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·Memoized Recursion

Fibonacci (DP)

⏱ O(n)◧ O(n)

F(0)	F(1)	F(2)	F(3)	F(4)	F(5)	F(6)	F(7)	F(8)	F(9)
0	1

Step 1 / 17

Speed

Speed

02Reasoning

Fibonacci (DP)

Memoized Recursion

Cache subproblem results to avoid recomputation.

Time

O(n)

Space

O(n)

Applications

Numerical sequences
Teaching memoization
Base-case for DP tutorials

Reasoning Trace

Base: F(0)=0, F(1)=1

Principle in Pseudocode

1dp[0]=0, dp[1]=1
2for i=2..n:
3 dp[i] = dp[i-1] + dp[i-2]

Reference implementation · python

dp = [0, 1] + [0] * (n - 1)
for i in range(2, n + 1):
  dp[i] = dp[i-1] + dp[i-2]