floyd算法学习笔记

算法思路

路径矩阵

时间复杂度与空间复杂度

时间复杂度：因为核心算法是采用松弛法的三个for循环，因此时间复杂度为O（n^3）

空间复杂度：整个算法空间消耗是一个n*n的矩阵，因此其空间复杂度为O（n^2）

C++代码

// floyd.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include"iostream"
#include"fstream"
#define maxlen 20
#define maximum 100
using namespace std;

typedef struct graph
{
 int vertex;
 int edge;
 int matrix[maxlen][maxlen];
};
int _tmain(int argc, _TCHAR* argv[])
{
 ofstream outwrite;
 outwrite.open("h.txt",ios::app|ios::out);
 outwrite<<"welcome to the graph world!\n";
 outwrite<<"the initial matrix is:\n";
 int vertexnumber;
 int edgenumber;
 int beginning,ending,weight;
 int mindistance[maxlen][maxlen];
 int interval[maxlen][maxlen];
 graph floydgraph;
 cout<<"welcome to the graph world!"<<endl;
 cout<<"input the number of the vertex: ";
 cin>>vertexnumber;
 cout<<"input the number of the edge: ";
 cin>>edgenumber;
 for (int i = 0; i < vertexnumber; i++)
 {
  for (int j = 0; j < vertexnumber; j++)
  {
   floydgraph.matrix[i][j]=maximum;
  }
 }
 for (int i = 0; i <edgenumber; i++)
 {
  cout<<"please input the beginning index: ";
  cin>>beginning;
  cout<<"please input the ending index: ";
  cin>>ending;
  cout<<"please input the distance of the two dot: ";
  cin>>weight;
  floydgraph.matrix[beginning][ending]=weight;
 }
 for (int i = 0; i <vertexnumber; i++)
 {
  for (int j = 0; j < vertexnumber; j++)
  {
   mindistance[i][j]=floydgraph.matrix[i][j];
   outwrite<<floydgraph.matrix[i][j]<<"\t";
   interval[i][j]=-1;
  }
  outwrite<<"\n";
 }
 for (int k = 0; k <vertexnumber; k++)
 {
  for (int i = 0; i < vertexnumber; i++)
  {
   for (int j = 0; j < vertexnumber; j++)
   {
    if(mindistance[i][j]>mindistance[i][k]+mindistance[k][j])
    {
     mindistance[i][j]=mindistance[i][k]+mindistance[k][j];
     interval[i][j]=k;
    }
   }
  }
 }
 outwrite<<"\n"<<"after the floyd transition, the matrix is: "<<"\n";
 for (int i = 0; i < vertexnumber; i++)
 {
  for (int j = 0; j < vertexnumber; j++)
  {
   cout<<"the mindistance between "<<i<<"  and  "<<j <<" is: ";
   cout<<mindistance[i][j]<<endl;
   cout<<"the two points pass through the point: "<<interval[i][j];
   cout<<endl;
   outwrite<<mindistance[i][j]<<"\t";
  }
  outwrite<<"\n";
 }
 outwrite<<"\n";
 outwrite<<"the points between the beginning point and the ending point is:"<<"\n";
 for (int i = 0; i < vertexnumber; i++)
 {
  for (int j = 0; j < vertexnumber; j++)
  {
   outwrite<<interval[i][j]<<"\t";
  }
  outwrite<<"\n";
 }
 outwrite.close();
 getchar();
 getchar();
 getchar();
 return 0;
}