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Binary Tree Maximum Path Sum
This problem is a state-machine in disguise, and DP is how you keep it under control. It's a hard one for a reason: it stresses state-and-transition thinking when the rules pile up. Don't rush the code—spend your time nailing the state definition first.
Learn this pattern
Dynamic Programming Patterns
Dynamic programming caches overlapping subproblem results so each is solved only once. Define your state in one sentence, write the transition, nail the base cases, and brute-force transforms into polynomial time.
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