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."

01Foundations·Halving Search

Binary Search

⏱ O(log n)◧ O(1)

1

3

5

7

9

11

13

15

17

19

21

0

1

2

3

4

5

6

7

8

9

10

State vector

[1,3,5,7,9,11,13,15,17,19,21]

Step 1 / 9

Speed

Speed

01Foundations

Binary Search

Halving Search

Repeatedly halve a sorted interval.

Time

O(log n)

Space

O(1)

Applications

Sorted-array lookup
Range queries
Numerical root-finding

Reasoning Trace

Binary search for 15

target15

low0

high10

Principle in Pseudocode

1l = 0, r = n-1
2while l <= r:
3 m = (l+r)/2
4 if a[m] == target: return m
5 if a[m] < target: l = m+1
6 else: r = m-1

Reference implementation · python

l, r = 0, len(a) - 1
while l <= r:
  m = (l + r) // 2
  if a[m] == target: return m
  if a[m] < target: l = m + 1
  else: r = m - 1