PROBLEM OF THE DAY : 11/09/2024 | Minimum Cost of Ropes

Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Heap but also build up problem-solving skills.

Given an array arr containing the lengths of the different ropes, we need to connect these ropes to form one rope. The cost to connect two ropes is equal to sum of their lengths. The task is to connect the ropes with minimum cost.  

Examples:

Input: arr[] = [4, 3, 2, 6] Output: 29 Explanation: We can connect the ropes in following ways. 1) First connect ropes of lengths 2 and 3. Which makes the array [4, 5, 6]. Cost of this operation 2 + 3 = 5. 2) Now connect ropes of lengths 4 and 5. Which makes the array [9, 6]. Cost of this operation 4 + 5 = 9. 3) Finally connect the two ropes and all ropes have connected. Cost of this operation 9 + 6 =15 Total cost for connecting all ropes is 5 + 9 + 15 = 29. This is the optimized cost for connecting ropes. Other ways of connecting ropes would always have same or more cost. For example, if we connect 4 and 6 first (we get three rope of 3, 2 and 10), then connect 10 and 3 (we gettwo rope of 13 and 2). Finally we connect 13 and 2. Total cost in this way is 10 + 13 + 15 = 38.

Give the problem a try before going through the video. All the best!!!
Problem Link: https://practice.geeksforgeeks.org/problems/minimum-cost-of-ropes-1587115620/1