• HDU 5988 最小费用流


    链接:

    http://acm.split.hdu.edu.cn/showproblem.php?pid=5988

    题意:

    n个点,每个点有a个人和b包饭,m条边,第一次经过这条边没有问题,以后每一个经过的有p概率出问题

    每条边有限制,问使得所有人都有饭吃且出问题的概率最小

    题解:

    无向图的费用流

    把相乘的取下对数变成相加的就可以用最小费用流了

    代码:

     30 #include <iomanip>
     31 const double eps = 1e-8;
     32 const int MAXM = 1e5 + 7;
     33 
     34 struct node{
     35     int to, next, cap;
     36     double cost;
     37 }edge[MAXM];
     38 int head[MAXN];
     39 int pre[MAXN];
     40 int vis[MAXN];
     41 double dist[MAXN];
     42 int n, m, tot;
     43 
     44 void init() {
     45     memset(head, -1, sizeof(head));
     46     tot = 0;
     47 }
     48 
     49 void add_edge(int u, int v, int cap, double  cost) {
     50     edge[tot].to = v;
     51     edge[tot].cap = cap;
     52     edge[tot].cost = cost;
     53     edge[tot].next = head[u];
     54     head[u] = tot++;
     55     edge[tot].to = u;
     56     edge[tot].cap = 0;
     57     edge[tot].cost = -cost;
     58     edge[tot].next = head[v];
     59     head[v] = tot++;
     60 }
     61 
     62 double mcf(int s, int t, int f) {
     63     double res = 0;
     64     while (f > 0) {
     65         rep(i, 0, n + 2) {
     66             dist[i] = 1e18;
     67             vis[i] = 0;
     68             pre[i] = -1;
     69         }
     70         queue<int> q;
     71         q.push(s);
     72         dist[s] = 0;
     73         vis[s] = 1;
     74         while (!q.empty()) {
     75             int u = q.front(); q.pop();
     76             vis[u] = 0;
     77             for (int i = head[u]; i != -1; i = edge[i].next) {
     78                 int v = edge[i].to;
     79                 if (edge[i].cap > 0 && 
     80                     dist[v] > dist[u] + edge[i].cost + eps){
     81                     dist[v] = dist[u] + edge[i].cost;
     82                     pre[v] = i;
     83                     if (!vis[v]) {
     84                         vis[v] = 1;
     85                         q.push(v);
     86                     }
     87                 }
     88             }
     89         }
     90         if (dist[t] == 1e18) return -1;
     91         int d = f;
     92         for (int v = pre[t]; v != -1; v = pre[edge[v ^ 1].to])
     93             d = min(d, edge[v].cap);
     94         f -= d;
     95         res += d * dist[t];
     96         for (int v = pre[t]; v != -1; v = pre[edge[v ^ 1].to]) {
     97             edge[v].cap -= d;
     98             edge[v ^ 1].cap += d;
     99         }
    100     }
    101     return res;
    102 }
    103 
    104 int main() {
    105     int T;
    106     scanf("%d", &T);
    107     while (T--) {
    108         init();
    109         cin >> n >> m;
    110         int s = 0, t = n + 1, f = 0;
    111         rep(i, 1, n + 1) {
    112             int a, b;
    113             scanf("%d%d", &a, &b);
    114             add_edge(s, i, a, 0);
    115             add_edge(i, t, b, 0);
    116             f += a;
    117         }
    118         while (m--) {
    119             int u, v, c;
    120             double p;
    121             scanf("%d%d%d%lf", &u, &v, &c, &p);
    122             p = -log2(1 - p);
    123             if (c > 0) add_edge(u, v, 1, 0);
    124             if (c > 1) add_edge(u, v, c - 1, p);
    125         }
    126         double p = mcf(s, t, f);
    127         printf("%.2f
    ", 1 - pow(2, -p));
    128     }
    129     return 0;
    130 }
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  • 原文地址:https://www.cnblogs.com/baocong/p/7710969.html
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