Add Partition Equal Subset and Decode Ways Algorithms

[miryala10sathvika]

What's Included

1. New Algorithm Modules

algorithms/partition-equal-subset.typ

• Formal DP recurrence definition.
• Mapcode-style specification (rho, F, pi).
• Concrete DP computation for sample instance [1, 5, 11, 5].
• Full 2D DP-table visualization using the project's mapcode-viz framework.
• Structured layout showing items vs. target sums with boolean (T/F/⊥) markers.

algorithms/decode-ways.typ

• Formal DP recurrence definition.
• Mapcode-style specification (rho, F, pi).
• Concrete DP computation for sample instances ("12", "226", "11106", "1201234").
• Full 1D DP-array visualization using the project's mapcode-viz framework.
• Summary table comparing multiple test cases and stepwise evaluation.

2. Documentation Integration

Updated main.typ:

• Added #include "algorithms/partition-equal-subset.typ" after the 0-1 Knapsack section.
• Added #include "algorithms/decode-ways.typ" after the Partition Equal Subset section.
• Ensures both chapters appear in output in correct sequence.

Why This Matters

• Brings two more classical DP problems into the mapcode framework, expanding coverage and enabling comparisons across problem classes.
• Demonstrates boolean DP (Partition) and counting DP (Decode Ways) patterns useful for understanding different DP variants.
• Serves as templates for future DP problem additions.

Files Changed

• algorithms/partition-equal-subset.typ — 150 lines added
• algorithms/decode-ways.typ — 180 lines added
• main.typ — 4 lines added

No existing code modified; additions are isolated and non-breaking.

Checklist

• Builds successfully
• Renders correctly in main.typ
• Follows repository style and structure
• No backward-incompatible changes