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Commit 860188c

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Merge pull request #218 from imVivekGupta/sort_doc
Updated doc for bfs dfs
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‎Competitive Coding/Graphs/Graph_Search/BreadthFirstSearch/BFS.md

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## Breadth-first search (BFS)
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An algorithm for traversing or searching tree or graph data structures. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a 'search key') and explores the neighbor nodes first, before moving to the next level neighbours.
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![](https://upload.wikimedia.org/wikipedia/commons/4/46/Animated_BFS.gif)
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--------------------
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This is the algorithm for Breadth First Search in a given graph.
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* We take a starting vertex , and push all its adjacent vertexes in a queue.
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* Now we pop an element from a queue and push all its vertexes in the queue , and we also mark down these vertexes as visited.
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* After executing the code, we will get the vertex visited in a breadth first manner.
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[More info](https://en.wikipedia.org/wiki/Breadth-first_search)

‎Competitive Coding/Graphs/Graph_Search/DepthFIrstSearch/DFS.md

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## Depth-first search (DFS)
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An algorithm for traversing or searching tree or graph data structures. One starts at the root (selecting some arbitrary node as the root in the case of a graph) and explores as far as possible along each branch before backtracking
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----
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![](https://upload.wikimedia.org/wikipedia/commons/7/7f/Depth-First-Search.gif)
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----
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This is the algorithm for Depth First Search in a given graph.
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* We take a starting vertex , and push all its adjacent vertexes in a stack.
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* Now we pop an element from a stack and push all its vertexes in the stack , and we also mark down these vertexes as visited.
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* After executing the code, we will get the vertex visited in a depth first manner.
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[more info](https://en.wikipedia.org/wiki/Depth-first_search)
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## Floyd–Warshall algorithm
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An algorithm for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles). A single execution of the algorithm will find the lengths (summed weights) of the shortest paths between all pairs of vertices.
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![](https://ds055uzetaobb.cloudfront.net/image_optimizer/bec3c44826d7cab9b828f339e4844b5a09df5fce.png)
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### Algorithm
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If w(i,j) is the weight of the edge between
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vertices i and j, we can define shortestPath (i,j,k) in terms of the following recursive formula: the base case is shortestPath (i,j,0)=w(i,j) and the recursive case is shortestPath (i,j,k) = min( shortestPath (i,j,k-1), shortestPath (i,k,k-1)+ shortestPath (k,j,k-1)).
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This formula is the heart of the Floyd–Warshall algorithm. The algorithm works by first computing shortestPath (i,j,k) for all (i,j) pairs for k=1, then k=2, etc. This process continues until k=N, and we have found the shortest path for all (i,j) pairs using any intermediate vertices.
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----------------------------
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### Performance Analysis
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* Worst-case performance O(|V|^3)
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* Best-case performance O(|V|^3)
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* Average performance O(|V|^3)

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