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Code Katas

Focused, repeatable coding exercises designed to build fluency between the math and the computational representation.

Kata 1: Counting Without Formula Guessing​

Time limit: 20 minutes
Goal: Implement functions for permutations, combinations, and multinomial counts with clear input validation.
Setup: Use Python or your preferred language. Add tests for edge cases such as zero selections and repeated categories.

Repeat until: You can explain which function matches which problem structure without looking at notes.

Kata 2: Recurrence to Dynamic Programming​

Time limit: 20 minutes
Goal: Implement the recurrence for binary strings with no consecutive 1s using both recursion and bottom-up DP.
Setup: Print the first 10 values and verify them against hand calculations.

Repeat until: You can move from recurrence statement to working DP table automatically.

Kata 3: Graph Invariants Checker​

Time limit: 20 minutes
Goal: Given an undirected graph as an adjacency list, compute degrees, test connectivity, and report whether an Euler path or circuit exists.
Setup: Include at least three sample graphs with different parity profiles.

Repeat until: You can connect the code output directly to the graph theorems you are using.

Kata 4: Bipartite and Tree Tests​

Time limit: 20 minutes
Goal: Implement one function that checks whether a graph is bipartite and another that checks whether it is a tree.
Setup: Use BFS or DFS; include disconnected and odd-cycle examples.

Repeat until: You can explain why the implementation mirrors the mathematical definitions.

Completion Standard​

  • Can implement each kata within the time limit
  • Can explain the mathematical invariant behind each implementation
  • Can write at least one test case that would catch a naive incorrect solution