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·Value-under-Constraint

0/1 Knapsack

⏱ O(nW)◧ O(nW)

	0	1	2	3	4	5	6	7	8
∅	0	0	0	0	0	0	0	0	0
w=2,v=3	0	0	0	0	0	0	0	0	0
w=3,v=4	0	0	0	0	0	0	0	0	0
w=4,v=5	0	0	0	0	0	0	0	0	0
w=5,v=6	0	0	0	0	0	0	0	0	0

Step 1 / 38

Speed

Speed

02Reasoning

0/1 Knapsack

Value-under-Constraint

Decide include/exclude each item to maximize value under weight.

Time

O(nW)

Space

O(nW)

Applications

Resource allocation
Budget planning
Portfolio selection

Reasoning Trace

Initialize DP table with 0s

Principle in Pseudocode

1for i=1..n:
2 for w=0..W:
3 dp[i][w] = max(dp[i-1][w], dp[i-1][w-wi]+vi)

Reference implementation · python

for i in range(1, n+1):
  for w in range(W+1):
    dp[i][w] = dp[i-1][w]
    if wt[i-1] <= w:
      dp[i][w] = max(dp[i][w], dp[i-1][w-wt[i-1]] + val[i-1])