Added Tree Height and Tower of Hanoi

[alext04]

What’s Included

1. New Algorithm Module: algorithms/TowerOfHanoi.typ

   • Formal algorithm definition for Tower of Hanoi.
   • Mapcode-style specification (rho, F, pi) using a 2D DP table (X[k][p]) to manage the 6 rod permutations.
   • Concrete DP computation for a sample instance (n=2 disks).
   • Visualization of the primary problem's state evolution using the mapcode-viz framework.

2. New Algorithm Module: algorithms/TreeHeight.typ

   • Formal recursive definition for the height of a binary tree.
   • Mapcode-style specification (rho, F, pi) using a 1D DP table (X[i]) to map node indices to heights.
   • Concrete computation for a sample 5-node tree instance.
   • Full state vector visualization showing the step-by-step height calculation.

3. Documentation Integration

   • Updated main.typ:
     • Added #include "algorithms/TowerOfHanoi.typ".
     • Added #include "algorithms/TreeHeight.typ".
   • Ensures the new chapters appear in the final output in the correct sequence.

Why This Matters

• Brings two classic recursive algorithms into the mapcode framework, expanding coverage.
• Demonstrates two different DP state structures:
  • Tree Height: A 1D DP table for a graph-based dependency.
  • Tower of Hanoi: A 2D DP table (X[k][p]) for a problem with complex, branching sub-dependencies.
• Serves as excellent templates for future recursive and DP problem additions.

Files Changed

• algorithms/TowerOfHanoi.typ — 188 Lines
• algorithms/TreeHeight.typ — 168 lines
• 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