111 lines
3.8 KiB
C++
111 lines
3.8 KiB
C++
#include <bits/stdc++.h>
|
||
|
||
using namespace std;
|
||
|
||
// 原始文档：https://www.cnblogs.com/xzxl/p/7246918.html
|
||
#pragma region SPFA算法模板
|
||
// 最短路径——SPFA算法
|
||
|
||
// 最大值
|
||
// https://blog.csdn.net/jiange_zh/article/details/50198097
|
||
/**
|
||
如果我们想要将某个数组清零，我们通常会使用memset(a,0,sizeof(a))，方便又高效，但是当我们想将某个数组全部赋值为无穷大时，
|
||
就不能使用memset函数而得自己写循环了，因为memset是按字节操作的，它能够对数组清零是因为0的每个字节都是0（一般我们只有赋值为-1
|
||
和0的时候才使用它）。现在好了，如果我们将无穷大设为0x3f3f3f3f，那么奇迹就发生了，0x3f3f3f3f的每个字节都是0x3f！所以要把一段
|
||
内存全部置为无穷大，我们只需要memset(a,0x3f,sizeof(a))。所以在通常的场合下，0x3f3f3f3f真的是一个非常棒的选择！
|
||
*/
|
||
const int INF = 0x3f3f3f3f;
|
||
|
||
// https://www.cnblogs.com/xzxl/p/7246918.html
|
||
int matrix[100][100]; //邻接矩阵
|
||
bool visited[100]; //标记数组
|
||
int dist[100]; //源点到顶点i的最短距离
|
||
int path[100]; //记录最短路的路径
|
||
int enqueue_num[100]; //记录入队次数
|
||
int vertex_num; //顶点数
|
||
int edge_num; //边数
|
||
int source; //源点
|
||
|
||
bool SPFA() {
|
||
memset(visited, 0, sizeof(visited));
|
||
memset(enqueue_num, 0, sizeof(enqueue_num));
|
||
for (int i = 1; i <= vertex_num; i++) {
|
||
dist[i] = INF;
|
||
path[i] = source;
|
||
}
|
||
queue<int> Q;
|
||
Q.push(source);
|
||
dist[source] = 0;
|
||
visited[source] = 1;
|
||
enqueue_num[source]++;
|
||
while (!Q.empty()) {
|
||
int u = Q.front();
|
||
Q.pop();
|
||
visited[u] = 0;
|
||
for (int v = 1; v <= vertex_num; v++) {
|
||
if (matrix[u][v] != INF) //u与v直接邻接
|
||
{
|
||
if (dist[u] + matrix[u][v] < dist[v]) {
|
||
dist[v] = dist[u] + matrix[u][v];
|
||
path[v] = u;
|
||
if (!visited[v]) {
|
||
Q.push(v);
|
||
enqueue_num[v]++;
|
||
if (enqueue_num[v] >= vertex_num)
|
||
return false;
|
||
visited[v] = 1;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
void Print() {
|
||
for (int i = 1; i <= vertex_num; i++) {
|
||
if (i != source) {
|
||
int p = i;
|
||
stack<int> s;
|
||
cout << "顶点 " << source << " 到顶点 " << p << " 的最短路径是： ";
|
||
while (source != p) //路径顺序是逆向的，所以先保存到栈
|
||
{
|
||
s.push(p);
|
||
p = path[p];
|
||
}
|
||
cout << source;
|
||
while (!s.empty()) //依次从栈中取出的才是正序路径
|
||
{
|
||
cout << "--" << s.top();
|
||
s.pop();
|
||
}
|
||
cout << " 最短路径长度是：" << dist[i] << endl;
|
||
}
|
||
}
|
||
}
|
||
|
||
#pragma endregion SPFA算法模板
|
||
|
||
int main() {
|
||
//输入+输出重定向
|
||
freopen("../MiniPath/SPFA.txt", "r", stdin);
|
||
|
||
cout << "请输入图的顶点数，边数，源点：";
|
||
cin >> vertex_num >> edge_num >> source;
|
||
for (int i = 1; i <= vertex_num; i++)
|
||
for (int j = 1; j <= vertex_num; j++)
|
||
matrix[i][j] = INF; //初始化matrix数组
|
||
cout << "请输入" << edge_num << "条边的信息：\n";
|
||
int u, v, w;
|
||
for (int i = 1; i <= edge_num; i++) {
|
||
cin >> u >> v >> w;
|
||
matrix[u][v] = w;
|
||
}
|
||
if (SPFA())
|
||
Print();
|
||
else
|
||
cout << "对不起，存在负权图，不能使用本算法!" << endl;
|
||
//关闭文件
|
||
fclose(stdin);
|
||
return 0;
|
||
} |