单元最短路径问题
1 #include <iostream> 2 #include <string> 3 #include <vector> 4 #include <cstdlib> 5 #include <cmath> 6 #include <map> 7 #include <algorithm> 8 #include <list> 9 #include <ctime> 10 #include <set> 11 #include <string.h> 12 #include <queue> 13 #include <cstdio> 14 using namespace std; 15 typedef double typep; 16 //int maxData = 0x3fffffff; 17 double maxData = 0; 18 19 bool relax(typep u, typep& v, typep w, typep com) { 20 if (v < ((u - com) * w)) { 21 v = ((u - com) * w); 22 return true; 23 } else 24 return false; 25 } 26 27 bool bellman_ford(int s, vector<typep> &d, vector<vector<typep> > path, 28 vector<vector<typep> > commssion) { 29 int n = d.size(); 30 int i, j, k; 31 bool judge; 32 33 for (i = 0; i < n - 1; i++) { 34 for (j = 0; j < n; j++) { 35 for (k = 0; k < n; k++) { 36 judge = relax(d[j], d[k], path[j][k], commssion[j][k]); 37 } 38 } 39 } 40 41 for (j = 0; j < n; j++) { 42 for (k = 0; k < n; k++) { 43 judge = relax(d[j], d[k], path[j][k], commssion[j][k]); 44 if (judge) { 45 return true; 46 } 47 48 } 49 } 50 51 return false; 52 } 53 54 bool SPFA(int s, vector<typep> &d, vector<vector<typep> > path, 55 vector<vector<typep> > commssion) { 56 int n = d.size(); 57 queue<int> myqueue; 58 int i; 59 vector<bool> final(n, false); //记录顶点是否在队列中，SPFA算法可以入队列多次 60 vector<int> cnt(n, 0); //记录顶点入队列次数 61 final[s] = true; 62 cnt[s]++; //源点的入队列次数增加 63 myqueue.push(s); 64 int topint; 65 bool judge; 66 while (!myqueue.empty()) { 67 topint = myqueue.front(); 68 myqueue.pop(); 69 final[topint] = false; 70 for (i = 0; i < n; ++i) { 71 if (d[topint] > maxData) { 72 judge = relax(d[topint], d[i], path[topint][i], 73 commssion[topint][i]); 74 if (judge) { 75 if (!final[i]) { //判断是否在当前的队列中 76 final[i] = true; 77 cnt[i]++; 78 if (cnt[i] >= n) //当一个点入队的次数>=n时就证明出现了负环。 79 return true; 80 myqueue.push(i); 81 } 82 } 83 } 84 } 85 } 86 return false; 87 } 88 89 int main() { 90 int n, m, s; 91 double v; 92 scanf("%d %d %d %lf", &n, &m, &s, &v); 93 s--; 94 vector<vector<typep> > path(n, vector<typep>(n, maxData)); 95 vector<vector<typep> > commssion(n, vector<typep>(n, maxData)); 96 int a, b; 97 double rab, cab, rba, cba; 98 for (int i = 0; i < m; i++) { 99 scanf("%d %d %lf %lf %lf %lf", &a, &b, &rab, &cab, &rba, &cba); 100 a--; 101 b--; 102 path[a][b] = rab; 103 path[b][a] = rba; 104 commssion[a][b] = cab; 105 commssion[b][a] = cba; 106 } 107 vector<typep> d(n, maxData); 108 d[s] = v; 109 // int judge = bellman_ford(s, d, path, commssion); 110 int judge = SPFA(s, d, path, commssion); 111 if (judge) 112 cout << "YES" << endl; 113 else 114 cout << "NO"; 115 return 0; 116 117 }