mediumDynamic ProgrammingPattern: DP
Optimal Traffic Cycle Synchronization Solution
Problem Statement
Given a travel time matrix and the number of intersections, find the optimal timing cycle for each intersection to minimize the total travel time of all vehicles.
Examples
Example 1:
Input:[[0, 0], [1, 1]]
Output:[0, 0]
Explanation: The optimal timing cycle is [0, 0], where both intersections have cycle 0.
Example 2:
Input:[[10, 20], [30, 40]]
Output:[0, 0]
Explanation: The optimal timing cycle is [0, 0], where both intersections have cycle 0.
Constraints
- The travel time matrix is a square matrix of size n x n.
- The input matrix contains non-negative integers.
- The number of intersections is at least 2.
Time: O(n^3) Space: O(n^2)
Use dynamic programming and memoization to optimize the solution.
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