Leetcode #743: Network Delay Time
In this guide, we solve Leetcode #743 Network Delay Time in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Depth-First Search, Breadth-First Search, Graph, Shortest Path, Heap (Priority Queue)
Intuition
We need to repeatedly access the smallest or largest element as the input changes.
A heap provides fast insertions and removals while keeping order.
Approach
Push candidates into the heap as you scan, and pop when you need the best element.
Keep the heap size bounded if the problem requires a top-k structure.
Steps:
- Push candidates into a heap.
- Pop the best candidate when needed.
- Maintain heap size or invariants.
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
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.