Part VII · Dynamic Programming: Comprehensive Problem Families
47. Advanced DP Optimizations and State Techniques
9 lessons•34 topics•Intermediate / Advanced
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47.01Outline
Divide-and-conquer DP optimization
- Monotone optimal split index
- Recurrence conditions
- Partition cost
- O(kn log n) patterns
47.02Outline
Knuth optimization
- Quadrangle inequality conditions
- Monotone opt bounds
- Interval partition recurrence
47.03Outline
Convex hull trick
- Line DP
- Monotone slopes/queries
- Deque hull
- Li Chao tree
- Discrete coordinates
47.04Outline
Aliens trick
- Lagrangian relaxation
- Penalty on group count
- Parametric search
- Recover optimal count
47.05Outline
Monotone queue optimization
- Sliding transition window
- Deque of candidate values
- Max/min DP
47.06Outline
Bitset acceleration
- Subset sum convolution using shifts
- Bit-parallel LCS idea
- Boolean state compression
47.07Outline
SOS and subset DP
- Sum over subsets
- Superset sums
- Fast zeta transform
- Mobius inversion on subsets
47.08Outline
Broken-profile and plug DP
- Contour states
- Connectivity encoding
- Grid coverings
- State pruning
47.09Outline
Advanced correctness
- Optimization preconditions
- Monge matrices
- Counterexample testing
- State dominance