[图算法]Floyd算法改进之打印路径.
[图算法]Floyd算法改进之打印路径.
Floyd算法虽然形式上简单,但功能强大,除了可以求出图中任意两点间的最短路径外
(参: http://blog.csdn.net/EmilMatthew/archive/ 2005/08/10/450051.aspx)
还能再稍加修改的情况下,通过一个信息矩阵来得出任意两点间最短路径的中结点的信息.
具体的算法如下:
Step1:
1) 准备原带权矩阵wArr及结点信息矩阵wAns.wAns中的元素wAns[i][j]表示的是从结点i到结点j的最短路径中，位于结点j前的那个结点;在原图权值矩阵wArr中,如果两个结点这之前在起始图中没有直接相连的路径，则用一个大整数表示它们间的权值.
2) For i<-1 to len
3) For j<-1 to len
4) If mapArr[i][j]<IntLimit then
5) ansArr[i][j]=i;//如果原图中两个结点I,j连通，则在j结点前的最近结点为i
6) End if
7) Next j
8) Next i
Step2:
1) 在Floy最短路径算法中加入对结点信息矩阵wAns相关的处理信信息，其实就多加了一句.
2) For k<-0 to len
3) For i<-0 to len
4) For j<-0 to len
5) newLen<-mapAr)[i][k]+mapArr[k][j]
6) If (newLen<mapArr[i][j]) then
7) mapArr[i][j]<-newLen;
8) ansArr[i][j]<-ansArr[k][j];//在找到最短路径后,更新结点信息矩阵wAns，使ansArr[i][j]始终表示的是从结点i到结点j的最短路径中，位于结点j前的那个结点
9) End if
10) Next j
11) Next i
12) Next k
至此，伴随着Floyd算法进行，最短路径的结点信息矩阵wAns构造也完成了.
Step2:
ansArr中内容的读取
由于ansArr[i][j]表示的是从结点i到结点j的最短路径中，位于结点j前的那个结点,所以，如果要获得由I到j的最短路径上的各个结点的信息，可以通过从j一直寻访到I的方式来做，将果存放在一个栈中，最后，将栈中内容弹出，即得由I到j的最短
路径上各结点的信息.
具体的算法如下:
1) 给出初结点startNodeId和终止结点endNodeId
2) 初始结点压栈myStack.push(endNodeId)
3) 得到中介结点midNode=wAns[startNodeId][endNodeId]
4) 中介点压栈myStack.push(midNode);
5) while(midNode!=startNodeId)
//如果中介点不是起始点，则进入循环，直到找起始点为止.
{
6) midNode=wAns[startNodeId][midNode];
7) myStack.push(midNode);
}
8) while(!myStack.isEmpty())//输出栈中的信息，即得最路径上各结点的信息.
9) print myStack.pop()
算法结束.
下面给出本算法的实现,在这里，除了输出两个结点的信息外，还输了图中所有结点间最短路径的信息.
/*The floyd2 algorithm ,with could trace out the shortest path node’s information
Made by EmilMatthew 05/8/13*/
/*A very simple stack */
#include <stdlib.h>
#ifndef SIMPLESTACK_H
#define SIMPLESTACK_H
#define StackDataType long
class SimpleStack
{
public:
SimpleStack()
{
mLen=100;
mData=new StackDataType[mLen];
nextSlot=0;
}
SimpleStack(int len)
{
mLen=len;
mData=new StackDataType[mLen];
nextSlot=0;
}
~SimpleStack()
{
mLen=100;
delete []mData;
nextSlot=0;
}
void deleteAllValues()
{
delete []mData;
nextSlot=0;
}
void push(StackDataType inVal);
StackDataType pop();
StackDataType top();
bool isEmpty()
{
return nextSlot==0;
}
private:
StackDataType* mData;
int mLen;
int nextSlot;
};
#endif
/*SimpleStack.cpp*/
#include "SimpleStack.h"
#include "MyAssert.h"
#include <stdio.h>
void SimpleStack::push(StackDataType inVal)
{
/*to enlarge the capacity of the arr*/
if(nextSlot>=mLen)
{
int i=0;
StackDataType* tmpArr;
/*memroy apply*/
tmpArr=new StackDataType[nextSlot];
assertF(tmpArr!=NULL,"in StackDataType SimpleStack::pop tmpArr is NULL/n");
/*copy from mData to tmpArr*/
for(i=0;i<nextSlot;i++)
tmpArr[i]=mData[i];
/*free the space before apply new space*/
delete []mData;
mLen+=100;/*stack length be bigger*/
mData=new StackDataType[mLen];/*memory apply*/
for(i=0;i<nextSlot;i++)
mData[i]=tmpArr[i];
delete []tmpArr;/*free the space of the tmp pointer*/
}
mData[nextSlot++]=inVal;
}
StackDataType SimpleStack::pop()
{
assertF(!isEmpty(),"in StackDataType SimpleStack::pop the stack is Empty./n");
return mData[--nextSlot];
}
StackDataType SimpleStack::top()
{
assertF(!isEmpty(),"in StackDataType SimpleStack::top the stack is Empty./n");
return mData[nextSlot-1];
}
/*Floy2 updated algorithm,the ansArr will return the node infomation*/
void Floyd2(Type*** mapArr,Type*** ansArr,int len)
{
int i,j,k;/*iterator index*/
Type newLen;/*tmp shortest len*/
assertF(*mapArr!=NULL,"in Floyd2 *mapArr is NULL");
assertF(*ansArr!=NULL,"in Floyd2 *ansArr is NULL");
/*Algorithm Core Reason*/
/*Mk+1[i,j]=1 <-> Mk[i,k+1]=1&&Mk[k+1,j]=1*/
for(i=0;i<len;i++)
for(j=0;j<len;j++)
if((*mapArr)[i][j]<IntLimit)
(*ansArr)[i][j]=i;
for(k=0;k<len;k++)
for(i=0;i<len;i++)
for(j=0;j<len;j++)
{
newLen=(*mapArr)[i][k]+(*mapArr)[k][j];
if(newLen<(*mapArr)[i][j])
{
(*mapArr)[i][j]=newLen;
(*ansArr)[i][j]=(*ansArr)[k][j];
}
}
}
/*Floy2 updated algorithm,the ansArr will return the node infomation*/
void Floyd2(Type*** mapArr,Type*** ansArr,int len)
{
int i,j,k;/*iterator index*/
Type newLen;/*tmp shortest len*/
assertF(*mapArr!=NULL,"in Floyd2 *mapArr is NULL");
assertF(*ansArr!=NULL,"in Floyd2 *ansArr is NULL");
/*Algorithm Core Reason*/
/*Mk+1[i,j]=1 <-> Mk[i,k+1]=1&&Mk[k+1,j]=1*/
for(i=0;i<len;i++)
for(j=0;j<len;j++)
if((*mapArr)[i][j]<IntLimit)
(*ansArr)[i][j]=i;
for(k=0;k<len;k++)
for(i=0;i<len;i++)
for(j=0;j<len;j++)
{
newLen=(*mapArr)[i][k]+(*mapArr)[k][j];
if(newLen<(*mapArr)[i][j])
{
(*mapArr)[i][j]=newLen;
(*ansArr)[i][j]=(*ansArr)[k][j];
}
}
}
#include "SimpleStack.h"
#include "MyAssert.h"
#include "Global.h"
#include "Ulti.h"
#include "GraphAlgorithm.h"
#include <iostream.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
char *inFileName="inputData.txt";
/*
input data specification
row,col
wArr
{
, , , ,
, , , ,
, , , ,
}
*/
char *outFileName="outputData.txt";
#define DEBUG 1
void main(int argc,char* argv[])
{
FILE *inputFile;/*input file*/
FILE *outputFile;/*output file*/
double startTime,endTime,tweenTime;/*time callopsed info*/
int row,col;
int startNodeId=0,endNodeId=0;
int i,j;/*iterator index*/
int n;/*arr deminision for squre matrix*/
SimpleStack myStack;
Type** wArr;
Type** wAns;
Type midNode;
/*input file open*/
if(argc>1)strcpy(inFileName,argv[1]);
assertF((inputFile=fopen(inFileName,"rb"))!=NULL,"input file error");
printf("input file open success/n");
/*outpout file open*/
if(argc>2)strcpy(outFileName,argv[2]);
assertF((outputFile=fopen(outFileName,"wb"))!=NULL,"output file error");
printf("output file open success/n");
fscanf(inputFile,"%d,%d,",&row,&col);
/*Memory apply*/
wArr=(Type**)malloc(sizeof(Type*)*row);
for(i=0;i<row;i++)
wArr[i]=(Type*)malloc(sizeof(Type)*col);
wAns=(Type**)malloc(sizeof(Type*)*row);
for(i=0;i<row;i++)
wAns[i]=(Type*)malloc(sizeof(Type)*col);
/*Read 2d arr data*/
for(i=0;i<row;i++)
{
for(j=0;j<col-1;j++)
fscanf(inputFile,"%d,",&wArr[i][j]);
fscanf(inputFile,"%d;",&wArr[i][j]);
}
/*big length adjust*/
for(i=0;i<row;i++)
for(j=0;j<col;j++)
if(wArr[i][j]==-1)wArr[i][j]=IntLimit;
show2DArrInt(wArr,row,col);
fscanf(inputFile,"%d,%d,",&startNodeId,&endNodeId);
printf("start:%d,end:%d.",startNodeId,endNodeId);
#if DEBUG
printf("/n*******start of test program******/n");
printf("now is runnig,please wait.../n");
startTime=(double)clock()/(double)CLOCKS_PER_SEC;
/******************Core program code*************/
/*argu prepare*/
assertF(col==row,"in test col!=row");
n=row;/*get the size of square matrix*/
Floyd2(&wArr,&wAns,n);
fprintf(outputFile,"===Output the node info matrix.===/r/n");
output2DArrInt(wAns,row,col,outputFile);
fprintf(outputFile,"===End of output the node info matrix.===/r/n");
assertF(startNodeId>=0&&endNodeId>=0&&startNodeId<n&&endNodeId<n,"in test,start and end id is illegal/n");
/*Trace out all the shortest path node information*/
for(i=0;i<row;i++)
{
for(j=0;j<col;j++)
{
startNodeId=i;
endNodeId=j;
myStack.push(endNodeId);
midNode=wAns[startNodeId][endNodeId];
myStack.push(midNode);
while(midNode!=startNodeId)
{
midNode=wAns[startNodeId][midNode];
myStack.push(midNode);
}
while(!myStack.isEmpty())
fprintf(outputFile,"%d,",myStack.pop());
fprintf(outputFile,"*");
}
fprintf(outputFile,"/r/n");
}
/******************End of Core program**********/
endTime=(double)clock()/(double)CLOCKS_PER_SEC;
tweenTime=endTime-startTime;/*Get the time collapsed*/
/*Time collapsed output*/
printf("the collapsed time in this algorithm implement is:%f/n",tweenTime);
fprintf(outputFile,"the collapsed time in this algorithm implement is:%f/r/n",tweenTime);
printf("/n*******end of test program******/n");
#endif
for(i=0;i<row;i++)
free(wArr[i]);
free(wArr);
printf("program end successfully,/n you have to preess any key to clean the buffer area to output,otherwise,you wiil not get the total answer./n");
getchar();/*Screen Delay Control*/
return;
}
测试结果:
输入文件:
4,4,
0,1,1,-1;
1,0,-1,2;
1,-1,0,1;
-1,2,1,0;
输出文件:
===Output the node info matrix.===
0,0,0,2;
1,1,0,1;
2,0,2,2;
2,3,3,3;
===End of output the node info matrix.===
0,0,*0,1,*0,2,*0,2,3,*
1,0,*1,1,*1,0,2,*1,3,*
2,0,*2,0,1,*2,2,*2,3,*
3,2,0,*3,1,*3,2,*3,3,*