Grasshopper Problem

Given a directed graph, two specified nodes, and the complete list of edges, determine whether you can travel from the start node to the end node following the directed edges.

You are provided with:

• n – the total number of nodes (labeled from 0 to n-1).
• m – the number of directed edges.
• The edges themselves, each given as a pair u v meaning a directed edge from node u to node v.
• A start node s and an end node t.

Return true if a directed path exists from s to t; otherwise return false.

Example

Input:
n = 5
m = 5
edges:
0 1
0 2
1 3
2 3
3 4
s = 0
t = 4

Output:
true

Explanation: We can follow edges 0 → 2 → 3 → 4 (or 0 → 1 → 3 → 4), so a path from 0 to 4 exists.

Constraints

• $1 \le n \le 10^{5}$
• $0 \le m \le 2 \times 10^{5}$
• All nodes are integers in the range [0, n-1].
• The edges may form cycles, and multiple edges between the same ordered pair are allowed.

Function Signature

Solve the problem with the following method:

def has_path(n: int, edges: list[list[int]], s: int, t: int) -> bool:
    pass

Your implementation should aim for time efficient enough to handle the upper bounds.