Minimum sum by choosing minimum of pairs from array

1

Given an array A[] of n-elements. We need to select two adjacent elements and delete the larger of them and store smaller of them to another array say B[]. We need to perform this operation till array A[] contains only single element. Finally, we have to construct the array B[] in such a way that total sum of its element is minimum. Print the total sum of array B[].

Examples:

Input : A[] = {3, 4} 
Output : 3

Input : A[] = {2, 4, 1, 3}
Output : 3

There is an easy trick to solve this question and that is always choose the smallest element of array A[] and its adjacent, delete the adjacent element and copy smallest one to array B[]. Again for next iteration we have same smallest element and any random adjacent element which is to be deleted. After n-1 operations all of elements of A[] got deleted except the smallest one and at the same time array B[] contains “n-1” elements and all are equal to smallest element of array A[].
Thus total sum of array B[] is equal to smallest * (n-1).

C++

// CPP program to minimize the cost
// of array minimization
#include <bits/stdc++.h>
using namespace std;

// Returns minimum possible sum in
// array B[]
int minSum(int A[], int n)
{
    int min_val = *min_element(A, A+n);
    return (min_val * (n-1));
}

// driver function
int main() 
{
    int A[] = { 3, 6, 2, 8, 7, 5};
    int n = sizeof(A)/ sizeof (A[0]);
    cout << minSum(A, n);
    return 0;
}

Python

# Python code for minimum cost of
# array minimization

# Function defintion for minCost
def minSum(A):

    # find the minimum element of A[]
    min_val = min(A);

    # return the answer
    return min_val * (len(A)-1)

# driver code
A = [7, 2, 3, 4, 5, 6] 
print (minSum(A)) 


Output:

10

Time Complexity : O(n) in finding the smallest element of the array.

This article is contributed by Shivam Pradhan (anuj_charm). 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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