DP Patterns

Dynamic programming interview questions — the patterns, the recognition, the drills

DP is the hardest-to-recognize coding interview pattern and the most rewarding when you nail it. This is the landing-page summary — link out to the full deep-dive guides + drill with the AI coach that grades your DP transitions in real time.

DP recognition in under 60 seconds

The hardest part of DP isn't the implementation — it's recognizing the pattern. Standard cues: 'count the ways', 'max/min value', 'overlapping subproblems'. The AI coach helps you spot these cues during drills.

The 5 DP subpatterns to master

1D DP on arrays, 2D DP (grids and matchings), DP on intervals, DP on trees, bitmask DP. 80% of DP interview questions are one of these five.

Top-down (memoization) vs bottom-up (tabulation)

Top-down is easier to write but harder to optimize; bottom-up is uglier but lets you reduce space. The coach helps you convert between them when the interviewer asks.

Standard transitions, indexed by pattern

Once you recognize the pattern, the state and transition are mostly mechanical. The drills cover the standard transitions for each subpattern so they become reflex.

Voice-paced DP practice with explanation grading

DP rounds win or lose on whether you can explain the state and transition. The AI coach grades not just the answer but how cleanly you described the recurrence.

Deep-dive guides cross-linked

Every DP pattern has a full written deep-dive on the blog. This page is the summary — the deep-dive blogs are where you'll spend the most prep time.

Recognition cues

Recognize a DP interview question in under 60 seconds

Recognition beats implementation. If you spot DP fast, the rest is mostly mechanical.

“Count the number of ways” to do something. Almost always DP (or backtracking with memoization).
“Find the maximum/minimum” value under constraints — and the constraints overlap across subproblems.
“Is it possible to” reach a target under rules. Reachability with overlapping subproblems → DP.
“Longest” anything — substring, subsequence, increasing path. Classic DP setup.
“Partition” something optimally. Interval DP territory.

The 5 DP subpatterns and their canonical problems

1D DP on arrays

Climbing stairs, house robber, jump game, longest increasing subsequence. Single index, state usually i-1 or i-2. DP patterns deep-dive →

2D DP (grids and pairs)

Unique paths, edit distance, longest common subsequence, regex matching. Two indices, state usually (i-1, j-1) or (i-1, j). DP interview guide →

DP on intervals

Burst balloons, matrix chain multiplication, palindrome partitioning. State is (left, right) range; you try every split point. Hardest subpattern.

DP on trees

Diameter of tree, robber on tree, longest path with constraints. Recurrence: solve children first, combine at the root.

Bitmask DP

Traveling salesman (small N), assignment problems, set cover. State includes a bitmask of visited subset. N ≤ 20 is the giveaway.

Top-down vs bottom-up — when to use which

Both produce the same answer. They differ in ergonomics and what the interviewer expects.

Top-down (memoization). Write the recursion naturally, cache results. Easier to write, harder to optimize space. Use this first; convert to bottom-up if asked.
Bottom-up (tabulation). Iterative, fills a table. Often allows space optimization (e.g., keep only last 1-2 rows). Use this if interviewer asks about constants or space.
Hybrid. Some interviewers want to see you do top-down first (proving you understand the recurrence), then bottom-up (proving you can optimize). PhantomCode’s drill mode covers both.

Most common DP questions in 2026 FAANG interviews

Climbing stairs / Fibonacci variants — 1D DP, ubiquitous warm-up
House robber / House robber II — 1D DP with adjacency constraint
Coin change — 1D DP with optimization choice
Longest increasing subsequence (LIS) — 1D DP, classic, has O(n log n) follow-up
Edit distance / Word break — 2D DP on strings
Unique paths / Minimum path sum — 2D DP on grids
Burst balloons — Interval DP, considered hard
Word break II — DP + backtracking, common follow-up

Frequently asked questions

How do I get better at dynamic programming interview questions?

Master the 5 subpatterns (1D, 2D, intervals, trees, bitmask) and the 8 canonical problems above. Then drill voice-paced — explain the state and transition out loud, not just code silently. Most candidates fail DP rounds because they can't articulate WHY the recurrence works, not because they can't code it.

How many DP problems should I solve before a FAANG interview?

Around 30-40 carefully chosen problems covering the 5 subpatterns deeply, with 24-hour-later review for each. Quality beats quantity — solving 200 DP problems without deliberate review yields worse interview performance than solving 30 with structured drilling.

What's the hardest part of DP in coding interviews?

Recognition. Once you know it's DP and which subpattern, the implementation is mostly mechanical. The interview test is whether you spot the pattern in under a minute. Practice with the recognition cues — 'count the ways', 'max/min under constraints', etc.

Top-down or bottom-up — which one should I write in the interview?

Top-down (memoization) first, because the recurrence is easier to derive and explain. If the interviewer asks about space optimization, convert to bottom-up. Showing you can do both demonstrates mastery.

Can AI tools help me practice DP?

Yes. PhantomCode's coach grades your DP transitions and state articulation — not just whether your code passes. The drills are voice-paced so you build the explanation skill that wins DP rounds. And during the live interview, the same coach can surface the right subpattern in sub-second.