[HDOJ2389]Rain on your Parade（二分图最大匹配，HK算法）

题目链接：http://acm.split.hdu.edu.cn/showproblem.php?pid=2389

题意：一个人请了m个人在院子里聚会，每个人有位置坐标和速度。院子里有n把伞，给出伞的位置。现在要下雨了，所有人应该在k秒内拿到伞，问如何拿伞能让尽可能多的人拿到伞，每把伞只能有一个人打。

以每个人到某把伞的时间是否在限定时间内来建立二分图，之后跑最大匹配就行。这里有一个问题出在了点的数量是3000，在点数量较大的情况下使用一般的匈牙利和KM算法会TLE，所以学习到了使用HK算法，尽管我暂时还不知道HK算法的具体解决问题的思路和方法，但是我会用板子…

  1 /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%I64d", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 53 #define lrt rt << 1
 54 #define rrt rt << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onecnt(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef pair<LL, LL> pll;
 65 typedef map<string, int> msi;
 66 typedef vector<int> vi;
 67 typedef vector<LL> vl;
 68 typedef vector<vl> vvl;
 69 typedef vector<bool> vb;
 70 const int maxn = 3030;
 71 const int inf = 0x3f3f3f3f;
 72 int nx, ny, dist;
 73 int Mx[maxn], My[maxn], dx[maxn], dy[maxn], vis[maxn], G[maxn][maxn];
 74 
 75 bool Dfs(int u){
 76     for(int v = 0; v < ny; v++)
 77         if(!vis[v] && G[u][v] && dy[v] == dx[u] + 1){
 78             vis[v] = 1;
 79             if(My[v] != -1 && dy[v] == dist)
 80                 continue;
 81             if(My[v] == -1|| Dfs(My[v])){
 82                 My[v] = u;
 83                 Mx[u] = v;
 84                 return 1;
 85             }
 86         }
 87     return 0;
 88 }
 89 bool Search(){
 90     queue<int> Q;
 91     dist = inf;
 92     memset(dx, -1, sizeof(dx));
 93     memset(dy, -1, sizeof(dy));
 94     for(int i = 0; i < nx; i++)
 95         if(Mx[i] == -1){
 96             Q.push(i);
 97             dx[i] = 0;
 98         }
 99     while(!Q.empty()){
100         int u = Q.front();
101         Q.pop();
102         if(dx[u] > dist)
103             break;
104         for(int v = 0; v < ny; v++)
105             if(G[u][v] && dy[v] == -1){
106                 dy[v] = dx[u] + 1;
107                 if(My[v] == -1)
108                     dist = dy[v];
109                 else{
110                     dx[My[v]] = dy[v] + 1;
111                     Q.push(My[v]); 
112                 }
113             } 
114     }
115     return dist != inf;
116 }
117 int MaxMatch() {
118     int res = 0;
119     memset(Mx, -1, sizeof(Mx));
120     memset(My, -1, sizeof(My));
121     while(Search()){
122         memset(vis, 0, sizeof(vis));
123         for(int i = 0; i < nx; i++)
124             if(Mx[i] == -1&& Dfs(i))
125                 res++;
126     }
127     return res;
128 }
129 int n, m, k;
130 typedef struct Node {
131     double x, y, v;
132 }Node;
133 Node num[maxn], pos[maxn];
134 
135 double dis(Node a, Node b) {
136     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
137 }
138 
139 inline bool scan_lf(double &num) {
140     char in;double Dec=0.1;
141     bool IsN=false,IsD=false;
142     in=getchar();
143     if(in==EOF) return false;
144     while(in!='-'&&in!='.'&&(in<'0'||in>'9'))
145             in=getchar();
146     if(in=='-'){IsN=true;num=0;}
147     else if(in=='.'){IsD=true;num=0;}
148     else num=in-'0';
149     if(!IsD){
150             while(in=getchar(),in>='0'&&in<='9'){
151                     num*=10;num+=in-'0';}
152     }
153     if(in!='.'){
154             if(IsN) num=-num;
155             return true;
156     }else{
157             while(in=getchar(),in>='0'&&in<='9'){
158                     num+=Dec*(in-'0');Dec*=0.1;
159             }
160     }
161     if(IsN) num=-num;
162     return true;
163 }
164 inline bool scan_d(int &num) {
165     char in;bool IsN=false;
166     in=getchar();
167     if(in==EOF) return false;
168     while(in!='-'&&(in<'0'||in>'9')) in=getchar();
169     if(in=='-'){ IsN=true;num=0;}
170     else num=in-'0';
171     while(in=getchar(),in>='0'&&in<='9'){
172             num*=10,num+=in-'0';
173     }
174     if(IsN) num=-num;
175     return true;
176 }
177 
178 int main() {
179     // FRead();
180     int T, _ = 1;
181     scan_d(T);
182     W(T) {
183         Cls(G);
184         scan_d(k); scan_d(m);
185         Rep(i, m) {
186             scan_lf(num[i].x);
187             scan_lf(num[i].y);
188             scan_lf(num[i].v);
189         }
190         Rint(n);
191         Rep(i, n) {
192             scan_lf(pos[i].x);
193             scan_lf(pos[i].y);
194         }
195         nx = m; ny = n;
196         Rep(i, m) {
197             Rep(j, n) {
198                 if(dis(num[i], pos[j]) / num[i].v <= k) {
199                     G[i][j] = 1;
200                 }
201             }
202         }
203         printf("Scenario #%d:\n%d\n\n", _++, MaxMatch());
204     }
205     RT 0;
206 }

 

posted @ 2016-08-24 20:52  Kirai  阅读(539)  评论(0)  编辑  收藏  举报