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2467. Most Profitable Path in a Tree
- The article discusses the problem of finding the most profitable path in a tree for Alice while considering Bob's movement in the game scenario.
- Alice and Bob traverse an undirected tree with gates at each node, with different costs and rewards associated with opening the gates.
- The goal is to maximize Alice's net income by reaching the optimal leaf node while Bob moves towards node 0.
- The solution involves constructing the tree, tracking parents, determining Bob's path and timing, and using DFS to calculate the maximum profit for Alice.
- Parent pointers are used to backtrack Bob's path from his starting node to the root, recording the time he arrives at each node.
- By comparing Alice's arrival time with Bob's along the path, her net income at each node is determined, leading to the maximum income overall.
- Efficient tree traversal methods like BFS and DFS are employed to handle the calculations and comparisons effectively.
- The solution ensures correctness and performance even for large trees, providing an optimal path for Alice to maximize her net income.
- The implementation of the solution in PHP is provided for reference, showcasing the steps involved in solving the problem.
- Overall, the approach offers a systematic way to solve the profitability problem in the tree traversal game scenario, catering to various edge cases.
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