LC 496 Next Greater Element I is the canonical entry point for monotonic stack thinking. Master the decreasing stack pattern and hash map lookup here, and you will recognize the same structure in Daily Temperatures, Largest Rectangle in Histogram, and Trapping Rain Water.
LC 739 Daily Temperatures is the most important medium-level monotonic stack problem. Unlike Next Greater Element, the stack stores indices so you can compute waiting distances. Every FAANG company uses this to gauge stack fluency.
LC 84 Largest Rectangle in Histogram is the canonical hard monotonic stack problem. The key insight — use an increasing stack and compute maximum rectangle area when a shorter bar causes a pop — unlocks both this problem and Maximal Rectangle.
LC 42 Trapping Rain Water is one of the most famous hard problems in FAANG interviews. The optimal two-pointer approach uses O(1) space. Knowing all three approaches and their trade-offs separates senior candidates from junior ones.
LC 316 Remove Duplicate Letters combines greedy with a monotonic stack to find the lexicographically smallest subsequence containing every character exactly once. The "pop only if the character appears again later" check using last_occurrence is the key insight.