Find Earliest Fully Connected Time

Problem Statement

You are given n computers labeled from 0 to n-1. Initially, no computers are connected. You are provided with a list of edges, where edges[i] = [u, v, t] represents a network cable being connected between computers u and v at time t.

All time values t are unique. A network is considered "fully connected" if there is a path between every pair of computers. Your task is to find the earliest time t at which the network becomes fully connected. If the network never becomes fully connected, return -1.

Function Signature

def earliest_fully_connected_time(n: int, edges: list[list[int]]) -> int:

Constraints

• 2 <= n <= 10^5
• 1 <= len(edges) <= 10^5
• 0 <= u, v < n
• Time values are positive integers.

Examples

Example 1: Input: n = 4, edges = [[0, 1, 10], [1, 2, 15], [2, 3, 20]] Output: 20 Explanation: At t=10, {0, 1} are connected. At t=15, {0, 1, 2} are connected. At t=20, all four nodes are in a single component.

Example 2: Input: n = 3, edges = [[0, 1, 5], [0, 2, 10]] Output: 10

Edge Cases:

• n is large with very few edges (should return -1).
• Disconnected components that never merge.
• Multiple edges between the same nodes.