poj 3436 最大流+拆点

今天总算明白了最大流中的拆点的含义，

因为最大流的中两个点u和v，流量的限制记为cap(u,v)，

如果一个点u的流量限制为m，那么我们可以把u拆成u₁和u₂，

并且对任意的s，将cap(s,u)换成cap(s,u₁)，

对任意的e，将cap(u,e)换成cap(u₁,e)，

最后将cap(u₁,u₂)置为m，然后套用最大流的通用算法即可

#include <iostream>
#include <string>
#include <vector>
#include <cstdlib>
#include <cmath>
#include <map>
#include <algorithm>
#include <list>
#include <ctime>
#include <set>
#include <string.h>
#include <queue>
using namespace std;

#define N 1050
int capacity[N][N]; //容量
int capacity2[N][N]; //容量
int flow[N]; //残余流量
int pre[N]; //前趋
#define INT_MAX 10000000;

int n, m;
queue<int> Q;

int BFS(int src, int des) {
    //初始化
    while (!Q.empty()) {
        Q.pop();
    }
    for (int i = 1; i < n + 1; i++) {
        pre[i] = -1;
    }
    pre[src] = 0;
    flow[src] = INT_MAX; //初始化源点的流量为无穷大
    Q.push(src);
    while (!Q.empty()) {
        int index = Q.front();
        Q.pop();
        if (index == des) { //找到了增广路径
            break;
        }
        for (int i = 1; i < n + 1; i++) {
            if (i != src && capacity[index][i] > 0 && pre[i] == -1) {
                pre[i] = index;
                //增广路残容流量
                flow[i] = min(capacity[index][i], flow[index]);
                Q.push(i);
            }
        }
    } //while
    if (pre[des] == -1) {
        return -1; //残留图中不存在增广路径
    } else {
        return flow[des];
    }
}

int MaxFlow(int src, int des) {
    int aug = 0;
    int sumflow = 0;
    while ((aug = BFS(src, des)) != -1) {
        int k = des; //利用前驱寻找路径
        while (k != src) {
            int last = pre[k];
            capacity[last][k] -= aug;
            capacity[k][last] += aug;
            k = last;
        }
        sumflow += aug;
    }
    return sumflow;
}
struct node {
    string in, out;
    int cap;
};
int checkin(string & a, string& b) {
    int sz = a.size();
    bool judge = 1;
    for (int i = 0; i < sz; i++) {
        if (a[i] == '2' || b[i] == '2') {
            continue;
        } else if (a[i] != b[i]) {
            judge = 0;
            break;
        }
    }
    if (1 == judge)
        return 1;
    return 0;
}
int main() {
    int kp, kn, cap;
    cin >> kp >> kn;
    n = 2 * kn + 2;
    vector<node> data;
    string startstate;
    string endstate;
    string csta = "0";
    string cend = "1";
    for (int i = 0; i < kp; i++) {
        startstate += csta;
        endstate += cend;
    }
    for (int i = 0; i < kn; i++) {
        cin >> cap;
        string t, t2;
        string statein, stateout;
        for (int j = 0; j < kp; j++) {
            cin >> t;
            statein = statein + t;
        }
        t = t2;
        for (int j = 0; j < kp; j++) {
            cin >> t;
            stateout = stateout + t;
        }
        node tmp;
        tmp.cap = cap;
        tmp.in = statein;
        tmp.out = stateout;
        data.push_back(tmp);
    }
    for (int i = 0; i < kn; i++) {
        node tmp = data[i];
        int u = i + 1;
        int v = i + 1 + kn;
        capacity[u][v] = tmp.cap;
        int judge = checkin(startstate, tmp.in);
        if (1 == judge) {
            capacity[0][u] = tmp.cap;
        }
        judge = checkin(tmp.out, endstate);
        if (1 == judge) {
            capacity[v][n - 1] = tmp.cap;
        }

        for (int j = 0; j < kn; j++) {
            if (j != i) {
                node tmp2 = data[j];
                int u2 = j + 1;
                int v2 = j + 1 + kn;
                judge = checkin(tmp2.out, tmp.in);
                if (1 == judge) {
                    capacity[v2][u] = tmp2.cap;
                }
                judge = checkin(tmp.out, tmp2.in);
                if (1 == judge) {
                    capacity[v][u2] = tmp.cap;
                }
            }

        }
    }
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            capacity2[i][j] = capacity[i][j];
        }
    }
    int sum = MaxFlow(0, n - 1);
    cout << sum <<" ";
    int num=0;
    for (int i = 0; i < kn; i++) {
        node tmp = data[i];
        int u = i + 1;
        int v = i + 1 + kn;
        int judge;

        for (int j = 0; j < kn; j++) {
            if (j != i) {
                node tmp2 = data[j];
                int u2 = j + 1;
                int v2 = j + 1 + kn;
                judge = checkin(tmp.out, tmp2.in);
                if (1 == judge) {
                    int cost = capacity2[v][u2] - capacity[v][u2];
                    if (cost > 0) {
                        num++;
                    }
                }
            }
        }
    }
    cout<<num<<endl;

    for (int i = 0; i < kn; i++) {
        node tmp = data[i];
        int u = i + 1;
        int v = i + 1 + kn;
        int judge;

        for (int j = 0; j < kn; j++) {
            if (j != i) {
                node tmp2 = data[j];
                int u2 = j + 1;
                int v2 = j + 1 + kn;
                judge = checkin(tmp.out, tmp2.in);
                if (1 == judge) {
                    int cost = capacity2[v][u2] - capacity[v][u2];
                    if (cost > 0) {
                        cout << i + 1 << " " << j + 1 << " " << cost << endl;
                    }
                }
            }

        }
    }
    return 0;
}