Below is a pattern-driven set of foundational dynamic programming (DP) problems. It’s organized to build from 1D → 2D → advanced state modeling, with emphasis on recognizing transitions and state definitions.

1. 1D DP — Linear Decisions

Core Skill

• Each state depends on previous states
• Typically dp[i]

Problems

• Climbing Stairs
• House Robber
• Maximum Subarray
• Min Cost Climbing Stairs

Patterns

Fibonacci-style

dp[i] = dp[i-1] + dp[i-2]

Decision DP

dp[i] = max(dp[i-1], nums[i] + dp[i-2])

What You Learn