[SWUST1742] 试题库问题（最大流）

题目链接：https://www.oj.swust.edu.cn/problem/show/1742

多重匹配问题，判断有无解可以通过最大流是否等于选的题目类型数量总和。

如下建图：

 

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 
  4 typedef struct Edge {
  5     int u, v, w, next;
  6 }Edge;
  7 
  8 const int inf = 0x7f7f7f7f;
  9 const int maxn = 9090;
 10 
 11 int cnt, dhead[maxn];
 12 int cur[maxn], dd[maxn];
 13 Edge dedge[maxn<<3];
 14 int S, T, N;
 15 
 16 void init() {
 17     memset(dhead, -1, sizeof(dhead));
 18     for(int i = 0; i < maxn; i++) dedge[i].next = -1;
 19     S = 0; cnt = 0;
 20 }
 21 
 22 void adde(int u, int v, int w, int c1=0) {
 23     dedge[cnt].u = u; dedge[cnt].v = v; dedge[cnt].w = w; 
 24     dedge[cnt].next = dhead[u]; dhead[u] = cnt++;
 25     dedge[cnt].u = v; dedge[cnt].v = u; dedge[cnt].w = c1; 
 26     dedge[cnt].next = dhead[v]; dhead[v] = cnt++;
 27 }
 28 
 29 bool bfs(int s, int t, int n) {
 30     queue<int> q;
 31     for(int i = 0; i < n; i++) dd[i] = inf;
 32     dd[s] = 0;
 33     q.push(s);
 34     while(!q.empty()) {
 35         int u = q.front(); q.pop();
 36         for(int i = dhead[u]; ~i; i = dedge[i].next) {
 37             if(dd[dedge[i].v] > dd[u] + 1 && dedge[i].w > 0) {
 38                 dd[dedge[i].v] = dd[u] + 1;
 39                 if(dedge[i].v == t) return 1;
 40                 q.push(dedge[i].v);
 41             }
 42         }
 43     }
 44     return 0;
 45 }
 46 
 47 int dinic(int s, int t, int n) {
 48     int st[maxn], top;
 49     int u;
 50     int flow = 0;
 51     while(bfs(s, t, n)) {
 52         for(int i = 0; i < n; i++) cur[i] = dhead[i];
 53         u = s; top = 0;
 54         while(cur[s] != -1) {
 55             if(u == t) {
 56                 int tp = inf;
 57                 for(int i = top - 1; i >= 0; i--) {
 58                     tp = min(tp, dedge[st[i]].w);
 59                 }
 60                 flow += tp;
 61                 for(int i = top - 1; i >= 0; i--) {
 62                     dedge[st[i]].w -= tp;
 63                     dedge[st[i] ^ 1].w += tp;
 64                     if(dedge[st[i]].w == 0) top = i;
 65                 }
 66                 u = dedge[st[top]].u;
 67             }
 68             else if(cur[u] != -1 && dedge[cur[u]].w > 0 && dd[u] + 1 == dd[dedge[cur[u]].v]) {
 69                 st[top++] = cur[u];
 70                 u = dedge[cur[u]].v;
 71             }
 72             else {
 73                 while(u != s && cur[u] == -1) {
 74                     u = dedge[st[--top]].u;
 75                 }
 76                 cur[u] = dedge[cur[u]].next;
 77             }
 78         }
 79     }
 80     return flow;
 81 }
 82 
 83 int k, n;
 84 
 85 int main() {
 86     // freopen("in", "r", stdin);
 87     int p, u;
 88     while(~scanf("%d%d",&k,&n)) {
 89         init();
 90         S = 0; T = k + n + 1; N = T + 1;
 91         int sum = 0;
 92         for(int i = 1; i <= n; i++) adde(S, i, 1);
 93         for(int i = 1; i <= k; i++) {
 94             scanf("%d", &p);
 95             adde(n + i, T, p);
 96             sum += p;
 97         }
 98         for(int i = 1; i <= n; i++) {
 99             scanf("%d", &p);
100             for(int j = 1; j <= p; j++) {
101                 scanf("%d", &u);
102                 adde(i, n+u, 1);
103             }
104         }
105         int ret = dinic(S, T, N);
106         if(ret != sum) {
107             puts("No Solution!");
108             continue;
109         }
110         for(int i = 1; i <= k; i++) {
111             printf("%d:", i);
112             for(int j = dhead[i+n]; ~j; j=dedge[j].next) {
113                 if(dedge[j].w && dedge[j].v != T) printf(" %d", dedge[j].v);
114             }
115             printf("\n");
116         }
117     }
118     return 0;
119 }

 

posted @ 2017-05-02 14:21  Kirai  阅读(175)  评论(0)  编辑  收藏  举报