#2642

Design Graph With Shortest Path Calculator

hard · 64.9% accepted · 875 likes · top 69%

graph theory · design · heap (priority queue) · shortest path

Description

There is a directed weighted graph that consists of n nodes numbered from 0 to n - 1. The edges of the graph are initially represented by the given array edges where edges[i] = [fromi, toi, edgeCosti] meaning that there is an edge from fromi to toi with the cost edgeCosti.

Implement the Graph class:

- Graph(int n, int[][] edges) initializes the object with n nodes and the given edges.

- addEdge(int[] edge) adds an edge to the list of edges where edge = [from, to, edgeCost]. It is guaranteed that there is no edge between the two nodes before adding this one.

- int shortestPath(int node1, int node2) returns the minimum cost of a path from node1 to node2. If no path exists, return -1. The cost of a path is the sum of the costs of the edges in the path.

Example 1:

Input

["Graph", "shortestPath", "shortestPath", "addEdge", "shortestPath"]

[[4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]], [3, 2], [0, 3], [[1, 3, 4]], [0, 3]]

Output

[null, 6, -1, null, 6]

Example 2:

Explanation

Graph g = new Graph(4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]);

g.shortestPath(3, 2); // return 6. The shortest path from 3 to 2 in the first diagram above is 3 -> 0 -> 1 -> 2 with a total cost of 3 + 2 + 1 = 6.

g.shortestPath(0, 3); // return -1. There is no path from 0 to 3.

g.addEdge([1, 3, 4]); // We add an edge from node 1 to node 3, and we get the second diagram above.

g.shortestPath(0, 3); // return 6. The shortest path from 0 to 3 now is 0 -> 1 -> 3 with a total cost of 2 + 4 = 6.

Solution