Network Delay Time — LeetCode 743 Python Solution

The problem

You are given a network of n nodes, labeled from 1 to n. You are also given times, a list of travel times as directed edges times[i] = (ui, vi, wi), where ui is the source node, vi is the target node, and wi is the time it takes for a signal to travel from source to target.

Example

Input

times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2

Output

2

Python solution

class Solution:
    def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int:
        g = [[inf] * n for _ in range(n)]
        for u, v, w in times:
            g[u - 1][v - 1] = w
        dist = [inf] * n
        dist[k - 1] = 0
        vis = [False] * n
        for _ in range(n):
            t = -1
            for j in range(n):
                if not vis[j] and (t == -1 or dist[t] > dist[j]):
                    t = j
            vis[t] = True
            for j in range(n):
                dist[j] = min(dist[j], dist[t] + g[t][j])
        ans = max(dist)
        return -1 if ans == inf else ans

Complexity

Pattern: Heap / Priority Queue

Keep only the best k elements, or always pull the smallest, in log time. LeetCode 743. Network Delay Time is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Heap (Priority Queue).

The heap / priority queue guide has the Python template for the pattern and the 163 LeetCode problems that use it.

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