LC 127 Word Ladder asks for the shortest sequence of one-letter transformations from beginWord to endWord, where every intermediate word must be in the dictionary. BFS on the implicit word-state graph finds the minimum in O(M^2 * N) using wildcard pattern grouping.
LeetCode 126 Word Ladder II asks for every shortest transformation path between two words. Master the layered BFS plus parent-map DFS pattern that survives the brutal time limits at Amazon, Google, and Facebook interviews.
LeetCode 815 Bus Routes is deceptively hard. The trick is that BFS levels count buses, not stops, so the graph you traverse is a route graph. Master the stop-to-routes inversion that beats the time limit at FAANG interviews.
LeetCode 886 Possible Bipartition reduces a real-world group split to a bipartite check. Master the BFS 2-coloring, DFS coloring, and Union Find variants that recruiters expect at FAANG.
LeetCode 785 Is Graph Bipartite asks whether you can 2-color a graph. Master the BFS and DFS coloring patterns, the disconnected-component handling, and the FAANG interview script that proves you understand bipartite theory.