#0065

Network Delay Time

HardDSA35 min25 XP

Problem

Given directed weighted edges times = [u, v, w], number of nodes n labeled 1..n, and start node k, return the time for all nodes to receive the signal. Return -1 if any node is unreachable.

Why This Matters

Shortest path is the foundation for routing, dependency costs, latency reasoning, and many graph interviews.

Function Signature

def network_delay_time(times, n, k):

Examples

Example 1

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

Output2

Node 4 receives the signal after 2 time units through 2 -> 3 -> 4.

Constraints

Edge weights are non-negative.
Nodes are labeled from 1 to n.
Return -1 if any node is unreachable.

CodePython

def network_delay_time(times, n, k):
    """
    Input example: times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
    Return: 2
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return -1

def network_delay_time(times, n, k):
    """
    Input example: times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
    Return: 2
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return -1

Visible browser tests run here when available.

Testcases1 visible / 3 hidden categories

Reach all nodes

Input[[2,1,1],[2,3,1],[3,4,1]], 4, 2

Expected2

The slowest shortest path from 2 takes two units.

Hidden Test Categories

Unreachable nodeMultiple paths to same nodeSingle-node graph