find the safest road

Problem Description

XX星球有很多城市，每个城市之间有一条或多条飞行通道，但是并不是所有的路都是很安全的，每一条路有一个安全系数s,s是在 0 和 1 间的实数(包括0，1)，一条从u 到 v 的通道P 的安全度为Safe(P) = s(e1)*s(e2)…*s(ek) e1,e2,ek是P 上的边 ，现在8600 想出去旅游，面对这这么多的路，他想找一条最安全的路。但是8600 的数学不好，想请你帮忙 ^_^

 

Input

输入包括多个测试实例，每个实例包括：
第一行：n。n表示城市的个数n<=1000;
接着是一个n*n的矩阵表示两个城市之间的安全系数，(0可以理解为那两个城市之间没有直接的通道)
接着是Q个8600要旅游的路线,每行有两个数字，表示8600所在的城市和要去的城市

 

Output

如果86无法达到他的目的地，输出"What a pity!",
其他的输出这两个城市之间的最安全道路的安全系数,保留三位小数。

 

Sample Input

31 0.5 0.50.5 1 0.40.5 0.4 131 22 31 3

 

Sample Output

0.5000.4000.500

SPFA:

#include <iostream>#include <cstdio>#include <cstring>#include <queue>using namespace std;double map[1003][1003];double d[1003];bool inQueue[1003];void spfa(int n,int x){memset(d,0,sizeof(d));d[x] = 1;queue<int> q;q.push(x);inQueue[x] = true;while(!q.empty()){int p = q.front();q.pop();inQueue[p] = false;for(int i = 1;i <= n;i++){if(d[i] < d[p] * map[p][i]){d[i] = d[p] * map[p][i];if(!inQueue[i]){inQueue[i] = true;q.push(i);}}}}}int main(){int n;while(scanf("%d",&n) != EOF){for(int i = 1;i <= n;i++){for(int j = 1;j <= n;j++){scanf("%lf",&map[i][j]);}}int q;cin>>q;while(q--){int u,v;scanf("%d%d",&u,&v);spfa(n,u);if(d[v] == 0){printf("What a pity!\n");}else{printf("%.3lf\n",d[v]);}}}return 0; } 

dijstra:

#include <iostream>#include <cstdio>#include <cstring>using namespace std;const double INF = 99999999.0;double map[1003][1003];double d[1003];bool visited[1003];void djistra(int n,int x){memset(visited,false,sizeof(visited));for(int i = 1;i <= n;i++){d[i] = map[x][i];}visited[x] = true;d[x] = 1;for(int i = 1;i < n;i++){double min = -1;int k;for(int j = 1;j <= n;j++){if(!visited[j] && min < d[j] && d[j] != 0){min = d[j];k = j;}}visited[k] = true;if(min == -1){break;}for(int j = 1;j <= n;j++){if(!visited[j] && d[j] < d[k] * map[k][j]){d[j] = d[k] * map[k][j];}}}}int main(){int n;while(scanf("%d",&n) != EOF){for(int i = 1;i <= n;i++){for(int j = 1;j <= n;j++){scanf("%lf",&map[i][j]);}}int q;cin>>q;int u,v;while(q--){scanf("%d%d",&u,&v);djistra(n,u);if(d[v] == 0){printf("What a pity!\n");}else{printf("%.3lf\n",d[v]);}}}return 0; } dijstra+堆优化：<pre name="code" class="cpp">#include <iostream>#include <cstdio>#include <cstring>#include <queue>using namespace std;double map[1003][1003];double d[1003];bool visited[1003];struct Node{int to;double safe;Node(int a,double b){to = a;safe = b;}bool operator< (Node t) const{return safe > t.safe;}};void dijstra(int n,int x){memset(visited,false,sizeof(visited));memset(d,0,sizeof(d));d[x] = 1;priority_queue<Node> q;q.push(Node(x,1));while(!q.empty()){Node p = q.top();q.pop();if(!visited[p.to]){for(int i = 1;i <= n;i++){if(!visited[i] && d[i] < d[p.to] * map[p.to][i]){d[i] = d[p.to] * map[p.to][i];q.push(Node(i,d[i]));}}}}}int main(){int n;while(scanf("%d",&n) != EOF){for(int i = 1;i <= n;i++){for(int j = 1;j <= n;j++){scanf("%lf",&map[i][j]);}}int q;scanf("%d",&q);while(q--){int u,v;scanf("%d%d",&u,&v);dijstra(n,u);if(d[v] == 0){printf("What a pity!\n");}else{printf("%.3lf\n",d[v]);}}}return 0;}

弗洛伊德：

#include <iostream>#include <cstdio>#include <cstring>#include <queue>using namespace std;double d[1003][1003];void floyd(int n){for(int k = 1;k <= n;k++){for(int i = 1;i <= n;i++){for(int j = 1;j <= n;j++){if(d[i][j] < d[i][k] * d[k][j]){d[i][j] = d[i][k] * d[k][j];}}}}}int main(){int n;while(scanf("%d",&n) != EOF){for(int i = 1;i <= n;i++){for(int j = 1;j <= n;j++){scanf("%lf",&d[i][j]);}}int q;scanf("%d",&q);floyd(n);while(q--){int u,v;scanf("%d%d",&u,&v);if(d[u][v] == 0.0){printf("What a pity!\n");}else{printf("%.3lf\n",d[u][v]);}}}return 0; }