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·Minimum-Cost Composition

Coin Change (Min Coins)

⏱ O(n·amt)◧ O(amt)

0	1	2	3	4	5	6	7	8	9	10	11
0	∞	∞	∞	∞	∞	∞	∞	∞	∞	∞	∞

Step 1 / 19

Speed

Speed

02Reasoning

Coin Change (Min Coins)

Minimum-Cost Composition

Fewest coins to make an amount via DP.

Time

O(n·amt)

Space

O(amt)

Applications

Currency systems
Change-making machines
Resource unit assembly

Reasoning Trace

Coins 1,2,5, amount 11

Principle in Pseudocode

1dp[0]=0; dp[i]=∞
2for i=1..amt:
3 for c in coins:
4 if c<=i: dp[i]=min(dp[i], dp[i-c]+1)

Reference implementation · python

dp = [inf] * (amt + 1)
dp[0] = 0
for i in range(1, amt + 1):
  for c in coins:
    if c <= i:
      dp[i] = min(dp[i], dp[i - c] + 1)