Dynamic Programming: Complete Interview Guide

Dynamic Programming: The Complete Interview Guide

Dynamic programming (DP) appears in approximately 30% of coding interviews at top tech companies and is consistently rated the most difficult topic by candidates. According to LeetCode statistics, DP problems have the lowest solve rate at 42%, compared to 71% for array problems.

Dynamic programming is an optimization technique that solves problems by breaking them into overlapping subproblems and storing results to avoid redundant computation. The two approaches are top-down (memoization) and bottom-up (tabulation).

The 5 Core DP Patterns

1. Fibonacci-Type — Climbing stairs, house robber. dp[i] depends on dp[i-1] and dp[i-2]
2. 0/1 Knapsack — Subset sum, partition equal subset. Choose to include or exclude each item
3. Longest Common Subsequence (LCS) — String matching, edit distance. 2D table comparing characters
4. Interval DP — Burst balloons, matrix chain multiplication. Process intervals of increasing size
5. Grid DP — Unique paths, minimum path sum. Move right or down in a 2D grid

Step-by-Step DP Approach

1. Identify subproblems — What decision am I making at each step?
2. Define state — What variables fully describe a subproblem? (usually index, remaining capacity, etc.)
3. Write recurrence — Express dp[i] in terms of smaller subproblems
4. Determine base cases — What are the trivial cases? (empty array, single element)
5. Choose approach — Top-down with memoization or bottom-up with tabulation
6. Optimize space — Many 2D DP can be reduced to 1D (rolling array)

Practice DP problems with AI hints from AissenceAI's coding copilot. See also recursion and backtracking as a prerequisite.