Is Minimum Distance Excluding One Maximum Weighted Edge easy or hard?

This problem is typically classified as Medium difficulty. Standard Dijkstra knowledge is required, but the twist of excluding the maximum edge weight requires tracking additional state during traversal.

Minimum Distance Excluding One Maximum Weighted Edge Python/Java solution

Implement the modified Dijkstra algorithm using a priority queue. In Python, use heapq; in Java, use PriorityQueue with a custom comparator based on adjusted distance (sum minus maxEdge). The same logic works in C++, Go, TypeScript, and Rust.

What is the best approach for Minimum Distance Excluding One Maximum Weighted Edge?

The most efficient approach uses a modified Dijkstra algorithm. While traversing the graph, track both the total path weight and the largest edge encountered so far. The effective cost becomes totalWeight minus maxEdge. Using a priority queue keeps the complexity at O(E log V), which is optimal for weighted graphs.

Is Minimum Distance Excluding One Maximum Weighted Edge asked at Google/Amazon/Meta?

Graph shortest‑path variations like this appear frequently in interviews at companies such as Google, Amazon, and Meta. Candidates are often expected to adapt Dijkstra's algorithm to support extra constraints like discounts, skipped edges, or modified path costs.

What data structure is used in Minimum Distance Excluding One Maximum Weighted Edge?

The core data structures are an adjacency list to store the graph and a min‑heap priority queue for Dijkstra traversal. Additional variables track the running sum and the maximum edge weight on the current path.

What is the time complexity of Minimum Distance Excluding One Maximum Weighted Edge?

The optimal solution runs in O(E log V) time using a priority queue based Dijkstra traversal. Each edge relaxation pushes a state into the heap, and heap operations dominate the runtime. Space complexity is O(V) for storing distances and state information.

3778. Minimum Distance Excluding One Maximum Weighted Edge - Practice Online

Q: How to solve Minimum Distance Excluding One Maximum Weighted Edge in O(E log V)?

Run Dijkstra while tracking two values for each path: the cumulative sum of weights and the maximum edge weight seen so far. The priority queue orders states by the adjusted distance (sum minus maxEdge). When relaxing edges, update both values and push the new state if it improves the effective cost for that node.

You are given a positive integer n and a 2D integer array edges, where edges[i] = [u_i, v_i, w_i].

There is a weighted connected simple undirected graph with n nodes labeled from 0 to n - 1. Each [u_i, v_i, w_i] in edges represents an edge between node u_i and node v_i with positive weight w_i.

The cost of a path is the sum of weights of the edges in the path, excluding the edge with the maximum weight. If there are multiple edges in the path with the maximum weight, only the first such edge is excluded.

Return an integer representing the minimum cost of a path going from node 0 to node n - 1.

Example 1:

Input: n = 5, edges = [[0,1,2],[1,2,7],[2,3,7],[3,4,4]]

Output: 13

Explanation:

There is only one path going from node 0 to node 4: 0 -> 1 -> 2 -> 3 -> 4.

The edge weights on this path are 2, 7, 7, and 4.

Excluding the first edge with maximum weight, which is 1 -> 2, the cost of this path is 2 + 7 + 4 = 13.

Example 2:

Input: n = 3, edges = [[0,1,1],[1,2,1],[0,2,50000]]

Output: 0

Explanation:

There are two paths going from node 0 to node 2:

0 -> 1 -> 2

The edge weights on this path are 1 and 1.

Excluding the first edge with maximum weight, which is 0 -> 1, the cost of this path is 1.

0 -> 2

The only edge weight on this path is 1.

Excluding the first edge with maximum weight, which is 0 -> 2, the cost of this path is 0.

The minimum cost is min(1, 0) = 0.

Constraints:

2 <= n <= 5 * 10⁴
n - 1 <= edges.length <= 10⁹
edges[i] = [u_i, v_i, w_i]
0 <= u_i < v_i < n
[u_i, v_i] != [u_j, v_j]
1 <= w_i <= 5 * 10⁴
The graph is connected.