[SDOI2013]费用流

嘟嘟嘟

看到这题目如果想费用流的话就gg了，就像LCA这道题一样，不要被题目迷惑……

我们考虑Bob，他想让总费用最大，那么他的所有费用一定都加到流量最大的那一条边上。而Alice想让总费用最小，那么就是让流量最大的那一条边最小，自然就想到二分边的容量啦！

不过这道题特殊的地方是要实数二分。其实终止条件就是当R - L小于自己设定的一个精度。然后如果当前不符合，不应该是L = mid + 1,因为(mid, mid + 1)中很有可能是答案，所以应该是L = mid +eps。

第一次写实数二分，总是死循环，调了有那么一会儿……

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<vector>
#include<stack>
#include<queue>
using namespace std;
#define enter puts("") 
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define rg register
typedef long long ll;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-8;
const int maxn = 105;
inline ll read()
{
    ll ans = 0;
    char ch = getchar(), last = ' ';
    while(!isdigit(ch)) {last = ch; ch = getchar();}
    while(isdigit(ch)) {ans = ans * 10 + ch - '0'; ch = getchar();}
    if(last == '-') ans = -ans;
    return ans;
}
inline void write(ll x)
{
    if(x < 0) x = -x, putchar('-');
    if(x >= 10) write(x / 10);
    putchar(x % 10 + '0');
}

int n, m, p, Max;

struct Edge
{
    int from, to;
    db cap, flow;
};
vector<Edge> edges;
vector<int> G[maxn];
void addEdge(int from, int to, int w)
{
    edges.push_back((Edge){from, to, (db)w, 0});
    edges.push_back((Edge){to, from, 0, 0});
    int sz = edges.size();
    G[from].push_back(sz - 2);
    G[to].push_back(sz - 1);
}

int dis[maxn];
bool bfs()
{
    Mem(dis, 0); dis[1] = 1;
    queue<int> q; q.push(1);
    while(!q.empty())
    {
        int now = q.front(); q.pop();
        for(int i = 0; i < (int)G[now].size(); ++i)
        {
            Edge& e = edges[G[now][i]];
            if(!dis[e.to] && e.cap > e.flow + eps)
            {
                dis[e.to] = dis[now] + 1;
                q.push(e.to);    
            }
        }
    }
    return dis[n];
}
int cur[maxn];
db dfs(int now, db res)
{
    if(now == n || res == 0) return res;
    db flow = 0, f;
    for(int& i = cur[now]; i < (int)G[now].size(); ++i)
    {
        Edge& e = edges[G[now][i]];
        if(dis[e.to] == dis[now] + 1 && (f = dfs(e.to, min(res, e.cap - e.flow))) > 0)
        {
            e.flow += f;
            edges[G[now][i] ^ 1].flow -= f;
            flow += f; res -= f;
            if(res == 0) break;
        }
    }
    return flow;
}

db maxflow()
{
    db flow = 0;
    while(bfs())
    {
        Mem(cur, 0);
        flow += dfs(1, (db)INF);
    }
    return flow;
}

void build_Gra(db x)        //不用重建，修改每一条边的参数就行 
{
    for(int i = 0; i < (int)edges.size(); i += 2)
    {
        edges[i].cap = x; edges[i].flow = 0;
        edges[i ^ 1].cap = 0; edges[i ^ 1].flow = 0;
    }
}

int main()
{
    n = read(); m = read(); p = read();
    for(int i = 1; i <= m; ++i)
    {
        int x = read(), y = read(), w = read();
        addEdge(x, y, w);
    }
    Max = maxflow();
    db L = 0, R = (db)INF;
    while(L < R - eps)
    {
        db mid = (L + R) / 2.00;
        build_Gra(mid);
        if(maxflow() > (db)Max - eps) R = mid;
        else L = mid + eps;
    }
    printf("%d %.6lf
", Max, (L + R) / 2.00 * p);
    return 0;
}