When should I use Top-Down Memoization vs Bottom-Up Tabulation?

Top-Down (recursion + hash/array) is easier to implement when subproblems are selective. Bottom-Up tabulation avoids recursion call stack overhead and makes space compression straightforward.

How do I optimize space from O(N*M) to O(M) in 2D DP?

If the state transition dp[i][j] only depends on dp[i-1][j], replace the 2D grid with two 1D rows (prev and curr), updating them iteratively.

Advanced Optimization

Time: States × Transitions per State

Space: O(N) 1D Array or O(N×M) 2D Matrix

15% Mastered

Dynamic Programming (DP)

Dynamic Programming optimizes exponential recursive solutions by storing subproblem results in memoization tables. Master 1D state transitions, 2D grid DP, 0/1 Knapsack variants, and space compression.

Practice Progress: 6 / 40 Solved15% Completed

Core Concepts & Algorithmic Principles

Concept 1

Optimal Substructure: An optimal solution to a problem contains optimal solutions to its subproblems.

Concept 2

Overlapping Subproblems: Recursion repeatedly evaluates identical parameters; memoization caches results.

Concept 3

Top-Down (Memoization) vs Bottom-Up (Tabulation): Recursion + cache vs iterative state array filling.

Concept 4

Space Optimization: Compress 2D matrices to 1D vectors when states only depend on previous rows.

Complexity Analysis Benchmark

TIME COMPLEXITYStates × Transitions per State

SPACE COMPLEXITYO(N) 1D Array or O(N×M) 2D Matrix

Dynamic Programming (DP)

Core Concepts & Algorithmic Principles

Concept 1

Concept 2

Concept 3

Concept 4

Complexity Analysis Benchmark

Frequently Asked Questions on Dynamic Programming (DP)

Dynamic Programming (DP)

Core Concepts & Algorithmic Principles

Concept 1

Concept 2

Concept 3

Concept 4

Complexity Analysis Benchmark

Frequently Asked Questions on Dynamic Programming (DP)