HDOJ1914 The Stable Marriage Problem

Posted 2020-06-13

稳定婚姻问题，Gale-Shapley算法可解。

  1 /* 1914 */
  2 #include <iostream>
  3 #include <sstream>
  4 #include <string>
  5 #include <map>
  6 #include <queue>
  7 #include <set>
  8 #include <stack>
  9 #include <vector>
 10 #include <deque>
 11 #include <algorithm>
 12 #include <cstdio>
 13 #include <cmath>
 14 #include <ctime>
 15 #include <cstring>
 16 #include <climits>
 17 #include <cctype>
 18 #include <cassert>
 19 #include <functional>
 20 #include <iterator>
 21 #include <iomanip>
 22 using namespace std;
 23 //#pragma comment(linker,"/STACK:102400000,1024000")
 24 
 25 #define sti                set<int>
 26 #define stpii            set<pair<int, int> >
 27 #define mpii            map<int,int>
 28 #define vi                vector<int>
 29 #define pii                pair<int,int>
 30 #define vpii            vector<pair<int,int> >
 31 #define rep(i, a, n)     for (int i=a;i<n;++i)
 32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 33 #define clr                clear
 34 #define pb                 push_back
 35 #define mp                 make_pair
 36 #define fir                first
 37 #define sec                second
 38 #define all(x)             (x).begin(),(x).end()
 39 #define SZ(x)             ((int)(x).size())
 40 #define lson            l, mid, rt<<1
 41 #define rson            mid+1, r, rt<<1|1
 42 
 43 const int maxn = 30;
 44 char s[40];
 45 char wname[40];
 46 int pref[maxn][maxn];
 47 int order[maxn][maxn];
 48 int nxt[maxn];
 49 int future_husband[maxn];
 50 int future_wife[maxn];
 51 queue<int> Q;
 52 int n;
 53 int ID[128];
 54 
 55 void engage(int man, int woman) {
 56     int m = future_husband[woman];
 57     
 58     if (m) {
 59         future_wife[m] = 0;
 60         Q.push(m);
 61     }
 62     
 63     future_husband[woman] = man;
 64     future_wife[man] = woman;
 65 }
 66 
 67 void solve() {
 68     while (!Q.empty()) {
 69         int man = Q.front();
 70         Q.pop();
 71         int woman = pref[man][nxt[man]++];
 72         if (!future_husband[woman]) {
 73             engage(man, woman);
 74         } else if (order[woman][man] < order[woman][future_husband[woman]]) {
 75             engage(man, woman);
 76         } else {
 77             Q.push(man);
 78         }
 79     }
 80     
 81     rep(i, ‘a‘, ‘z‘+1) {
 82         if (!ID[i])
 83             continue;
 84         printf("%c %c\n", i, wname[future_wife[ID[i]]]);
 85     }
 86 }
 87 
 88 int main() {
 89     ios::sync_with_stdio(false);
 90     #ifndef ONLINE_JUDGE
 91         freopen("data.in", "r", stdin);
 92         freopen("data.out", "w", stdout);
 93     #endif
 94     
 95     int t;
 96     int nlc, nuc;
 97     
 98     scanf("%d", &t);
 99     while (t--) {
100         scanf("%d", &n);
101         memset(ID, 0, sizeof(ID));
102         nlc = nuc = 0;
103         rep(i, 0, n+n) {
104             scanf("%s", s);
105             if (islower(s[0])) {
106                 ID[s[0]] = ++nlc;
107             } else {
108                 ID[s[0]] = ++nuc;
109                 wname[nuc] = s[0];
110             }
111         }
112         
113         while (!Q.empty())
114             Q.pop();
115         
116         int lid, uid;
117         
118         rep(i, 0, n) {
119             scanf("%s", s);
120             lid = ID[s[0]];
121             rep(j, 1, n+1) {
122                 uid = ID[s[1+j]];
123                 pref[lid][j] = uid;
124             }
125             nxt[lid] = 1;
126             future_wife[lid] = 0;
127             Q.push(lid);
128         }
129         
130         rep(i, 0, n) {
131             scanf("%s", s);
132             uid = ID[s[0]];
133             rep(j, 1, n+1) {
134                 lid = ID[s[1+j]];
135                 order[uid][lid] = j;
136             }
137             future_husband[uid] = 0;
138         }
139         solve();
140         if (t)
141             putchar(‘\n‘);
142     }
143     
144     #ifndef ONLINE_JUDGE
145         printf("time = %d.\n", (int)clock());
146     #endif
147     
148     return 0;
149 }