Rod Cutting and Subset Sum Problem

[vanshg1729]

What's Included

1. New Algorithm Module: Rod Cutting

algorithms/RodCutting.typ

• Formal DP recurrence definition for $r(n, k)$, the maximum revenue obtainable by cutting a rod of length $n$.
• Mapcode-style specification $(ρ, F, π)$.
• Concrete DP computation for a sample instance $(n = 4, P = (1, 5, 8, 9))$.
• Full DP-table visualization using the project's mapcode-viz framework.

2. New Algorithm Module: Subset Sum

algorithms/SubsetSum.typ

• Formal recursive definition for $D(i, j)$, determining if sum $j$ can be made using the first $i$ items.
• Mapcode-style specification $(ρ, F, π)$.
• Computation for a sample instance $(S = (3, 5, 8), T = 11)$.
• Visualization of the 2D DP table $X(i, j)$, showing the evolution of valid partial sum solutions.

3. Documentation Integration

Updated main.typ:

• Added #include "algorithms/SubsetSum.typ" after the previous algorithm section.
• Added #include "algorithms/RodCutting.typ" directly after the Subset Sum section.
• Ensures the new algorithm chapters appear in the output in correct sequence.

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Why This Matters

• Brings two more classical computational problems into the mapcode framework, expanding coverage.
• Demonstrates the framework's versatility in handling both 1D tensor-based DP problems (Rod Cutting) and 2D matrix-based DP problems (Subset Sum).
• Provides additional templates for future algorithm additions, showcasing incremental computation and proper dependency checking.
• Enhances the educational value of the repository with well-documented, classic optimization problems.

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Files Changed

• algorithms/RodCutting.typ — 117 lines added
• algorithms/SubsetSum.typ — 139 lines added
• main.typ — 4 lines added

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

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Checklist

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

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Additional Notes

Both algorithms have been thoroughly tested:

• Rod Cutting: Correctly computes maximum revenue of 10 for length 4 (optimal cut: 2+2)
• Subset Sum: Correctly determines that sum 11 can be achieved from {3, 5, 8} using subset {3, 8}

The implementations follow the mapcode framework's conventions with proper initialization (ρ), iterative function application (F), and projection (π) to extract the final answer.

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