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Search Related Algorithms
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Graph Code Adjacency List Representation:
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Searches BFS & DFS produce trees – Spanning trees if graph is connected from starting vertex
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Path Reconstruction Search tree can be stored as parent of each vertex
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Path Reconstruction Reconstruct path to 6: Got to 6 from 4
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Path Reconstruction Reconstruct path to 6: Got to 6 from 4 Got to 4 from 0
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Path Reconstruction Reconstruct path to 6: Got to 6 from 4 Got to 4 from 0 Got to 0 from 1
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Path Reconstruction Reconstruct path to 6: Got to 6 from 4 Got to 4 from 0 Got to 0 from 1 1 was root
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Path Reconstruction Reconstruct path to 6: Got to 6 from 4 Got to 4 from 0 Got to 0 from 1 1 was root 1 0 4 6
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Search Tree Requirements Storage = O(V) Time to build: O(V + E) Time to reconstruct path: O(path length)
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SearchTree Code Info to reconstruct search tree
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BFS Search Process Maintain: – Queue of vertices to explore – List of discovered vertices
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BFS BFS (startVertex) Make queue of vertices Put starting vertex on queue Build discovered array – mark start discovered Make parentList While queue is not empty current = queue.dequeue() For each neighbor index from current If( !discovered[neighbor] ) discovered[neighbor] = true parentList[neighbor] = current enqueue neighbor bool array 1 = visited, 0 = not visited List of ints vertices to visit int array
![BFS BFS (startVertex) Make queue of vertices Put starting vertex on queue Build discovered array – mark start discovered Make parentList While queue is not empty current = queue.dequeue() For each neighbor index from current If( !discovered[neighbor] ) discovered[neighbor] = true parentList[neighbor] = current enqueue neighbor bool array 1 = visited, 0 = not visited List of ints vertices to visit int array](http://images.slideplayer.com/33/6977280/slides/slide_13.jpg "BFS BFS (startVertex) Make queue of vertices Put starting vertex on queue Build discovered array – mark start discovered Make parentList While queue is not empty current = queue.dequeue() For each neighbor index from current If( !discovered[neighbor] ) discovered[neighbor] = true parentList[neighbor] = current enqueue neighbor bool array 1 = visited, 0 = not visited List of ints vertices to visit int array")
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BFS
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DFS Search Process Maintain: – Stack of vertices to explore – List of visited vertices
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DFS Search Process Same vertex may end up on stack multiple times: 1 ParentVisited 0 1 2 3 4 5 6 7
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DFS Search Process Same vertex may end up on stack multiple times: 6320 ParentVisited 01 1Y 21 31 4 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 63242 ParentVisited 01Y 1Y 20 31 40 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 6324 ParentVisited 01Y 1Y 20Y 31 40 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 63244 ParentVisited 01Y 1Y 20Y 31 42 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 6324 ParentVisited 01Y 1Y 20Y 31 42Y 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 632 ParentVisited 01Y 1Y 20Y 31 42Y 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 63 ParentVisited 01Y 1Y 20Y 31 42Y 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 6 ParentVisited 01Y 1Y 20Y 31Y 42Y 5 61 7
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DFS Search Process Same vertex may end up on stack multiple times: 67 ParentVisited 01Y 1Y 20Y 31Y 42Y 5 61 73
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DFS Search Process Same vertex may end up on stack multiple times: 6 ParentVisited 01Y 1Y 20Y 31Y 42Y 5 61 73Y
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DFS Search Process Same vertex may end up on stack multiple times: 65 ParentVisited 01Y 1Y 20Y 31Y 42Y 57 61 73Y
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DFS Search Process Same vertex may end up on stack multiple times: 6 ParentVisited 01Y 1Y 20Y 31Y 42Y 57Y 61 73Y
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DFS Search Process Same vertex may end up on stack multiple times: 66 ParentVisited 01Y 1Y 20Y 31Y 42Y 57Y 65 73Y
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DFS Search Process Same vertex may end up on stack multiple times: 6 ParentVisited 01Y 1Y 20Y 31Y 42Y 57Y 65Y 73Y
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DFS Search Process Same vertex may end up on stack multiple times: ParentVisited 01Y 1Y 20Y 31Y 42Y 57Y 65Y 73Y
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DFS DFS (startVertex) Make stack of vertices Put starting vertex on stack Build visited array Make parentList While stack is not empty current = stack.pop() if( !visited[current] ) visited[current] = true For each neighbor index from current if( !visited[neighbor] ) parent[neighbor] = current push neighbor onto stack bool array 1 = visited, 0 = not visited List of ints vertices to visit int array
![DFS DFS (startVertex) Make stack of vertices Put starting vertex on stack Build visited array Make parentList While stack is not empty current = stack.pop() if( !visited[current] ) visited[current] = true For each neighbor index from current if( !visited[neighbor] ) parent[neighbor] = current push neighbor onto stack bool array 1 = visited, 0 = not visited List of ints vertices to visit int array](http://images.slideplayer.com/33/6977280/slides/slide_33.jpg "DFS DFS (startVertex) Make stack of vertices Put starting vertex on stack Build visited array Make parentList While stack is not empty current = stack.pop() if( !visited[current] ) visited[current] = true For each neighbor index from current if( !visited[neighbor] ) parent[neighbor] = current push neighbor onto stack bool array 1 = visited, 0 = not visited List of ints vertices to visit int array")
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DFS
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DFS Recursive DFSRecursive (startVertex) Build visited array Make parentList BFSHelper(startVertex, parentList, visited) DFSHelper (currentVertex, &parentList, &visited) visited[currentVertex] = true For each edge of currentVertex newVertex = edge destination if( !isVisited[newVertex] parentList[newVertex] = currentVertex DFSHelper(newVertex, parentList, visited)
![DFS Recursive DFSRecursive (startVertex) Build visited array Make parentList BFSHelper(startVertex, parentList, visited) DFSHelper (currentVertex, &parentList, &visited) visited[currentVertex] = true For each edge of currentVertex newVertex = edge destination if( !isVisited[newVertex] parentList[newVertex] = currentVertex DFSHelper(newVertex, parentList, visited)](http://images.slideplayer.com/33/6977280/slides/slide_36.jpg "DFS Recursive DFSRecursive (startVertex) Build visited array Make parentList BFSHelper(startVertex, parentList, visited) DFSHelper (currentVertex, &parentList, &visited) visited[currentVertex] = true For each edge of currentVertex newVertex = edge destination if( !isVisited[newVertex] parentList[newVertex] = currentVertex DFSHelper(newVertex, parentList, visited)")
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