Algorithm note _071:SPFA algorithm Brief introduction (Java)

Directory

1 Problem Description

2 Solutions

2.1 Specific Code

  1 problem description

What is the spfa(shortest Path Faster algorithm) algorithm?

SPFA algorithm function: Given a weighted connected graph, select a vertex, called the starting point, to find the shortest distance from the starting point to all other vertices, the notable feature is that you can PS: reference from Baidu Encyclopedia : SPFA Bellman-ford algorithm, which reduces the redundancy of the Span style= "font-family: Arial" > relaxation operation

SPFA algorithm idea:SPFA is A way of realization of Bellmanford, the specific difference is that, for handling the relaxation operation, The queue (FIFO) operation is used, which greatly improves the complexity of time. (PS: For Bellmanford algorithm can refer to my other article algorithm note _070:bellmanford algorithm simple introduction (Java))

2 Solutions 2.1 specific code

The time complexity of SPFA algorithm for finding single source shortest path is O (m*e). (where m is the average number of all vertices entering the team, it can be shown that m is generally less than or equal to the number of vertices ,E is the edge collection of the given graph)

first look at the connected graphs used in the code ( PS: The graph is undirected connected, so there are two edges between each of the two vertices):

now take the middle vertex the shortest distance from B to all other vertices.

The specific code is as follows:

 PackageCom.liuzhen.chapter9;Importjava.util.ArrayList;ImportJava.util.Scanner; Public classSPFA { Public Long[] result;//used to get the shortest distance between the first s vertices and the other vertices//inner class for storing specific edge data of a diagram    classEdge { Public intA//the beginning of the side         Public intb//the end of the edge         Public intValue//weighted value of the edgeEdge (intAintBintvalue) {             This. A =A;  This. B =b;  This. Value =value; }    }    /** Parameter N: The number of vertices of the given graph * parameter s: the shortest distance between the first s vertex and all other vertices * parameter edge: The specific side of the given graph * Function function: If the given graph does not contain negative weight loop, then the final result can be obtained, if it contains a negative weight loop, it cannot be Get the final result*/     Public BooleanGetshortestpaths (intNints, edge[] A) {ArrayList<Integer> list =NewArraylist<integer>(); Result=New Long[n]; Boolean[] used =New Boolean[n]; int[] num =New int[n];  for(inti = 0;i < n;i++) {Result[i]=Integer.max_value; Used[i]=false; } Result[s]= 0;//the first s vertex to self distance is 0Used[s] =true;//represents the first s vertex into the array teamNum[s] = 1;//indicates that the first s vertex has been traversed onceList.add (s);//The first s vertex is enqueued         while(List.size ()! = 0) {            intA = List.get (0);//gets the first element in the array teamList.remove (0);//Delete the first element in the array team             for(inti = 0;i < a.length;i++) {                //When the first element of the list array team equals the beginning of the edge A[i]                if(A = = A[i].a && result[a[i].b] > RESULT[A[I].A] +a[i].value) {RESULT[A[I].B]= Result[a[i].a] +A[i].value; if(!used[a[i].b])                        {List.add (a[i].b); NUM[A[I].B]++; if(Num[a[i].b] >N)return false; USED[A[I].B]=true;//endpoint B representing Edge A[i] has entered the array team}}} Used[a]=false;//vertex a array pairs        }        return true; }         Public Static voidMain (string[] args) {SPFA test=NewSPFA (); Scanner in=NewScanner (system.in); System.out.println ("Please enter the total number of vertices of a graph n start subscript s and the total number of sides P:"); intn =In.nextint (); ints =In.nextint (); intp =In.nextint (); Edge[] A=NewEdge[p]; System.out.println ("Please enter data for specific edges:");  for(inti = 0;i < p;i++) {             intA =In.nextint (); intb =In.nextint (); intValue =In.nextint (); A[i]= Test.NewEdge (A, B, value); }        if(Test.getshortestpaths (n, S, A)) { for(inti = 0;i < test.result.length;i++) System.out.print (Test.result[i]+" "); } ElseSystem.out.println ("There is a negative ring in the given graph, there is no shortest distance"); }}

Operation Result:

Please enter the total number of vertices of a graph n start subscript s and the total number of sides P:6 1 Please enter data for specific edges:

Resources:

1. SPFA Algorithm Detailed

Algorithm note _071:SPFA algorithm Brief introduction (Java)