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Hdu 2389 二分匹配

2024-07-15 09:25:14   228人阅读

题目链接

Rain on your Parade

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 655350/165535 K (Java/Others)
Total Submission(s): 2644    Accepted Submission(s): 823


Problem Description
You’re giving a party in the garden of your villa by the sea. The party is a huge success, and everyone is here. It’s a warm, sunny evening, and a soothing wind sends fresh, salty air from the sea. The evening is progressing just as you had imagined. It could be the perfect end of a beautiful day.
But nothing ever is perfect. One of your guests works in weather forecasting. He suddenly yells, “I know that breeze! It means its going to rain heavily in just a few minutes!” Your guests all wear their best dresses and really would not like to get wet, hence they stand terrified when hearing the bad news.
You have prepared a few umbrellas which can protect a few of your guests. The umbrellas are small, and since your guests are all slightly snobbish, no guest will share an umbrella with other guests. The umbrellas are spread across your (gigantic) garden, just like your guests. To complicate matters even more, some of your guests can’t run as fast as the others.
Can you help your guests so that as many as possible find an umbrella before it starts to pour? 

Given the positions and speeds of all your guests, the positions of the umbrellas, and the time until it starts to rain, find out how many of your guests can at most reach an umbrella. Two guests do not want to share an umbrella, however. 

 

Input
The input starts with a line containing a single integer, the number of test cases.
Each test case starts with a line containing the time t in minutes until it will start to rain (1 <=t <= 5). The next line contains the number of guests m (1 <= m <= 3000), followed by m lines containing x- and y-coordinates as well as the speed si in units per minute (1 <= si <= 3000) of the guest as integers, separated by spaces. After the guests, a single line contains n (1 <= n <= 3000), the number of umbrellas, followed by n lines containing the integer coordinates of each umbrella, separated by a space.
The absolute value of all coordinates is less than 10000.

 

Output
For each test case, write a line containing “Scenario #i:”, where i is the number of the test case starting at 1. Then, write a single line that contains the number of guests that can at most reach an umbrella before it starts to rain. Terminate every test case with a blank line.

 

Sample Input
2121 0 33 0 324 06 0121 1 23 3 222 24 4

 

Sample Output
Scenario #1:2Scenario #2:2
 题目也是很裸的最大匹配问题，匈牙利算法复杂度太高（对于这题而言, O(n*m)）, 而Hopcroft-Karp算法复杂度只有O(sqrt(n)*m).关于算法的具体实现，
网上百度一大推。1A......:D
Accepted Code:
  1 /*************************************************************************  2     > File Name: 2389.cpp  3     > Author: Stomach_ache  4     > Mail: sudaweitong@gmail.com  5     > Created Time: 2014年08月01日 星期五 22时08分50秒  6     > Propose: Hopcroft-Karp  7  ************************************************************************/  8 #include <queue>  9 #include <cmath> 10 #include <string> 11 #include <cstdio> 12 #include <vector> 13 #include <fstream> 14 #include <cstring> 15 #include <iostream> 16 #include <algorithm> 17 using namespace std; 18  19 const int maxn = 3002; 20 const int INF = 0x3f3f3f3f; 21 int cx[maxn], cy[maxn]; 22 int dx[maxn], dy[maxn]; 23 bool mark[maxn]; 24 vector<int> next[maxn]; 25 int n, m; 26 struct node { 27       int x, y, s; 28 }g[maxn]; 29  30 int dist(int x1, int y1, int x2, int y2) { 31       return (x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2); 32 } 33  34 int searchPath() { 35       memset(dx, -1, sizeof(dx)); 36     memset(dy, -1, sizeof(dy)); 37     queue<int> Q; 38     for (int i = 1; i <= m; i++) if (cx[i] == -1) { 39           dx[i] = 0; 40         Q.push(i); 41     } 42     int dist = INF; 43     while (!Q.empty()) { 44           int u = Q.front(); Q.pop(); 45         if (dx[u] > dist) break; 46         for (int i = 0; i < (int)next[u].size(); i++) { 47               int v = next[u][i]; 48               if (dy[v] == -1) { 49                   dy[v] = dx[u] + 1; 50                 if (cy[v] == -1) { 51                       dist = dy[v]; 52                 } else { 53                       dx[cy[v]] = dy[v] + 1; 54                     Q.push(cy[v]); 55                 } 56             } 57         } 58     } 59     return dist != INF; 60 } 61  62 int findPath(int u) { 63       for (int i = 0; i < (int)next[u].size(); i++) { 64           int v = next[u][i]; 65         if (!mark[v] && dy[v] == dx[u] + 1) { 66               mark[v] = true; 67             if (cy[v] == -1 || findPath(cy[v])) { 68                   cy[v] = u; 69                 cx[u] = v; 70                 return 1; 71             } 72         } 73     } 74     return 0; 75 } 76  77 int MaxMatch() { 78       int res = 0; 79       memset(cx, -1, sizeof(cx)); 80     memset(cy, -1, sizeof(cy)); 81     while (searchPath()) { 82           memset(mark, false, sizeof(mark)); 83         for (int i = 1; i <= m; i++) { 84               if (cx[i] == -1) { 85                   res += findPath(i); 86             } 87         } 88     } 89     return res; 90 } 91  92 int main(void) { 93       int T, cas = 1; 94     scanf("%d", &T); 95     while (T--) { 96           int t; 97           scanf("%d", &t); 98         scanf("%d", &m); 99         for (int i = 1; i <= m; i++) {100               next[i].clear();101               scanf("%d %d %d", &g[i].x, &g[i].y, &g[i].s);102         }103         scanf("%d", &n);104         for (int i = 1; i <= n; i++) {105               int x, y;106             scanf("%d %d", &x, &y);107             for (int j = 1; j <= m; j++) {108                   if (t*t*g[j].s*g[j].s >= dist(x, y, g[j].x, g[j].y)) {109                       next[j].push_back(i);110                 }111             }112         }113         printf("Scenario #%d:\n%d\n\n", cas++, MaxMatch());114     }115 116     return 0;117 }

 


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