# Minimum sum by choosing minimum of pairs from array

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;` `}` |

## Java

`// Java program to minimize the` `// cost of array minimization` `import` `java.util.Arrays;` `public` `class` `GFG {` `// Returns minimum possible` `// sum in array B[]` ` ` `static` `int` `minSum(` `int` `[] A, ` `int` `n) {` ` ` `int` `min_val = Arrays.stream(A).min().getAsInt();` ` ` `return` `(min_val * (n - ` `1` `));` ` ` `}` ` ` `// Driver Code` ` ` `static` `public` `void` `main(String[] args) {` ` ` `int` `[] A = {` `3` `, ` `6` `, ` `2` `, ` `8` `, ` `7` `, ` `5` `};` ` ` `int` `n = A.length;` ` ` `System.out.println((minSum(A, n)));` ` ` `}` `}` `// This code is contributed by Rajput-Ji` |

## 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))` |

## C#

`// C# program to minimize the` `// cost of array minimization` `using` `System;` `using` `System.Linq;` `public` `class` `GFG` `{` `// Returns minimum possible` `// sum in array B[]` `static` `int` `minSum(` `int` `[]A, ` `int` `n)` `{` ` ` `int` `min_val = A.Min();` ` ` `return` `(min_val * (n - 1));` `}` ` ` ` ` `// Driver Code` ` ` `static` `public` `void` `Main()` ` ` `{` ` ` `int` `[]A = {3, 6, 2, 8, 7, 5};` ` ` `int` `n = A.Length;` ` ` `Console.WriteLine(minSum(A, n));` ` ` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to minimize the` `// cost of array minimization` `// Returns minimum possible` `// sum in array B[]` `function` `minSum(` `$A` `, ` `$n` `)` `{` ` ` `$min_val` `= min(` `$A` `);` ` ` `return` `(` `$min_val` `* (` `$n` `- 1));` `}` ` ` `// Driver Code` ` ` `$A` `= ` `array` `(3, 6, 2, 8, 7, 5);` ` ` `$n` `= ` `count` `(` `$A` `);` ` ` `echo` `minSum(` `$A` `, ` `$n` `);` `// This code is contributed by vt_m.` `?>` |

## Javascript

`<script>` `// JavaScript program to minimize the cost` `// of array minimization` `// Returns minimum possible sum in` `// array B[]` `function` `minSum(A, n)` `{` ` ` `let min_val = Math.min(...A);` ` ` `return` `(min_val * (n-1));` `}` `// driver function` ` ` ` ` `let A = [3, 6, 2, 8, 7, 5];` ` ` `let n = A.length;` ` ` `document.write(minSum(A, n));` ` ` `// This code is contributed by Mayank Tyagi` ` ` `</script>` |

**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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