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  • [HDOJ1054]Strategic Game(最小点覆盖,最大二分匹配,HK算法)

    题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=1054

    题意:给一棵树,选几个节点,使得这个节点相连的所有边都能被走到。求最少的点数。

    这就是最小点覆盖的原始定义,根据König定理,最小点覆盖=最大匹配数可求。应该是点太稀疏了,用邻接矩阵的匈牙利会TLE。。

      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 Rs(a) scanf("%s", a)
     44 #define Cin(a) cin >> a
     45 #define FRead() freopen("in", "r", stdin)
     46 #define FWrite() freopen("out", "w", stdout)
     47 #define Rep(i, len) for(int i = 0; i < (len); i++)
     48 #define For(i, a, len) for(int i = (a); i < (len); i++)
     49 #define Cls(a) memset((a), 0, sizeof(a))
     50 #define Clr(a, x) memset((a), (x), sizeof(a))
     51 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
     52 #define lrt rt << 1
     53 #define rrt rt << 1 | 1
     54 #define pi 3.14159265359
     55 #define RT return
     56 #define lowbit(x) x & (-x)
     57 #define onecnt(x) __builtin_popcount(x)
     58 typedef long long LL;
     59 typedef long double LD;
     60 typedef unsigned long long ULL;
     61 typedef pair<int, int> pii;
     62 typedef pair<string, int> psi;
     63 typedef pair<LL, LL> pll;
     64 typedef map<string, int> msi;
     65 typedef vector<int> vi;
     66 typedef vector<LL> vl;
     67 typedef vector<vl> vvl;
     68 typedef vector<bool> vb;
     69 
     70 const int maxn = 1530;
     71 const int inf = 0x3f3f3f3f;
     72 int n;
     73 int nx, ny, dist;
     74 int Mx[maxn], My[maxn], dx[maxn], dy[maxn], vis[maxn], G[maxn][maxn];
     75 
     76 bool dfs(int u){
     77   for(int v = 0; v < ny; v++)
     78     if(!vis[v] && G[u][v] && dy[v] == dx[u] + 1){
     79       vis[v] = 1;
     80       if(My[v] != -1 && dy[v] == dist)
     81         continue;
     82       if(My[v] == -1|| dfs(My[v])){
     83         My[v] = u;
     84         Mx[u] = v;
     85         return 1;
     86       }
     87     }
     88   return 0;
     89 }
     90 bool bfs(){
     91   queue<int> Q;
     92   dist = inf;
     93   memset(dx, -1, sizeof(dx));
     94   memset(dy, -1, sizeof(dy));
     95   for(int i = 0; i < nx; i++)
     96     if(Mx[i] == -1){
     97       Q.push(i);
     98       dx[i] = 0;
     99     }
    100   while(!Q.empty()){
    101     int u = Q.front();
    102     Q.pop();
    103     if(dx[u] > dist)
    104       break;
    105     for(int v = 0; v < ny; v++)
    106       if(G[u][v] && dy[v] == -1){
    107         dy[v] = dx[u] + 1;
    108         if(My[v] == -1)
    109           dist = dy[v];
    110         else{
    111           dx[My[v]] = dy[v] + 1;
    112           Q.push(My[v]); 
    113         }
    114       } 
    115   }
    116   return dist != inf;
    117 }
    118 int hk() {
    119   int res = 0;
    120   memset(Mx, -1, sizeof(Mx));
    121   memset(My, -1, sizeof(My));
    122   while(bfs()){
    123     memset(vis, 0, sizeof(vis));
    124     for(int i = 0; i < nx; i++)
    125       if(Mx[i] == -1&& dfs(i))
    126         res++;
    127   }
    128   return res;
    129 }
    130 
    131 
    132 int main() {
    133     // FRead();
    134     int u, v, k;
    135     while(~Rint(n)) {
    136         nx = ny = n; Cls(G);
    137         Rep(i, n) {
    138             scanf("%d:(%d)", &u, &k);
    139             Rep(i, k) {
    140                 Rint(v);
    141                 G[u][v] = G[v][u] = 1;
    142             }
    143         }
    144         printf("%d
    ", hk()/2);
    145     }
    146     RT 0;
    147 }
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  • 原文地址:https://www.cnblogs.com/kirai/p/5806515.html
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