LC 91 Decode Ways counts the number of ways to decode a digit string as letters A-Z. The recurrence combines one-digit and two-digit transitions — a conditional Fibonacci DP. Heavily tested at Amazon, Google, and Meta because it combines string parsing, edge case handling, and DP reasoning in a single problem.
LC 139 Word Break checks if a string can be segmented into dictionary words. The reachability DP dp[i] = true if some dp[j] is true and s[j:i] is in the dictionary. Asked heavily at Amazon, Google, and Microsoft as a test of string DP with set-based lookups.
LC 300 Longest Increasing Subsequence finds the length of the longest strictly increasing subsequence. The O(n²) DP is the expected starting point; the O(n log n) patience sorting binary search optimization is what FAANG interviewers look for. This problem is asked at Amazon, Google, and Microsoft and is the foundation for Russian Doll Envelopes.
LeetCode 354 Russian Doll Envelopes is a sneaky 2D Longest Increasing Subsequence problem. Sort by width ascending and height descending so equal widths cannot stack, then run patience-sort LIS on heights for an O(n log n) DP solution beloved by FAANG interviewers.
LeetCode 647 Palindromic Substrings is the canonical center-expansion problem. We derive the 2D DP recurrence, simplify it to expand-around-center for O(1) memory, and walk through a full DP table dry run with FAANG interview tips on why this beats Manacher in real interviews.