[BZOJ 1733] [Usaco2005 feb] Secret Milking Machine 【二分 + 最大流】

题目链接：BZOJ - 1733

题目分析

直接二分这个最大边的边权，然后用最大流判断是否可以有 T 的流量。

代码

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

const int MaxN = 200 + 5, MaxM = 80000 + 5, INF = 999999999;

inline int gmin(int a, int b) {return a < b ? a : b;}
inline int gmax(int a, int b) {return a > b ? a : b;}

int n, m, Ts, Top, Ans, S, T, Tot;
int d[MaxN], Num[MaxN];

struct Edge
{
    int u, v, w, len;
    Edge *Next, *Other;
} E[MaxM * 2], *P = E, *Point[MaxN], *Last[MaxN], *EA[MaxM];

inline void AddEdge(int x, int y, int z)
{
    Edge *Q = ++P; ++P; EA[++Top] = P;
    P -> u = x; P -> v = y; P -> len = z;
    P -> Next = Point[x]; Point[x] = P; P -> Other = Q;
    Q -> u = y; Q -> v = x; Q -> len = z;
    Q -> Next = Point[y]; Point[y] = Q; Q -> Other = P;
}

void Set_Edge(int x)
{
    for (int i = 1; i <= Top; ++i)
    {
        if (EA[i] -> len <= x) EA[i] -> w = 1;
        else EA[i] -> w = 0;
        EA[i] -> Other -> w = 0;
    }
}

int DFS(int Now, int Flow)
{
    if (Now == T) return Flow;
    int ret = 0;
    for (Edge *j = Last[Now]; j; j = j -> Next)
        if (j -> w && d[j -> u] == d[j -> v] + 1)
        {
            Last[Now] = j;
            int p = DFS(j -> v, gmin(j -> w, Flow - ret));
            j -> w -= p; j -> Other -> w += p; ret += p;
            if (ret == Flow) return ret;
        }
    if (d[S] >= Tot) return ret;
    if (--Num[d[Now]] == 0) d[S] = Tot;
    ++Num[++d[Now]];
    Last[Now] = Point[Now];
    return ret;
}

bool Check()
{
    int MaxFlow = 0;
    S = 1; T = n; Tot = n;
    memset(d, 0, sizeof(d));
    memset(Num, 0, sizeof(Num)); Num[0] = Tot;
    for (int i = 1; i <= Tot; ++i) Last[i] = Point[i];
    while (d[S] < Tot) MaxFlow += DFS(S, INF);
    if (MaxFlow >= Ts) return true;
    else return false;
}

int main()
{
    scanf("%d%d%d", &n, &m, &Ts);
    int a, b, c;
    int l, r, mid;
    l = INF; r = -INF;
    Top = 0;
    for (int i = 1; i <= m; ++i)
    {
        scanf("%d%d%d", &a, &b, &c);
        AddEdge(a, b, c);
        AddEdge(b, a, c);
        l = gmin(l, c);
        r = gmax(r, c);
    }
    while (l <= r)
    {
        mid = (l + r) >> 1;
        Set_Edge(mid);
        if (Check())
        {
            Ans = mid;
            r = mid - 1;
        }
        else l = mid + 1;
    }
    printf("%d\n", Ans);
    return 0;
}