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LC 337 House Robber III extends the classic House Robber DP to a binary tree where adjacent nodes cannot both be robbed. The optimal O(n) solution uses post-order DFS returning a (rob, skip) pair — a fundamental tree DP pattern tested at Amazon and Microsoft.
LC 968 Binary Tree Cameras asks for the minimum number of cameras to monitor all nodes. The O(n) greedy solution assigns three states per node in a bottom-up DFS — delay camera placement as high as possible, a pattern tested at Amazon and Google.
LC 979 Distribute Coins in Binary Tree asks for minimum moves to give each node exactly one coin. The O(n) solution tracks coin excess flowing through each edge via post-order DFS — a pattern tested at Amazon and Google that elegantly converts a counting problem into a flow problem.
LC 1483 Kth Ancestor of a Tree Node answers each query in O(log k) after O(n log n) preprocessing using binary lifting — a sparse table DP technique that also powers LCA algorithms and is commonly tested at Amazon.
LC 124 Binary Tree Maximum Path Sum finds the highest-value path in a binary tree where the path can start and end at any node. The O(n) solution uses a post-order DFS that tracks the global max while returning only one branch to the parent — a critical FAANG interview problem at Amazon, Google, and Facebook.