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·Dependency Ordering

Topological Sort (Kahn's)

⏱ O(V+E)◧ O(V)

Queue (front → back)

5

7

3

Step 1 / 23

Speed

Speed

02Reasoning

Topological Sort (Kahn's)

Dependency Ordering

Emit nodes with no remaining prerequisites first.

Time

O(V+E)

Space

O(V)

Applications

Build systems
Task schedulers
Course prerequisites

Reasoning Trace

Compute in-degrees; enqueue zeros

21

30

50

70

82

92

101

112

Principle in Pseudocode

1compute in-degrees
2queue nodes with in-deg 0
3pop → order; decrement neighbors

Reference implementation · python

indeg = compute_in_degrees(G)
q = deque([u for u in G if indeg[u] == 0])
order = []
while q:
  u = q.popleft(); order.append(u)
  for v in adj[u]:
    indeg[v] -= 1
    if indeg[v] == 0: q.append(v)