Hard
🕸 Graph
Dijkstra's Shortest Path
The backbone of Google Maps. Watch Dijkstra's leverage a priority queue to definitively find cheapest routes across weighted graphs, completely dodging cycles.
Time: O((V + E) log V)
Space: O(V)
25 min
000
PyAnimateMastery
Mastery
All tracks
Track
Mastery
Experts exploring internals
The deep end. This is where we stop writing scripts and start engineering systems. Master the graph algorithms and dynamic programming patterns that get you through staff-level screens.
Graph traversal
Dynamic programming
System-level thinking
10 algorithms in this track
Start
Hard
🧮 Dynamic Programming
0/1 Knapsack (DP)
The DP classic. You have a weight limit; cram in the max value. See the 2D matrix build up sub-answers row by row so you don't repeat work.
Time: O(n × W)
Space: O(n × W)
25 min
000
Hard
🧮 Dynamic Programming
Longest Common Subsequence
Longest Common Subsequence. Core to how `git diff` works. Watch DP align two strings character by character without scrambling their relative order.
Time: O(m × n)
Space: O(m × n)
20 min
000
Hard
🕸 Graph
Topological Sort
Task resolution. See Kahn’s algorithm strip out zero-dependency nodes one by one—the exact logic underlying package managers like npm or pip.
Time: O(V + E)
Space: O(V)
20 min
000
Hard
🕸 Graph
Kruskal's MST
Spanning trees on a budget. Greedily grab the cheapest edges and rely on a union-find structure to guarantee you never accidentally close a cycle.
Time: O(E log E)
Space: O(V)
25 min
000
Hard
🌳 Trees
Trie (Prefix Tree)
The auto-complete engine. Watch strings break into single-character nodes, building a prefix tree that makes searching incredibly scalable over massive dictionaries.
Time: O(m) per op
Space: O(m × n)
20 min
000
Hard
🕸 Graph
Floyd-Warshall
All pairs, everywhere. A savage 3-nested-loop DP that updates a massive matrix until it knows the shortest path between literally every single node.
Time: O(V³)
Space: O(V²)
22 min
000
Hard
🌳 Trees
Segment Tree
Fast interval crunching. Watch the tree build upwards, enabling O(log n) range queries and point updates. Perfect for high-frequency live dashboard stats.
Time: O(log n) query/update
Space: O(n)
25 min
000
Hard
🧮 Dynamic Programming
Coin Change (DP)
Finding exact change with minimal coins. See how dynamic programming sweeps away the failures of the greedy approach when coin denominations get weird.
Time: O(amount × n)
Space: O(amount)
18 min
000
Hard
Bit Ops
Bit Manipulation Tricks
Bare metal mechanics. AND, OR, XOR, and bit-shifts. These power cryptography, graphics systems, and crazy low-level micro-optimizations. Learn to speak CPU.
Time: O(1)
Space: O(1)
18 min
000