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.

02Reasoning·Sequence Alignment

Longest Common Subsequence

⏱ O(nm)◧ O(nm)

	∅	G	A	C
∅	0	0	0	0
A	0	0	0	0
G	0	0	0	0
C	0	0	0	0
A	0	0	0	0
T	0	0	0	0

Step 1 / 17

Speed

Speed

02Reasoning

Longest Common Subsequence

Sequence Alignment

Best matching subsequence via 2D DP table.

Time

O(nm)

Space

O(nm)

Applications

Diff/merge tools
DNA sequence alignment
Plagiarism detection

Reasoning Trace

LCS("AGCAT", "GAC")

Principle in Pseudocode

1if a[i]==b[j]: dp[i][j]=dp[i-1][j-1]+1
2else: dp[i][j]=max(dp[i-1][j], dp[i][j-1])

Reference implementation · python

for i in range(1, n+1):
  for j in range(1, m+1):
    if A[i-1] == B[j-1]:
      dp[i][j] = dp[i-1][j-1] + 1
    else:
      dp[i][j] = max(dp[i-1][j], dp[i][j-1])