Dijkstra 算法 c语言原生实现

// Dijkstra.cpp: 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <stdio.h>
#include <stdlib.h>
#include<limits.h>

void Dijkstra(int n, int v, int distance[], int previous[], int **G)
//distance 为起点到这个点的最短距离
// previous为每个节点的先序节点
{
int * sign = (int *)malloc(sizeof(int)*n);
for (int i = 0; i < n; i++)//初始化
{
distance[i] = G[v][i];//到i的最短距离数组初始化 到达不了的节点为INT_MAX
if (i == v)
{
sign[i] = 1;

}
else
{
sign[i] = 0;
}

if (G[v][i] == INT_MAX)
{
previous[i] = -1;
}
else
{
previous[i] = v;//起始节点的先序节点是它本身
}

}

for (int i = 0; i < n-1; i++)//n个节点，n-1次
{
int temp = INT_MAX;
int min_v=INT_MAX;
for (int j = 0; j < n; j++)
{
if ((!sign[j]) && distance[j] < temp)
//选出一个未处理而且距离初始节点最短的节点
{
min_v = j;
temp = distance[j];
}
}
sign[min_v] = 1;
for (int j = 0; j < n; j++)
{
if ((!sign[j]) && G[min_v][j] < INT_MAX)
//定点未处理且顶点可达
{
int newdist = distance[min_v] + G[min_v][j];
//最短节点 + 这个节点的路径 产生的路经才有可能是最短的路径

if (newdist < distance[j])
{
//更新源点通向j点的距离
distance[j] = newdist;
previous[j] = min_v;//经过最短节点 min_v
}
}

}
}

}
void showPath(int start, int end, int n, int previous[])

{
int *way = (int*)malloc(sizeof(int)*n);//路径数组
int previous_v=end;
int count = 0;
while (true)
{
way[count] = previous_v;
count++;
previous_v = previous[previous_v];
if (previous_v == start)
{
way[count] = previous_v;
count++;
break;
}

}
printf("The start : %d The end %d\n", start, end);
for (int i = count-1; i >=0; i--)
{
if(i==0)
{
printf("%d", way[i]);

}
else {
printf("%d->", way[i]);
}
}
printf("\n");
}
int ** generateGraph(int n)
{
int ** Graph = (int**)malloc(sizeof(int *)*n);
for (int i = 0; i < n; i++)
{
Graph[i] = (int*)malloc(sizeof(int)*n);
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i == j)
{
Graph[i][j] = 0;
}
else
{
Graph[i][j] = INT_MAX;
}
}
}
Graph[1][0] = 2;
Graph[2][0] = 1;
Graph[3][0] = 4;
Graph[4][0] = 0;
Graph[5][0] = 1;

Graph[2][1] = 7;
Graph[3][1] = 0;
Graph[4][1] = 5;
Graph[5][1] = 0;
Graph[3][2] = 3;
Graph[4][2] = 0;
Graph[5][2] = 0;

Graph[4][3] = 2;
Graph[5][3] = 0;
Graph[5][4] = 3;
for (int i = 0; i < n; i++)
{
for (int j = i + 1; j < n; j++)
{
Graph[i][j] = Graph[j][i];
}
}

return Graph;
}

int main()
{
int ** Graph = generateGraph(6);
int * distance = (int*)malloc(sizeof(int)*6);
int * previous = (int*)malloc(sizeof(int) * 6);
Dijkstra(6, 2, distance, previous, Graph);
for (int i = 0; i < 6; i++)
{
showPath(2, i, 6,previous);
}
system("pause");
return 0;
}