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·Breadth Reasoning

Breadth-First Search

⏱ O(V+E)◧ O(V)

Queue (front → back)

A

Step 1 / 35

Speed

Speed

02Reasoning

Breadth-First Search

Breadth Reasoning

Expand outward by layer — shortest hop-count.

Time

O(V+E)

Space

O(V)

Applications

Shortest unweighted path
Web crawlers
Social-graph radius

Reasoning Trace

Start BFS from A. Enqueue A.

Principle in Pseudocode

1queue = [source]
2while queue:
3 u = queue.pop_front()
4 for v in adj[u]:
5 if not visited[v]: enqueue

Reference implementation · python

from collections import deque
q = deque([src]); visited = {src}
while q:
  u = q.popleft()
  for v in adj[u]:
    if v not in visited:
      visited.add(v); q.append(v)