AlgoSolveoRoadmap › Stage 9: Greedy & Dynamic Programming › Pattern 43 of 53
DSA pattern guide
DP — 1D Linear
Answer at i depends on a few earlier positions (stairs, robber, decode).
Use it when
Answer at i depends on a few earlier positions (stairs, robber, decode).
Key idea
Define dp[i], write the recurrence from dp[i−1] and dp[i−2], then compress to O(1) space.
Practice problems, in order
- Climbing StairsEasy
- Min Cost Climbing StairsEasy
- House RobberMedium
- Decode WaysMedium
- House Robber IIMedium
- Longest Increasing SubsequenceMedium
- Perfect SquaresMedium
How to practise this pattern
- Read the problem and look for the signal above before writing any code.
- Say the brute force out loud, with its time complexity, then ask what work it repeats.
- Apply the key idea and write the optimised version yourself.
- If you're stuck for more than 10 minutes, take one small hint, not the full solution.
- Move to the next problem only when you can explain why this pattern fits.
Stuck on one of these?
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