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
![=a[i]*a[1]+a[i]*a[2]+....+a[i]*a[n-1],](https://web.archive.org/web/20201124231823im_/https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-59a35df5d43aa699b814ec38706116d4_l3.png "Rendered by QuickLaTeX.com")
=
![a[i]*(a[1]+a[2]+....+a[n-1]);](https://web.archive.org/web/20201124231823im_/https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-88574eeefca737e5ebf627fd3084f7a8_l3.png "Rendered by QuickLaTeX.com")
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 ?> |
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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
Recommended Posts:
- Minimum Cost of Simple Path between two nodes in a Directed and Weighted Graph
- Minimum cost required to connect all houses in a city
- Minimum cost to connect all cities
- Minimum difference between any two weighted nodes in Sum Tree of the given Tree
- Minimum cost to empty Array where cost of removing an element is 2^(removed_count) * arr[i]
- Count the nodes of the given tree whose weighted string is a palindrome
- Count the nodes of a tree whose weighted string does not contain any duplicate characters
- Count the nodes of a tree whose weighted string is an anagram of the given string
- Minimum Cost using Dijkstra by reducing cost of an Edge
- Find the root of the sub-tree whose weighted sum is minimum
- Find the root of the sub-tree whose weighted sum XOR with X is minimum
- Check if all nodes of the Binary Tree can be represented as sum of two primes
- Minimum cost to reverse edges such that there is path between every pair of nodes
- Minimum Cost Path in a directed graph via given set of intermediate nodes
- Program to find weighted median of a given array
- Count array elements that can be represented as sum of at least two consecutive array elements
- Shortest path with exactly k edges in a directed and weighted graph
- Shortest Path in a weighted Graph where weight of an edge is 1 or 2
- Graph implementation using STL for competitive programming | Set 2 (Weighted graph)
- Program for weighted mean of natural numbers.
