Problem: Optimal Network Topology for Latency ReductionYou are given a network of N computers, each connected by bidirectional cables. Each cable has an associated latency. Your task is to design an algorithm that reconfigures the network's topology such that the maximum latency between any two computers is minimized. However, you must do so under the following constraints:You cannot add new cables; you can only reconfigure existing ones.The network must remain fully connected $($i$.$e$.,$ every computer must be reachable from every other computer$).$The reconfiguration should minimize the overall cost, defined as the sum of the differences between the original and new latencies of each cable.Input:A list of computers $($as nodes$).$A list of cables connecting the computers $($as edges$),$ each with an associated latency $($as edge weights$).$Output:A new configuration of the network that meets the criteria.Example:Input: A network of $5$ computers connected by a set of cables with varying latencies.Output: A reconfiguration of the network that minimizes the maximum latency between any two computers and the overall cost.Challenge:Develop the algorithm to solve this problem.Prove that your algorithm can always find the optimal solution.Analyze the time and space complexity of your solution.This problem touches on areas like graph theory, optimization, and network design. It's challenging because it requires not only a deep understanding of algorithms and data structures but also an innovative approach to optimizing network topology under multiple constraints.