Week 36 of 43
Advanced DSA
WEEK 36 LEARNING MODULE
Dynamic Programming II: Bottom-Up Tabulation
Concludes Phase 2 with Bottom-Up Tabulation, iterative DP tables, base case seeding, space optimization (rolling arrays / state compression), and 2D grid DP.
4 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Bottom-Up DP: building iterative tables from base cases up to final target state.
- ✓Eliminate recursion call stack overhead and avoid Python recursion depth limits.
- ✓Implement Space Optimization (Rolling Array / State Compression): reduce $O(n)$ space to $O(1)$, or $O(m \times n)$ to $O(n)$.
- ✓Solve 1D and 2D grid path DP problems: Tribonacci, Triangle Minimum Path, Perfect Squares, and Unique Paths.
Core Concepts
Bottom-Up Tabulation
O(states * transitions)Iteratively filling an array/table starting from base cases, evaluating dependencies in topological order.
State Compression / Rolling Array
O(1) spaceRetaining only the previous state row or last k values to reduce auxiliary memory from O(N) to O(1).
2D Grid DP Transitions
O(R * C)dp[r][c] = grid[r][c] + min(dp[r+1][c], dp[r+1][c+1]) for triangle and grid path optimization.
Algorithms Covered
Tabulated DPRolling Array Space OptimizationTriangle Minimum Path SumPerfect Squares DecompositionUnbounded Knapsack (Coin Change II)
Data Structures Applied
1D / 2D DP Tables / Arrays
“We worry top-down, but we invest bottom-up.”
— Seth Klarman