BZOJ 1570 JSOI 2008 Blue Mary的旅行 网络流

题目大意

给出一个有向图，每天每人只能做一次飞机。现在给出起点，终点，和需要走的人数，还有每条航线的限制人数，问最少多少天最慢的人到达终点。

思路

很明显是网络流的模型，至于如何去验证，其实连二分都不用，枚举最少天数，然后每次加一层边进行验证就行了。

CODE

#define _CRT_SECURE_NO_WARNINGS#include <queue>#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define MAX 100010#define MAXE 1000010#define S 0#define SS (MAX - 2)#define T (MAX - 1)#define INF 0x3f3f3f3fusing namespace std;struct Edge{    int x, y, z;    void Read() {        scanf("%d%d%d", &x, &y, &z);    }}edge[MAXE];struct MaxFlow{    int head[MAX], total;    int _next[MAXE], aim[MAXE], flow[MAXE];    int backup_flow[MAXE];    int deep[MAXE];    MaxFlow():total(1) {}    void Add(int x, int y, int f) {        _next[++total] = head[x];        aim[total] = y;        backup_flow[total] = f;        head[x] = total;    }    void Insert(int x, int y, int f) {        Add(x, y, f);        Add(y, x, 0);    }    bool BFS() {        static queue<int> q;        while(!q.empty())   q.pop();        memset(deep, 0, sizeof(deep));        deep[S] = 1;        q.push(S);        while(!q.empty()) {            int x = q.front(); q.pop();            for(int i = head[x]; i; i = _next[i])            if(flow[i] && !deep[aim[i]]) {                deep[aim[i]] = deep[x] + 1;                q.push(aim[i]);                if(aim[i] == T) return true;            }        }        return false;    }    int Dinic(int x, int f) {        if(x == T)  return f;        int temp = f;        for(int i = head[x]; i; i = _next[i])        if(flow[i] && temp && deep[aim[i]] == deep[x] + 1) {            int away = Dinic(aim[i], min(flow[i], temp));            if(!away)   deep[aim[i]] = 0;            flow[i] -= away;            flow[i ^ 1] += away;            temp -= away;        }        return f - temp;    }}solver;int points, edges, persons;int main(){    cin >> points >> edges >> persons;    for(int i = 1; i <= edges; ++i)        edge[i].Read();    solver.Insert(S, SS, persons);    int now = 0;    for(int i = 1;; ++i) {        for(int j = 1; j <= edges; ++j)            solver.Insert(now + edge[j].x, now + edge[j].y + points, edge[j].z);        solver.Insert(now + points + points, T, INF);        solver.Insert(SS, now + 1, INF);        memcpy(solver.flow, solver.backup_flow, sizeof(solver.flow));        int max_flow = 0;        while(solver.BFS())            max_flow += solver.Dinic(S, INF);        if(max_flow == persons) {            cout << i << endl;            return 0;        }        now += points;    }    return 0;}