How to Master Dynamic Programming for Tier-1 MNC Placement Assessments

The 4-Step DP Framework for MNC Tests

Dynamic Programming questions terrify candidates because they try to write the bottom-up table immediately. In real placement tests, follow this proven 4-step framework:

1. Formulate the plain recursion: Express the solution in terms of sub-problems and define clear base cases.
2. Verify Optimal Substructure & Overlapping Subproblems: Identify which state parameters change during recursive calls.
3. Memoize with Top-Down Cache: Add a hash table or 2D array to eliminate redundant recursive subtree calls.
4. Convert to Bottom-Up DP with Space Optimization: If state dp[i] only depends on dp[i-1], reduce space complexity from O(N) to O(1).