Dinics Algo For Max Flow.cpp

/********************************************************************************

    MaxFlow Dinic algorithm with scaling. 
    O(N * M * log(MC)), where MC is maximum edge capacity.
    
    Based on problem 2784 from informatics.mccme.ru 
    http://informatics.mccme.ru/mod/statements/view3.php?chapterid=2784#1

********************************************************************************/

#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <utility>
#include <iomanip>

using namespace std;

struct edge {
    int a, b, f, c;
};

const int inf = 1000 * 1000 * 1000;
const int MAXN = 1050;

int n, m;
vector <edge> e;
int pt[MAXN]; // very important performance trick
vector <int> g[MAXN];
long long flow = 0;
queue <int> q;
int d[MAXN];
int lim;
int s, t;

void add_edge(int a, int b, int c) {                                                                           
    edge ed;

    //keep edges in vector: e[ind] - direct edge, e[ind ^ 1] - back edge 

    ed.a = a; ed.b = b; ed.f = 0; ed.c = c;
    g[a].push_back(e.size());
    e.push_back(ed);

    ed.a = b; ed.b = a; ed.f = c; ed.c = c;
    g[b].push_back(e.size());
    e.push_back(ed);
}

bool bfs() {
    for (int i = s; i <= t; i++)
        d[i] = inf;
    d[s] = 0; 
    q.push(s);
    while (!q.empty() && d[t] == inf) {
        int cur = q.front(); q.pop();
        for (size_t i = 0; i < g[cur].size(); i++) {
            int id = g[cur][i];
            int to = e[id].b;

            //printf("cur = %d id = %d a = %d b = %d f = %d c = %d\n", cur, id, e[id].a, e[id].b, e[id].f, e[id].c);

            if (d[to] == inf && e[id].c - e[id].f >= lim) {
                d[to] = d[cur] + 1;
                q.push(to);
            }
        }
    }
    while (!q.empty()) 
        q.pop();
    return d[t] != inf;
}

bool dfs(int v, int flow) {
    if (flow == 0) 
        return false;
    if (v == t) {
        //cout << v << endl;
        return true;
    }
    for (; pt[v] < g[v].size(); pt[v]++) {
        int id = g[v][pt[v]];
        int to = e[id].b;

        //printf("v = %d id = %d a = %d b = %d f = %d c = %d\n", v, id, e[id].a, e[id].b, e[id].f, e[id].c);

        if (d[to] == d[v] + 1 && e[id].c - e[id].f >= flow) {
            int pushed = dfs(to, flow); 
            if (pushed) {
                e[id].f += flow;
                e[id ^ 1].f -= flow;
                return true;
            }               
        }
    }
    return false;
}

void dinic() {
    for (lim = (1 << 30); lim >= 1;) {
        if (!bfs()) {
            lim >>= 1;
            continue;
        }

        for (int i = s; i <= t; i++) 
            pt[i] = 0;

        int pushed;

        while (pushed = dfs(s, lim)) { 
            flow = flow + lim;
        }

        //cout << flow << endl;
    }
}

int main() {
    //freopen("input.txt","r",stdin);
    //freopen("output.txt","w",stdout);
    scanf("%d %d", &n, &m);
    
    s = 1; t = n;

    for (int i = 1; i <= m; i++) {
        int a, b, c;
        scanf("%d %d %d", &a, &b, &c);
        add_edge(a, b, c);
    }

    dinic();

    cout << flow << endl;

    return 0;
}