum element of {5, 16} is 5.
Their Sum is equal to 8 which is the minimum possible.

Input: arr[] = {19, 11, 21, 16, 22, 18, 14, 12}, K = 3, L = 3
Output: -1
Explanation:
It is not possible to construct 3 subsequences of length 3 from arr[].

Approach:
To optimize the above approach, we need to observe the following details:

• The K smallest elements of the array contribute to finding the minimum sum of the smallest elements of K subsequences.
• The length of the array must be greater than or equal to (K * L) in order to form K subsequences of length L.

Follow the steps below to solve the problem:

• Check if the size of the array arr[] is greater than equal to (K * L).
• If so, sort the array arr[] and print the sum of the first K elements of the array after sorting.
• Otherwise, return -1.

Below is the implementation of the above approach:

## C++

 `// C++ Program to find the minimum``// possible sum of the smallest``// elements from K subsequences` `#include ``using` `namespace` `std;` `// Function to find the minimum sum``int` `findMinSum(``int` `arr[], ``int` `K,``               ``int` `L, ``int` `size)``{` `    ``if` `(K * L > size)``        ``return` `-1;` `    ``int` `minsum = 0;` `    ``// Sort the array``    ``sort(arr, arr + size);` `    ``// Calculate sum of smallest``    ``// K elements``    ``for` `(``int` `i = 0; i < K; i++)``        ``minsum += arr[i];` `    ``// Return the sum``    ``return` `minsum;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 2, 15, 5, 1,``                  ``35, 16, 67, 10 };``    ``int` `K = 3;``    ``int` `L = 2;` `    ``int` `length = ``sizeof``(arr)``                ``/ ``sizeof``(arr);` `    ``cout << findMinSum(arr, K,``                       ``L, length);` `    ``return` `0;``}`

## Java

 `// Java program to find the minimum``// possible sum of the smallest``// elements from K subsequences``import` `java.util.Arrays;` `class` `GFG{` `// Function to find the minimum sum``static` `int` `findMinSum(``int` `[]arr, ``int` `K,``                      ``int` `L, ``int` `size)``{``    ``if` `(K * L > size)``        ``return` `-``1``;` `    ``int` `minsum = ``0``;` `    ``// Sort the array``    ``Arrays.sort(arr);` `    ``// Calculate sum of smallest``    ``// K elements``    ``for``(``int` `i = ``0``; i < K; i++)``        ``minsum += arr[i];` `    ``// Return the sum``    ``return` `minsum;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `arr[] = { ``2``, ``15``, ``5``, ``1``,``                  ``35``, ``16``, ``67``, ``10` `};``    ``int` `K = ``3``;``    ``int` `L = ``2``;``    ``int` `length = arr.length;` `    ``System.out.print(findMinSum(arr, K,``                                ``L, length));``}``}` `// This code is contributed by Ritik Bansal`

## Python3

 `# Python3 program to find the minimum``# possible sum of the smallest``# elements from K subsequences` `# Function to find the minimum sum`  `def` `findMinSum(arr, K, L, size):` `    ``if` `(K ``*` `L > size):``        ``return` `-``1` `    ``minsum ``=` `0` `    ``# Sort the array``    ``arr.sort()` `    ``# Calculate sum of smallest``    ``# K elements``    ``for` `i ``in` `range``(K):``        ``minsum ``+``=` `arr[i]` `    ``# Return the sum``    ``return` `minsum`  `# Driver code``if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``2``, ``15``, ``5``, ``1``,``           ``35``, ``16``, ``67``, ``10``]``    ``K ``=` `3``    ``L ``=` `2` `    ``length ``=` `len``(arr)` `    ``print``(findMinSum(arr, K, L, length))` `# This code is contributed by Shivam Singh`

## C#

 `// C# program to find the minimum``// possible sum of the smallest``// elements from K subsequences``using` `System;``  ` `class` `GFG{``  ` `// Function to find the minimum sum``static` `int` `findMinSum(``int` `[]arr, ``int` `K,``                      ``int` `L, ``int` `size)``{``    ``if` `(K * L > size)``        ``return` `-1;``  ` `    ``int` `minsum = 0;``  ` `    ``// Sort the array``    ``Array.Sort(arr); ``  ` `    ``// Calculate sum of smallest``    ``// K elements``    ``for``(``int` `i = 0; i < K; i++)``        ``minsum += arr[i];``  ` `    ``// Return the sum``    ``return` `minsum;``}``  ` `// Driver Code``public` `static` `void` `Main() ``{``    ``int``[] arr = { 2, 15, 5, 1,``                  ``35, 16, 67, 10 };``    ``int` `K = 3;``    ``int` `L = 2;``    ``int` `length = arr.Length;``  ` `    ``Console.Write(findMinSum(arr, K,``                             ``L, length));``}``}` `// This code is contributed by code_hunt`

## Javascript

 ``
Output
`8`

Time Complexity: O(N * log(N))
Space Complexity: O(1)

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