# Minimum cost to connect weighted nodes represented as array

Given an array of N elements(nodes), where every element is weight of that node.Connecting two nodes will take a cost of product of their weights.You have to connect every node with every other node(directly or indirectly).Output the minimum cost required.**Examples:**

Input : a[] = {6, 2, 1, 5} Output : 13 Explanation : Here, we connect the nodes as follows: connect a[0] and a[2], cost = 6*1 = 6, connect a[2] and a[1], cost = 1*2 = 2, connect a[2] and a[3], cost = 1*5 = 5. every node is reachable from every other node: Total cost = 6+2+5 = 13. Input : a[] = {5, 10} Output : 50 Explanation : connections: connect a[0] and a[1], cost = 5*10 = 50, Minimum cost = 50.

We need to make some observations that we have to make a connected graph with N-1 edges. As the output will be sum of products of two numbers, we have to minimize the product of every term in that sum equation. How can we do it? Clearly, choose the minimum element in the array and connect it with every other. In this way we can reach every other node from a particular node.

Let, minimum element = a[i], (let it’s index be 0) **Minimum Cost**

So, answer is *product of minimum element and sum of all the elements except minimum element. *

## C++

`// cpp code for Minimum Cost Required to connect weighted nodes` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `minimum_cost(` `int` `a[], ` `int` `n)` `{` ` ` `int` `mn = INT_MAX;` ` ` `int` `sum = 0;` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `// To find the minimum element` ` ` `mn = min(a[i], mn);` ` ` `// sum of all the elements` ` ` `sum += a[i];` ` ` `}` ` ` `return` `mn * (sum - mn);` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a[] = { 4, 3, 2, 5 };` ` ` `int` `n = ` `sizeof` `(a) / ` `sizeof` `(a[0]);` ` ` `cout << minimum_cost(a, n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java code for Minimum Cost Required to` `// connect weighted nodes` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `static` `int` `minimum_cost(` `int` `a[], ` `int` `n)` ` ` `{` ` ` ` ` `int` `mn = Integer.MAX_VALUE;` ` ` `int` `sum = ` `0` `;` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) {` ` ` `// To find the minimum element` ` ` `mn = Math.min(a[i], mn);` ` ` `// sum of all the elements` ` ` `sum += a[i];` ` ` `}` ` ` `return` `mn * (sum - mn);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `a[] = { ` `4` `, ` `3` `, ` `2` `, ` `5` `};` ` ` `int` `n = a.length;` ` ` ` ` `System.out.println(minimum_cost(a, n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## Python 3

`# Python 3 code for Minimum Cost` `# Required to connect weighted nodes` `import` `sys` `def` `minimum_cost(a, n):` ` ` `mn ` `=` `sys.maxsize` ` ` `sum` `=` `0` ` ` `for` `i ` `in` `range` `(n):` ` ` `# To find the minimum element` ` ` `mn ` `=` `min` `(a[i], mn)` ` ` `# sum of all the elements` ` ` `sum` `+` `=` `a[i]` ` ` `return` `mn ` `*` `(` `sum` `-` `mn)` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` ` ` `a ` `=` `[ ` `4` `, ` `3` `, ` `2` `, ` `5` `]` ` ` `n ` `=` `len` `(a)` ` ` `print` `(minimum_cost(a, n))` `# This code is contributed` `# by ChitraNayal` |

## C#

`// C# code for Minimum Cost Required` `// to connect weighted nodes` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to calculate minimum cost` ` ` `static` `int` `minimum_cost(` `int` `[]a, ` `int` `n)` ` ` `{` ` ` ` ` `int` `mn = ` `int` `.MaxValue;` ` ` `int` `sum = 0;` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `{` ` ` `// To find the minimum element` ` ` `mn = Math.Min(a[i], mn);` ` ` `// sum of all the elements` ` ` `sum += a[i];` ` ` `}` ` ` `return` `mn * (sum - mn);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[]a = {4, 3, 2, 5};` ` ` `int` `n = a.Length;` ` ` ` ` `Console.WriteLine(minimum_cost(a, n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP code for Minimum Cost Required` `// to connect weighted nodes` `function` `minimum_cost(` `$a` `, ` `$n` `)` `{` ` ` `$mn` `= PHP_INT_MAX;` ` ` `$sum` `= 0;` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `{` ` ` `// To find the minimum element` ` ` `$mn` `= min(` `$a` `[` `$i` `], ` `$mn` `);` ` ` `// sum of all the elements` ` ` `$sum` `+= ` `$a` `[` `$i` `];` ` ` `}` ` ` `return` `$mn` `* (` `$sum` `- ` `$mn` `);` `}` `// Driver code` `$a` `= ` `array` `( 4, 3, 2, 5 );` `$n` `= sizeof(` `$a` `);` `echo` `minimum_cost(` `$a` `, ` `$n` `), ` `"\n"` `;` `// This code is contributed` `// by Kiit_Tush` `?>` |

## Javascript

`<script>` ` ` `// Javascript code for Minimum Cost Required` ` ` `// to connect weighted nodes` ` ` ` ` `// Function to calculate minimum cost` ` ` `function` `minimum_cost(a, n)` ` ` `{` ` ` ` ` `let mn = Number.MAX_VALUE;` ` ` `let sum = 0;` ` ` ` ` `for` `(let i = 0; i < n; i++)` ` ` `{` ` ` ` ` `// To find the minimum element` ` ` `mn = Math.min(a[i], mn);` ` ` ` ` `// sum of all the elements` ` ` `sum += a[i];` ` ` `}` ` ` ` ` `return` `mn * (sum - mn);` ` ` `}` ` ` ` ` `let a = [4, 3, 2, 5];` ` ` `let n = a.length;` ` ` `document.write(minimum_cost(a, n));` ` ` `</script>` |

**Output:**

24

**Time complexity:** O(n).

This article is contributed by **Harsha Mogali**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.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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