How do you solve Maximum Weighted K-Edge Path on LeetCode?

Maximum Weighted K-Edge Path (LeetCode #3543) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * k) time complexity and O(n * k) space complexity. Key insight: Dynamic programming can efficiently track multiple states.

What is the brute force solution for Maximum Weighted K-Edge Path?

The brute force approach for Maximum Weighted K-Edge Path is Brute Force, with O(n²) time complexity and O(1) space complexity. Explore all possible paths in the graph that contain exactly k edges. Calculate the sum of weights for each path and check if it meets the criteria. The optimal Optimal Solution approach improves this to O(n * k).

What algorithm or data structure is used to solve Maximum Weighted K-Edge Path?

Maximum Weighted K-Edge Path uses the following concepts: Hash Table, Dynamic Programming, Graph Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Weighted K-Edge Path?

Explain your thought process clearly. Discuss edge cases and how you handle them. Practice similar problems to build intuition.

What are common mistakes when solving Maximum Weighted K-Edge Path?

Not considering paths that exceed the weight limit. Failing to initialize DP states properly.

#3543

Maximum Weighted K-Edge Path

Medium

Hash TableDynamic ProgrammingGraph TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * k)
Space	O(1)	O(n * k)

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Intuition

Time O(n * k)Space O(n * k)

Utilize dynamic programming to keep track of the maximum weight sums for paths of different lengths ending at each node, updating iteratively.

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Algorithm

3 steps

1Step 1: Create a DP table where dp[i][j] represents the maximum weight sum using exactly i edges ending at node j.
2Step 2: Initialize dp[0][node] = 0 for all nodes and iterate through edges to update the DP table.
3Step 3: After processing, find the maximum value in dp[k][j] that is less than t.

solution.py7 lines

1def maxWeightedKEdgePath(n, edges, k, t):
2    dp = [[-1] * n for _ in range(k + 1)]
3    for u, v, w in edges:
4        for i in range(k, 0, -1):
5            if dp[i - 1][u] != -1:
6                dp[i][v] = max(dp[i][v], dp[i - 1][u] + w)
7    return max((dp[k][j] for j in range(n) if dp[k][j] < t), default=-1)

ℹ

Complexity note: This complexity arises from iterating through edges and updating the DP table for k edges, leading to a linear relationship with respect to edges and path length.

1Dynamic programming can efficiently track multiple states.
2DAG properties allow for topological sorting and optimized pathfinding.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.