You are given an undirected, weighted, and connected graph with n nodes labeled from $0$ to n $- 1$, and an array edges where edges[i] = [u_i, v_i, w_i] represents an edge between node u_i and node v_i with a positive weight w_i.

You are also given three integers s, d, and k, representing the starting node, the destination node, and the maximum number of hops you can make, respectively. In a single hop, you can traverse an edge and set its weight contribution to $0$.

Return the minimum total weight of a path from s to d after reducing the weight of at most k traversed edges to $0$.

Constraints:

• $2 \leq$ n $\leq 500$

• n $- 1 \leq$ edges.length $\leq \min(10^4, \frac{ {`n`} \times ( {`n`} - 1)}{2})$

• edges[i].length $= 3$

• $0 \leq$ edges[i][0], edges[i][1] $\leq$ n $- 1$

• $1 \leq$ edges[i][2] $\leq 10^6$

• $0 \leq$ s, d, k $\leq$ n $- 1$

• s $\neq$ d

• The graph is connected and contains no repeated edges or self loops.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.