POJ 2502 最短路
题意略。
思路：
本题有必要记录一下。首先是dijkstra求最短路没问题，关键是在建图的时候，地铁沿线还要加上行走互达的边，因为：
在本图中，AC之间的最短时间有可能不是A->B->C这么走，而是有可能从A走到C，这个地方没有考虑周全，wa了几发。
代码如下：
堆优化版：
1 #include<iostream> 2 #include<algorithm> 3 #include<cstdio> 4 #include<cstring> 5 #include<cmath> 6 #include<vector> 7 #include<queue> 8 using namespace std; 9 const int maxn = 255; 10 const int INF = 0x3f3f3f3f; 11 const double eps = 1e-6; 12 13 struct edge{ 14 int to; 15 double cost; 16 edge(int to = 0,double cost = 0){ 17 this->to = to,this->cost = cost; 18 } 19 }; 20 struct Point{ 21 double x,y; 22 Point(double x = 0,double y = 0){ 23 this->x = x,this->y = y; 24 } 25 }; 26 struct node{ 27 int v; 28 double c; 29 node(int v = 0,double c = 0){ 30 this->v = v,this->c = c; 31 } 32 }; 33 struct cmp{ 34 bool operator() (const node& n1,const node& n2){ 35 return n1.c > n2.c; 36 } 37 }; 38 39 bool vis[maxn]; 40 double dist[maxn]; 41 vector<edge> graph[maxn]; 42 priority_queue<node,vector<node>,cmp> que; 43 Point st,ed,store[maxn]; 44 int tail = 0; 45 46 double calDist(Point p1,Point p2,bool signal){ 47 double dx = p1.x - p2.x; 48 double dy = p1.y - p2.y; 49 double len = sqrt(dx * dx + dy * dy); 50 len /= 1000.0; 51 double denominator = signal ? 40.0 : 10.0; 52 double ret = len / denominator; 53 ret *= 60.0; 54 return ret; 55 } 56 int sgn(double x){ 57 if(fabs(x) < eps) return 0; 58 else if(x > 0) return 1; 59 return -1; 60 } 61 int dijkstra(){ 62 while(que.size()) que.pop(); 63 for(int i = 0;i < tail;++i) dist[i] = INF; 64 memset(vis,false,sizeof(vis)); 65 dist[0] = 0; 66 int idx = tail - 1; 67 que.push(node(0,0)); 68 while(que.size()){ 69 node temp = que.top(); 70 que.pop(); 71 int v = temp.v; 72 if(vis[v]) continue; 73 vis[v] = true; 74 for(int i = 0;i < graph[v].size();++i){ 75 edge e = graph[v][i]; 76 int to = e.to; 77 double cost = e.cost; 78 if(vis[to] || sgn(dist[to] - cost - dist[v]) <= 0) continue; 79 dist[to] = cost + dist[v]; 80 que.push(node(to,dist[to])); 81 } 82 } 83 int ret = int(dist[idx] + 0.5); 84 return ret; 85 } 86 bool Read(){ 87 double x,y; 88 bool jud = (scanf("%lf%lf",&x,&y) == 2); 89 if(!jud) return false; 90 store[tail++] = Point(x,y); 91 while(scanf("%lf%lf",&x,&y) == 2 && sgn(x + 1) != 0){ 92 store[tail++] = Point(x,y); 93 } 94 return true; 95 } 96 void add_e(int from,int to,bool signal){ 97 double cost = calDist(store[from],store[to],signal); 98 graph[from].push_back(edge(to,cost)); 99 graph[to].push_back(edge(from,cost)); 100 } 101 102 int main(){ 103 scanf("%lf%lf%lf%lf",&st.x,&st.y,&ed.x,&ed.y); 104 store[tail++] = st; 105 int keep = tail; 106 while(Read()){ 107 for(int i = keep;i < tail - 1;++i){ 108 add_e(i,i + 1,true); 109 } 110 for(int i = keep;i < tail;++i) 111 for(int j = 0;j < i;++j) 112 add_e(i,j,false); 113 keep = tail; 114 } 115 store[tail++] = ed; 116 int idx = tail - 1; 117 for(int i = 0;i < idx;++i) add_e(idx,i,false); 118 int ans = dijkstra(); 119 printf("%d\n",ans); 120 return 0; 121 }
普通Dijkstra:
#include<iostream> #include<algorithm> #include<cstdio> #include<cstring> #include<vector> #include<cmath> using namespace std; const int maxn = 255; const double v1 = 10000; const double v2 = 40000; const double INF = 0x3f3f3f3f; const double eps = 1e-6; struct edge{ int to; double cost; edge(int to,double cost = 0){ this->to = to,this->cost = cost; } }; struct Point{ double x,y; Point(double x = 0,double y = 0){ this->x = x,this->y = y; } }; Point store[maxn],st,ed; vector<edge> graph[maxn]; double dist[maxn]; bool vis[maxn]; int tail = 0; int sgn(double x){ if(fabs(x) < eps) return 0; else if(x > 0) return 1; return -1; } double calDist(Point p1,Point p2){ double dx = p1.x - p2.x; double dy = p1.y - p2.y; return sqrt(dx * dx + dy * dy); } void add_e(int from,int to,double cost){ graph[from].push_back(edge(to,cost)); graph[to].push_back(edge(from,cost)); } int Dijkstra(){ for(int i = 0;i < tail;++i){ vis[i] = false; dist[i] = INF; } int cnt = tail; dist[0] = 0; while(cnt > 0){ int idx = -1; for(int i = 0;i < tail;++i){ if(vis[i]) continue; if(idx == -1 || sgn(dist[idx] - dist[i]) > 0) idx = i; } vis[idx] = true; --cnt; for(int i = 0;i < graph[idx].size();++i){ edge e = graph[idx][i]; int to = e.to; double cost = e.cost; if(vis[to] || sgn(dist[to] - dist[idx] - cost) <= 0) continue; dist[to] = dist[idx] + cost; } } int ret = int(dist[tail - 1] + 0.5); return ret; } bool Read(){ double x,y; bool jud = (scanf("%lf%lf",&x,&y) == 2); if(!jud) return false; store[tail++] = Point(x,y); while(scanf("%lf%lf",&x,&y) == 2 && sgn(x + 1) != 0){ store[tail++] = Point(x,y); } return true; } int main(){ scanf("%lf%lf%lf%lf",&st.x,&st.y,&ed.x,&ed.y); tail = 0; store[tail++] = st; int keep = tail; while(Read()){ for(int i = keep;i < tail - 1;++i){ double c = calDist(store[i],store[i + 1]) / v2 * 60.0; add_e(i,i + 1,c); } for(int i = keep;i < tail;++i){ for(int j = 0;j < i;++j){ double c = calDist(store[i],store[j]) / v1 * 60.0; add_e(i,j,c); } } keep = tail; } store[tail++] = ed; int idx = tail - 1; for(int i = 0;i < idx;++i){ double c = calDist(store[idx],store[i]) / v1 * 60.0; add_e(idx,i,c); } int ans = Dijkstra(); printf("%d\n",ans); return 0; }
