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·Weighted Planning

Dijkstra's Shortest Path

⏱ O((V+E) log V)◧ O(V)

Distances

A0

B∞

C∞

D∞

E∞

F∞

G∞

Step 1 / 26

Speed

Speed

02Reasoning

Dijkstra's Shortest Path

Weighted Planning

Greedy relaxation from source over non-negative weights.

Time

O((V+E) log V)

Space

O(V)

Applications

Road-network routing
Network packet paths
Robot motion planning

Reasoning Trace

Start Dijkstra from A

Principle in Pseudocode

1dist[src] = 0
2while unvisited:
3 u = min-dist unvisited
4 for (v, w) in adj[u]:
5 dist[v] = min(dist[v], dist[u]+w)

Reference implementation · python

dist = {n: inf for n in G}; dist[src] = 0
pq = [(0, src)]
while pq:
  d, u = heappop(pq)
  for v, w in adj[u]:
    if d + w < dist[v]:
      dist[v] = d + w
      heappush(pq, (dist[v], v))