Skip to content

Dynamic Programming Ladders

These ladders follow the DP path from state design to structured variants.

  1. foundations
  2. knapsack family
  3. bitmask DP
  4. tree DP
  5. digit DP
  6. interval DP
  7. SOS DP
  8. FWHT / xor convolution / subset convolution
  9. bit-parallelism / bitset optimization
  10. broken profile / plug DP
  11. divide and conquer DP
  12. Knuth optimization
  13. CHT / Li Chao
  14. slope trick
  15. Lagrangian relaxation / Aliens trick
  16. sliding window / mixed optimization notes

Subtopic Ladders

Representative Solved Note

  • VMSCALE: exact budget DP for a non-uniform comparison tree
  • Ciel and Gondolas: partition DP with monotone split optimization on each row
  • Knuth Division: split-point interval DP with additive interval cost and Knuth opt windows
  • Counting Tilings: frontier-mask DP on a small-width grid
  • Compatible Numbers: complement-mask witness propagation over all submasks of the bitwise complement
  • Bitwise XOR Convolution: exact boolean-cube transform route once pair-combining under xor replaces one-array SOS sweeps
  • School Excursion: DSU component sizes collapsed into one packed boolean reachability row
  • Line Add Get Min: direct full-domain line-container verifier inside the affine-DP family
  • Monster Game II: affine-DP optimization via online line insertion and point queries
  • Snuketoon: convex piecewise-linear DP updated by one-sided hinge penalties and bounded movement
  • Red and Blue Lamps: exact-R non-adjacent picks recovered from a penalized linear DP
  • TFIELD: weighted window reasoning over sorted polygon layers