Shortest Transmission Time

You are given an undirected graph with n nodes and m edges. Each edge connects two nodes and has an associated positive weight. Your task is to determine the minimum transmission time between two specified nodes, A and B. If there is no valid path from A to B, output -1.

The problem can be mathematically formulated as follows:

Given a graph \(G=(V,E)\) with \(|V|=n\) and \(|E|=m\), and two vertices \(A, B \in V\), find the minimum value of \(\sum_{(u,v)\in P} w(u,v)\) over all paths \(P\) from \(A\) to \(B\). If no such path exists, return -1.

You are advised to use Dijkstra's algorithm to solve this problem efficiently.

inputFormat

The input is read from standard input (stdin) and has the following format:

• The first line contains four integers: n m A B, where n is the number of nodes, m is the number of edges, A is the starting node, and B is the destination node.
• The next m lines each contain three integers: u v w, representing an edge between nodes u and v with weight w.

outputFormat

Output a single integer representing the minimum transmission time (path weight) from node A to node B. If there is no path between these nodes, output -1.

4 4 1 4
1 2 1
2 3 2
3 4 1
1 3 4

4