3543 - Maximum Weighted K-Edge Path.

Medium

You are given an integer n and a Directed Acyclic Graph (DAG) with n nodes labeled from 0 to n - 1. This is represented by a 2D array edges, where <code>edgesi = u_i, v_i, w_i</code> indicates a directed edge from node <code>u_i</code> to <code>v_i</code> with weight <code>w_i</code>.

You are also given two integers, k and t.

Your task is to determine the maximum possible sum of edge weights for any path in the graph such that:

• The path contains exactly k edges.

• The total sum of edge weights in the path is strictly less than t.

Return the maximum possible sum of weights for such a path. If no such path exists, return -1.

Example 1:

Input: n = 3, edges = [0,1,1,1,2,2], k = 2, t = 4

Output: 3

Explanation:

• The only path with k = 2 edges is 0 -> 1 -> 2 with weight 1 + 2 = 3 < t.

• Thus, the maximum possible sum of weights less than t is 3.

Example 2:

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

Output: 2

Explanation:

• There are two paths with k = 1 edge:

• Thus, the maximum possible sum of weights less than t is 2.

Example 3:

Input: n = 3, edges = [0,1,6,1,2,8], k = 1, t = 6

Output: \-1

Explanation:

• There are two paths with k = 1 edge:

• Since there is no path with sum of weights strictly less than t, the answer is -1.

Constraints:

• 1 <= n <= 300

• 0 <= edges.length <= 300

• <code>edgesi = u_i, v_i, w_i</code>

• <code>0 <= u_i, v_i< n</code>

• <code>u_i != v_i</code>

• <code>1 <= w_i<= 10</code>

• 0 <= k <= 300

• 1 <= t <= 600

• The input graph is guaranteed to be a DAG.

• There are no duplicate edges.