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1 Introduction2 algorithm instance:3 Attachment: bidirectional breadth­first search4 algorithm introduced

Introduction

Breadth­first search (BFS)

In depth-first search algorithm, is the greater depth of more first node expanded. If you put in a search algorithm to hierarchical node search,The layer node does not search processed, it can not be processed on the lower nodes, ie the smaller the depth of the more nodes expanded first, that first produced The nodes can be extended at first, this search algorithm called breadth-first search method. English using Breadth-First-Search said, so weAlso the breadth-first search method referred to as BFS.

Breadth­first search of the basic algorithm:

1) starting from a start vertex visit, be accessed vertices labeled accordingly, and output access vertex number;

2) starting from the vertex to be accessed sequentially search the edges associated with the vertex adjacency point is not accessible to all, and make the appropriate tag.

3) in turn based on 2) all the neighbors being accessed, the access point associated with the adjacent neighbors are not accessible to all, until all vertices are accessed so far.

[Process] algorithm

program BFS; var Head , tail , i : LongInt ; a : array [ 0 .. Max ] of nodes; begin initial node assignment a [ 0 ] Head : = - 1 ; tail : = 1 ; REPEAT inc ( Head ) ; / / extract a not visited nodes. if ( current node has a child node ) Then for i : = 1 to the maximum number of nodes can be extended do / / expand each child node of the current node if ( the child node does not appear too ) Then begin inc ( tail ) ; a [ tail ] : = new node End ; until Head = tail; / / All nodes have been generated. End .

(ABOVE FROM http://noip.tanghu.net/aosai/shuanfa/024.htm )

Algorithm instance:

Problem description: A, B, C three bucket capacity were 3L, 7L, 10L. There are now C 10L bucket of water. Required only in the context of water transfer between thebarrel, making the C and B buckets equally 10L bucket of water. Find the most simple operation.

program ; BFS const V : array [ 1 .. 3 ] of Integer = ( 3 , 7 , 10 ) ; / / three barrel capacity. type node = record L : array [ 1 .. 3 ] of LongInt ; / / three buckets. P : LongInt ; / / parent node of each node. End ; var i , J , Head , tail : LongInt ; t : boolean ; / / find the target sign. a : array [ 0 .. 100 ] of node; procedure init; var i , J : LongInt ; begin FillChar ( a , sizeof ( a ) , 0 ) ; t : = false ; a [ 0 ] . L [ 3 ] : = 10 ; Head : = - 1 ; tail : = 0 ; End ; procedure pour ( x , y : LongInt ) ; var i , J : LongInt ; begin

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if ( a [ Head ] . L [ x ] = 0 ) or t Then Exit; inc ( tail ) ; a [ tail ] : = a [ Head ] ; a [ tail ] . P : = Head; if a [ tail ] . L [ x ] > V [ y ] - a [ tail ] . L [ y ] Then begin Dec ( a [ tail ] . L [ x ] , V [ y ] - a [ tail ] . L [ y ] ) ; a [ tail ] . L [ y ] : = V [ y ] ; End else begin inc ( a [ tail ] . L [ y ] , a [ tail ] . L [ x ] ) ; a [ tail ] . L [ x ] : = 0 ; End ; for i : = 0 to tail - 1 do / / check the status of whether there had been, it is, then delete it. begin if a [ i ] = a [ tail ] Then begin Dec ( tail ) ; exit; End ; End ; if a [ tail ] . L [ 3 ] = 5 Then t : = true ; End ; procedure main; var i , J : LongInt ; begin REPEAT inc ( Head ) ; pour ( 1 , 2 ) ; / / action function is to try to pour a bucket of water into the x y barrel, see if I can produce the new state. pour ( 2 , 1 ) ; pour ( 1 , 3 ) ; pour ( 3 , 1 ) ; pour ( 2 , 3 ) ; pour ( 3 , 2 ) ; until ( a [ tail ] . L [ 3 ] = 5 ) or ( tail = 100 ) ; / / When you find the target or has exceeded a predetermined search range when to quit. End ; procedure Print; var c : array [ 1 .. 100 ] of LongInt ; i , J : LongInt ; begin i : = 0 ; while a [ tail ] . P <> 0 do begin inc ( i ) ; c [ i ] : = tail; tail : = a [ tail ] . P ; End ; for J : = i downto 1 do writeln ( a [ c [ J ] ] . L [ 1 ] , '' , a [ c [ J ] ] . L [ 2 ] , '' , a [ c [ J ] ] . L [ 3 ] ) ; End ; begin init; main; print;End .

Attachment: Bidirectional breadth­first search

Bidirectional breadth­first search (BIBFS) refers to the search in two directions simultaneously:

Forward search: search from the initial node to the destination node direction;Reverse Search: Search from the target node to the initial node direction;

Bidirectional breadth­first search data structure than the one­way BFS complicated. Since the formation of two trees bidirectional breadth­first search in the search processdirection opposite answer tree, so will

Shall be provided with four tables:

OPEN0 table, CLOSE0 table - storage to be expanded and produced in the forward search has been expanded nodeOPEN1 table, CLOSE1 table - to be expanded and produced the reverse search has been extended storage node

Which set the CL [0,0], OP [0,0], CL [1,0], OP [1,0] is a pointer.

Algorithm introduced

procedure Print ( st , k : Integer ) ; begin if k <> 1 Then begin if st = 1 Then the output list [ st , k ] . State / / reverse search, press f pointer output list [1, k] ... list [1,1] path Print ( st , list [ st , k ] . f ) ; if st = 0 Then Output list [ st , k ] . State / / forward search, the output list [0, k] .. . list [0,1] End ; End ; procedure Check ( st : 0 .. 1 ) ; var i : Integer ; begin for i : = 1 to op [ 1 . st ] - 1 do / / check st extend in opposite directions to each node. if list [ st , op [ 1 . st ] - 1 Then if list [ st , op [ st ] ] . State intersects the list [ 1 - st , i ] . State Then begin if st = 0 Then begin

最短路：Dijkstra ­ Bellman­Ford（SPFA） ­ Floyd­Warshall ­

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Print ( O , op [ st ] ) ; / / this is a positive direction, the first output list [0 .. 1] .. list [0, op [st]], then outputs the list [1, i] .. list [1,1 ] Print ( 1 , i ) ; End else begin Print [ 0 , i ] ; / / this is the reverse direction. Print [ 1 , op [ st ] ) ; End ; halt; End ; End ; procedure expand ( st : 0 .. 1 ) ; begin q : = list ( st , cl [ st ] ) ; while ( q nodes can be expanded ) and ( op [ st ] <MAXN ) do begin along the direction of extension of the q st The child node qt. State ; list [ st , op [ st ] ] . State : = qt. State ; list [ st , op [ st ] ] . Father : = cl [ st ] ; Check ( st ) ; / / both directions Search intersects qt output. op [ st ] : = sp [ st ] + 1 ; End ; cl [ st ] : = cl [ st ] + 1 End ; begin list [ 0 , 1 ] : = start state; list [ 0 , 1 ] . Father : = 0 ; op [ 0 ] = 2 ; cl [ 0 ] : = 1 ; list [ 1 , 1 ] : = target state; list [ 1 , 1 ] . Father : = 0 ; op [ 1 ] = 2 ; cl [ 1 ] : = 1 ; while ( ( op [ 0 ] < = MAXN ) and ( cl [ 0 ] <op [ 0 ] ) ) or ( ( op [ 1 ] < = MAXN ) and ( cl [ 1 ] <op [ 1 ] ) ) do if op [ 0 ] <op [ 1 else expand ( 1 ) ; End .

Graph theory and graph theoryalgorithms

Figure ­ directed graph ­ undirected graph ­ connected graph ­ strongly connected graph ­ complete graph ­ sparse graphs ­ zero figure ­ tree ­ Network

The basic traversal algorithms: breadth­first search ­ depth­first search ­ A * ­ and check collection requirements connected components ­ Flood Fill

Minimum Spanning Tree : Prim ­ Kruskal

Strongly connected components : Kosaraju ­ Gabow ­ Tarjan

Network Flow : augmenting path method ( Ford­Fulkerson , Edmonds­Karp , Dinic ) ­ preflow push ­ Relabel­to­Front

Figure match ­ bipartite graph matching : Hungarian algorithm ­ Kuhn­Munkres ­ Edmonds' Blossom­Contraction

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Shortest : Dijkstra ­ Bellman­Ford ( SPFA ) ­ Floyd­Warshall ­ Johnson algorithm

Johnson算法

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