洛谷——P2935 [USACO09JAN]最好的地方Best Spot
P2935 [USACO09JAN]最好的地方Best Spot
題目描述
Bessie, always wishing to optimize her life, has realized that she really enjoys visiting F (1 <= F <= P) favorite pastures F_i of the P (1 <= P <= 500; 1 <= F_i <= P) total pastures (conveniently
numbered 1..P) that compose Farmer John‘s holdings.
Bessie knows that she can navigate the C (1 <= C <= 8,000) bidirectional cowpaths (conveniently numbered 1..C) that connect various pastures to travel to any pasture on the entire farm. Associated with each path P_i is a time T_i (1 <= T_i <= 892) to traverse that path (in either direction) and two path endpoints a_i and b_i (1 <= a_i <= P; 1 <= b_i <= P).
Bessie wants to find the number of the best pasture to sleep in so that when she awakes, the average time to travel to any of her F favorite pastures is minimized.
By way of example, consider a farm laid out as the map below shows, where *‘d pasture numbers are favorites. The bracketed numbers are times to traverse the cowpaths.
1*--[4]--2--[2]--3
| |
[3] [4]
| |
4--[3]--5--[1]---6---[6]---7--[7]--8*
| | | |
[3] [2] [1] [3]
| | | |
13* 9--[3]--10*--[1]--11*--[3]--12*The following table shows distances for potential ‘best place‘ of pastures 4, 5, 6, 7, 9, 10, 11, and 12:
* * * * * * Favorites * * * * * *
Potential Pasture Pasture Pasture Pasture Pasture Pasture Average
Best Pasture 1 8 10 11 12 13 Distance
------------ -- -- -- -- -- -- -----------
4 7 16 5 6 9 3 46/6 = 7.67
5 10 13 2 3 6 6 40/6 = 6.67
6 11 12 1 2 5 7 38/6 = 6.33
7 16 7 4 3 6 12 48/6 = 8.00
9 12 14 3 4 7 8 48/6 = 8.00
10 12 11 0 1 4 8 36/6 = 6.00 ** BEST
11 13 10 1 0 3 9 36/6 = 6.00
12 16 13 4 3 0 12 48/6 = 8.00
Thus, presuming these choices were the best ones (a program would have to check all of them somehow), the best place to sleep is pasture 10.
約翰擁有P(1<=P<=500)個牧場.貝茜特別喜歡其中的F個.所有的牧場 由C(1 < C<=8000)條雙向路連接，第i路連接著ai,bi，需要1(1<=Ti< 892)單 位時間來通過.
作為一只總想優化自己生活方式的奶牛，貝茜喜歡自己某一天醒來，到達所有那F個她喜歡的 牧場的平均需時最小.那她前一天應該睡在哪個牧場呢？請幫助貝茜找到這個最佳牧場.
此可見，牧場10到所有貝茜喜歡的牧場的平均距離最小，為最佳牧場.
輸入輸出格式
輸入格式：
-
Line 1: Three space-separated integers: P, F, and C
-
Lines 2..F+1: Line i+2 contains a single integer: F_i
- Lines F+2..C+F+1: Line i+F+1 describes cowpath i with three
space-separated integers: a_i, b_i, and T_i
輸出格式：
- Line 1: A single line with a single integer that is the best pasture in which to sleep. If more than one pasture is best, choose the smallest one.
輸入輸出樣例
輸入樣例#1：13 6 15 11 13 10 12 8 1 2 4 3 7 11 3 10 11 1 4 13 3 9 10 3 2 3 2 3 5 4 5 9 2 6 7 6 5 6 1 1 2 4 4 5 3 11 12 3 6 10 1 7 8 7輸出樣例#1：
10
說明
As the problem statement
As the problem statement.
代碼：
#include<cstdio> #include<cstdlib> #include<cstring> #include<iostream> #include<algorithm> #define N 501 #define maxn 999999 using namespace std; int n,m,t,x,y,z,s=maxn,ans,maxx,a[N],dis[N][N]; int read() { int x=0,f=1; char ch=getchar(); while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1; ch=getchar();} while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘; ch=getchar();} return x*f; } int main() { n=read(),t=read(),m=read(); for(int i=1;i<=t;i++) a[i]=read(); for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) dis[i][j]=(i!=j)*maxn; for(int i=1;i<=m;i++) x=read(),y=read(),z=read(),dis[x][y]=z,dis[y][x]=z; for(int k=1;k<=n;k++) for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) if (dis[i][j]>dis[i][k]+dis[k][j]) dis[i][j]=dis[i][k]+dis[k][j]; for(int i=1;i<=n;i++) { maxx=0; for(int j=1;j<=t;j++) maxx+=dis[i][a[j]]; if(s>maxx) s=maxx,ans=i; } printf("%d",ans); }
洛谷——P2935 [USACO09JAN]最好的地方Best Spot