Personal notes and implementations for dynamic programming, drawn from LeetCode, CLRS (4th ed.), and Levitin Introduction to the Design and Analysis of Algorithms (3rd ed.). Python 3.12+.

The point of this repo is to compare DP strategies on the same problem. A second implementation (space-optimized, top-down memo, brute force, …) is more useful than a new abstraction.

Keep solvers small and comparable. One spec, several implementations; tests run all of them. When adding a problem, follow this loop.

• Readability counts.
  • Docstring: module, function, statement, source, examples, constraints.
  • Each public function: the state, the recurrence, then Time / Space with the symbols defined.
  • Comment the DP transition and any non-obvious cost.
• Keep the logic simple and clean.
  • Write the recurrence as one expression when it fits.
  • Public API is functions; classes only for data structures.
  • Prefer a dummy / index sentinel or an early return over a special-case branch.
  • Return int | None when the result is impossible or absent; do not use a magic value like inf.
  • No unused helpers or shared framework.
• Strategy over abstraction.
  • Prefer another solver of the same spec over a shared framework.
  • Keep problem variants separate from algorithm variants. Encode problem variants in the type.
• Reliability.
  • Types as contracts, collections.abc.Sequence for read-only inputs.
  • PEP 695 generics when a structure needs them.
  • assert preconditions.
• Constant factors count.
  • Avoid an intermediate slice when a cheaper equivalent exists.
  • Rolling state and index-based recursion are first-class variants.
• One test body.
  • Parametrize impl over every solver of a spec.
  • Empty and edge cases first, then book or LeetCode samples.

poetry sync                     # env + dependencies from pyproject.toml

poetry run pytest               # unit tests (benchmarks off)
poetry run pytest -m benchmark  # perf only
poetry run pytest -m ""         # everything, as in CI

poetry run flake8 src tests     # style lint
poetry run isort src tests      # sort imports
poetry run mypy src             # type check

./scripts/run.sh                # pytest + flake8 + isort + mypy

Default pytest skips @pytest.mark.benchmark cases (-m "not benchmark"). Benchmark inputs stay small enough that brute-force variants can still run.

• ch8_1_example1_coin_row.py — Chapter 8.1 Example 1 Coin-row
• ch8_1_example2_change_making.py — Chapter 8.1 Example 2 Change-making
• ch8_1_example3_coin_collecting.py — Chapter 8.1 Example 3 Coin-collecting
• ch8_2_knapsack.py — Chapter 8.2 Knapsack

• ch14_1_rod_cutting.py — Chapter 14.1 Rod Cutting

• p3_longest_substring_without_repeating_characters.py — 3. Longest Substring Without Repeating Characters
• p5_longest_palindromic_substring.py — 5. Longest Palindromic Substring
• p23_merge_k_sorted_lists.py — 23. Merge k Sorted Lists
• p53_maximum_subarray.py — 53. Maximum Subarray
• p139_word_break.py — 139. Word Break