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

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:

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 `

Output

```8
```

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

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Improved By : SHIVAMSINGH67, btc_148