V

Algorithm Visualizer

ZHEN
Share on WeiboShare on XGitHub repositoryAuthor website
Learning ToolsAlgorithm Complexity ReferenceAlgorithm Learning Paths
Data StructuresArrayLinked ListStackQueue and DequeBinary Search TreeBinary HeapHash TableGraphTrieDisjoint Set UnionLRU CacheSkip ListSegment TreeB+ TreeBloom FilterFenwick Tree
SortingBubble SortCocktail Shaker SortBitonic SortSelection SortInsertion SortBinary Insertion SortShell SortMerge SortTop-Down Merge SortQuick SortThree-Way Quick SortDual-Pivot Quick SortHeap SortCounting SortRadix SortBucket Sort
Graph AlgorithmsDijkstra's Shortest PathKruskal's Minimum Spanning TreePrim's Minimum Spanning TreeBellman-Ford Shortest PathsTopological SortFloyd-WarshallStrongly Connected Components2-SATMaximum FlowBipartite MatchingLowest Common AncestorEulerian Path
Dynamic ProgrammingEdit Distance0/1 KnapsackUnbounded KnapsackLongest Common SubsequenceLongest Increasing SubsequenceCoin ChangeStone MergingTraveling Salesperson DPTree Dynamic ProgrammingDigit DPRerooting DP
Backtracking and SearchN-QueensSubsetsPermutationsCombination SumMaze Solving with DFSNumber of IslandsWord SearchSudoku SolverA* Search
StringsKMP String MatchingRabin-Karp String MatchingBoyer-Moore String MatchingManacher's Longest Palindromic SubstringSuffix ArrayLCP ArrayAho-Corasick AutomatonZ Function
Math and Number TheorySieve of EratosthenesLinear SieveEuclidean AlgorithmBinary ExponentiationExtended Euclidean AlgorithmChinese Remainder TheoremEuler's Totient FunctionMiller-Rabin Primality TestFast Fourier TransformPollard's Rho Factorization
Computational GeometryConvex HullRotating CalipersClosest Pair of PointsLine Segment IntersectionBentley-Ottmann Sweep Line
SearchingBinary SearchLower and Upper BoundSearch in a Rotated Sorted ArrayBinary Search on the AnswerTernary Search

Graph

Vertices and edges for relationships that are not purely linear

Model connections explicitly

A graph contains vertices and edges. Edges may be directed or undirected, weighted or unweighted. An adjacency list stores only existing neighbors and uses O(V + E) space; an adjacency matrix uses O(V^2) space but answers edge-existence queries in constant time.

BFS and DFS differ only in the frontier

Breadth-first search uses a queue, so it expands one distance layer at a time and finds shortest paths in an unweighted graph. Depth-first search uses a stack, so it follows a branch until it must backtrack. Both mark vertices to avoid revisiting cycles.

Try it
ABCDEF
　
Run BFS or DFS

Choose a start vertex, then run BFS or DFS. The current start is A.

Traversal bound: with adjacency lists, BFS and DFS each visit every reachable vertex and edge at most a constant number of times, for O(V + E) time.

Continue with Dijkstra's algorithm for weighted shortest paths or Topological Sort for dependency order.