Bubble Sort
Selection Sort
Insertion Sort
Merge Sort
Quick Sort
Heap Sort
Linear Search
Binary Search
Jump Search
BST Insert
BST Search
In-order Traversal

Breadth-First Search
Depth-First Search
Dijkstra's Shortest Path
Prim's MST
Kruskal's MST
Topological Sort (Kahn's)
Tower of Hanoi
N-Queens
Permutations (Backtracking)
Fibonacci (DP)
0/1 Knapsack
Longest Common Subsequence
Coin Change (Min Coins)

Hill Climbing
Simulated Annealing
Differential Evolution

Q-Learning

Genetic Algorithm
Particle Swarm Optimization
Ant Colony Optimization

Monte Carlo Simulation

Placeholder — future integration.

"The invisible architecture through which intelligence becomes impact."

02Reasoning·Recursive Decomposition

Tower of Hanoi

⏱ O(2ⁿ)◧ O(n)

4

3

2

1

A

B

C

Step 1 / 32

Speed

Speed

02Reasoning

Tower of Hanoi

Recursive Decomposition

Solve n by first solving n−1 twice.

Time

O(2ⁿ)

Space

O(n)

Applications

Teaching recursion
State-space enumeration
Backup rotation schemes

Reasoning Trace

Move 4 disks from A to C

Principle in Pseudocode

1hanoi(k, from, to, via):
2 if k == 1: move from → to
3 else: hanoi(k-1, from, via, to)
4 move from → to
5 hanoi(k-1, via, to, from)

Reference implementation · python

def hanoi(k, frm, to, via):
  if k == 1: move(frm, to); return
  hanoi(k-1, frm, via, to)
  move(frm, to)
  hanoi(k-1, via, to, frm)