Compute minimax grid path and network delay

## Problem (two related shortest-path tasks) ### Part 1 — Minimize the maximum value along a grid path ("minimax" path) You are given an `m x n` integer grid `H`, where `H[r][c]` is the “difficulty/height” of cell `(r,c)`. - Start at `(0,0)` and want to reach `(m-1, n-1)`. - You may move **up/down/left/right** to adjacent cells (no diagonals). - The **cost of a path** is **not the sum** of values; instead it is: > the maximum `H[r][c]` value encountered on that path (including start and end). **Return** the minimum possible path cost (i.e., minimize the maximum cell value you ever step on). **Assumptions/constraints (typical interview constraints):** - `1 <= m,n <= 200` - `0 <= H[r][c] <= 10^9` ### Part 2 (follow-up) — Time for a signal to reach all nodes in a weighted graph You are given a weighted graph with `n` nodes labeled `1..n` and a list of directed edges `edges`, where each edge is `(u, v, w)` meaning it takes time `w > 0` to travel from `u` to `v`. A signal starts at node `k` at time `0` and travels along edges. - Let `dist[i]` be the shortest time for the signal to reach node `i`. - **Return**: - `max(dist[i])` over all nodes `i` if every node is reachable, or - `-1` if some node is unreachable. **Assumptions/constraints (typical interview constraints):** - `1 <= n <= 10^5` (or smaller in an interview) - `1 <= |edges| <= 2*10^5` - `1 <= w <= 10^9` ## Edge cases to consider - Start equals end (Part 1: `m=n=1`; Part 2: `n=1`). - Unreachable nodes (Part 2). - Multiple edges between the same nodes (Part 2). - Repeated states pushed into a heap/priority queue (both parts).