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·Combinatorial Enumeration

Permutations (Backtracking)

⏱ O(n·n!)◧ O(n)

start

1

2

3

4

0

1

2

3

State vector

[1,2,3,4]

Step 1 / 218

Speed

Speed

02Reasoning

Permutations (Backtracking)

Combinatorial Enumeration

Recursively swap-in each unused element.

Time

O(n·n!)

Space

O(n)

Applications

Test-case generation
Symmetry breaking
Brute-force baselines

Reasoning Trace

Enter start=0

Call stack

permute(start=0)

Principle in Pseudocode

1permute(a, start):
2 if start == n: emit a
3 for i in start..n:
4 swap(a[start], a[i])
5 permute(a, start+1)
6 swap back

Reference implementation · python

def permute(a, start):
  if start == len(a):
    print(a); return
  for i in range(start, len(a)):
    a[start], a[i] = a[i], a[start]
    permute(a, start + 1)
    a[start], a[i] = a[i], a[start]