洛谷P3094 [USACO13DEC]假期计划Vacation Planning
题目描述
有N(1 <= N <= 200)个农场,用1..N编号。航空公司计划在农场间建立航线。对于任意一条航线,选择农场1..K中的农场作为枢纽(1 <= K <= 100, K <= N)。
当前共有M (1 <= M <= 10,000)条单向航线连接这些农场,从农场u_i 到农场 v_i, 将花费 d_i美元。(1 <= d_i <= 1,000,000).
航空公司最近收到Q (1 <= Q <= 10,000)个单向航行请求。第i个航行请求是从农场a_i到农场 b_i,航行必须经过至少一个枢纽农场(可以是起点或者终点农场),因此可能会多次经过某些农场。
请计算可行航行请求的数量,及完成所有可行请求的总费用。
输入输出格式
输入格式:
-
Line 1: Four integers: N, M, K, and Q.
-
Lines 2..1+M: Line i+1 contains u_i, v_i, and d_i for flight i.
- Lines 2+M..1+M+Q: Line 1+M+i describes the ith trip in terms of a_i and b_i
输出格式:
-
Line 1: The number of trips (out of Q) for which a valid route is possible.
- Line 2: The sum, over all trips for which a valid route is possible, of the minimum possible route cost.
输入输出样例
3 3 1 3 3 1 10 1 3 10 1 2 7 3 2 2 3 1 2
2 24
说明
There are three farms (numbered 1..3); farm 1 is a hub. There is a $10 flight from farm 3 to farm 1, and so on. We wish to look for trips from farm 3 to farm 2, from 2->3, and from 1->2.
The trip from 3->2 has only one possible route, of cost 10+7. The trip from 2->3 has no valid route, since there is no flight leaving farm 2. The trip from 1->2 has only one valid route again, of cost 7.
floyd求出最短路,对于每个询问枚举枢纽找最小花费。
1 /*by SilverN*/ 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<cstdio> 6 #include<cmath> 7 using namespace std; 8 const int mxn=300; 9 int read(){ 10 int x=0,f=1;char ch=getchar(); 11 while(ch<'0' || ch>'9'){if(ch=='-')f=-1;ch=getchar();} 12 while(ch>='0' && ch<='9'){x=x*10+ch-'0';ch=getchar();} 13 return x*f; 14 } 15 int mp[mxn][mxn]; 16 int n,m,k,Q; 17 18 int main(){ 19 memset(mp,0x3f,sizeof mp); 20 n=read();m=read();k=read();Q=read(); 21 int i,j; 22 int u,v,d; 23 for(i=1;i<=m;i++){ 24 u=read();v=read();d=read(); 25 mp[u][v]=min(mp[u][v],d); 26 } 27 for(int e=1;e<=n;e++) 28 for(i=1;i<=n;i++) 29 for(j=1;j<=n;j++){ 30 if(i==j)mp[i][j]=0; 31 else mp[i][j]=min(mp[i][j],mp[i][e]+mp[e][j]); 32 } 33 long long ans=0;int cnt=0; 34 while(Q--){ 35 u=read();v=read(); 36 d=0x3f3f3f3f; 37 for(i=1;i<=k;i++){ 38 d=min(d,mp[u][i]+mp[i][v]); 39 } 40 if(d<0x3f3f3f3f){ 41 cnt++; 42 ans+=d; 43 } 44 } 45 printf("%d\n%lld\n",cnt,ans); 46 return 0; 47 }