23 articles
The complete 1D Dynamic Programming roadmap for FAANG interviews — Fibonacci, House Robber, Kadane, Coin Change, LIS, Jump Game, Decode Ways, and Palindrome patterns with Python and JavaScript templates.
LC 70 Climbing Stairs is the canonical introduction to 1D dynamic programming. The recurrence dp[n] = dp[n-1] + dp[n-2] is pure Fibonacci, and mastering why it works — recursion to memoization to tabulation — unlocks the entire family of staircase DP problems asked at Google, Amazon, and Meta.
LC 746 Min Cost Climbing Stairs extends the Climbing Stairs Fibonacci DP with per-step costs. The recurrence dp[i] = cost[i] + min(dp[i-1], dp[i-2]) computes the minimum total cost to leave each step. Asked at Amazon and Google as a direct test of whether you can adapt a known recurrence pattern under new constraints.
LC 198 House Robber asks you to maximize stolen money without robbing adjacent houses. The recurrence dp[i] = max(dp[i-1], dp[i-2] + nums[i]) is the canonical skip-one DP pattern asked at Amazon, Google, and Microsoft. Master the derivation, the three-phase DP evolution, and the O(1) space solution.
LC 213 House Robber II extends House Robber to a circular arrangement where the first and last houses are adjacent. The elegant solution runs the linear House Robber DP twice — once excluding the first house, once excluding the last — and returns the maximum. A top FAANG interview problem that tests systematic problem decomposition.
LC 740 Delete and Earn looks like a game problem but reduces to House Robber DP after a preprocessing step. Choosing value v earns v * count(v) points and forces deletion of v-1 and v+1, exactly the skip-adjacent constraint. Asked at Amazon and Meta to test whether candidates see through surface-level descriptions to the underlying DP pattern.
LC 53 Maximum Subarray is the foundational problem behind Kadane's Algorithm — a deceptively simple O(n) DP that asks: at each position, should I extend the current subarray or start fresh? Asked at Amazon, Google, and Microsoft and the basis for Maximum Product Subarray and other contiguous-subarray problems.
LC 152 Maximum Product Subarray extends Kadane's Algorithm by tracking both the running maximum and minimum products simultaneously. A negative number flips today's minimum into tomorrow's maximum. This dual-tracking insight is tested at Amazon, Google, and LinkedIn as a harder follow-up to Maximum Subarray.
LC 322 Coin Change finds the minimum number of coins to make a target amount using unlimited coin supply. The recurrence dp[i] = min(dp[i - coin] + 1) over all coins is the canonical unbounded knapsack minimization problem, asked at Amazon, Google, and Microsoft as a core DP interview question.
LC 518 Coin Change II counts the number of combinations (not permutations) of coins that sum to a target amount. The key insight is the loop order: coins outer, amounts inner. This unbounded knapsack counting pattern is tested at Amazon and Google to distinguish candidates who understand loop-order reasoning from those who memorize templates.
LC 279 Perfect Squares finds the minimum number of perfect square integers that sum to n. It is isomorphic to Coin Change (LC 322) where the "coins" are all perfect squares up to n. The DP recurrence dp[i] = min(dp[i - j*j] + 1) runs in O(n * sqrt(n)) time and is asked at Google and Amazon.
LC 55 Jump Game asks if you can reach the last index given maximum jump lengths. The DP approach is O(n^2) but the greedy insight — tracking the farthest reachable index — reduces it to O(n) O(1). Asked at Amazon and Google as a test of recognizing when greedy is provably optimal over DP.
LC 45 Jump Game II finds the minimum number of jumps to reach the last index. The DP solution is O(n^2), but the greedy window technique — extending the current reachable window whenever a boundary is crossed — achieves O(n) O(1). Asked at Amazon and Google as a harder follow-up to Jump Game.
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.
LeetCode 516 Longest Palindromic Subsequence is the cleanest interval DP recurrence in interview prep. We derive the dp[i][j] formulation, fill the table along diagonals, and reduce memory from O(n^2) to O(n) — exactly the depth Amazon and Google look for.
LeetCode 416 Partition Equal Subset Sum is the cleanest 0/1 knapsack disguise on the platform. We reduce it to subset-sum-equals-half, derive the boolean DP recurrence, walk through the reverse-iteration trick, and finish with a one-liner bitset version that crushes interviews.
LeetCode 494 Target Sum looks like sign-assignment but reduces to subset-sum count via a beautiful algebra trick. We derive the reduction, build the 1D DP, dry-run a tabulation, and discuss why this O(n * sum) solution beats 2^n brute force at FAANG.
LeetCode 1143 Longest Common Subsequence is the foundational two-string DP every FAANG interviewer expects you to nail. We derive the dp[i][j] recurrence, walk a full table, optimize space from O(m*n) to O(min(m,n)), and trace why this template powers Edit Distance, Shortest Common Supersequence, and diff tooling.
The full 1D Dynamic Programming cheatsheet for FAANG interviews — eight pattern transitions, knapsack loop directions, LIS patience sort, and the complete problem index in one place.