AOJ GRL_6_A: Network Flow - Maximum Flow

最大流 | グラフ | Aizu Online Judge

Ford-Fulkerson版。ほぼ蟻本の写経。

#include <bits/stdc++.h>

using namespace std;

struct edge {
  int to, cap, rev;
};

vector<vector<edge>> G(101);
vector<bool> used(1001);

void add_edge(int from, int to, int cap) {
  G[from].push_back((edge){to, cap, (int)G[to].size()});
  G[to].push_back((edge){from, 0, (int)G[from].size() - 1});
}

int dfs(int v, int t, int f) {
  if (v == t) return f;
  used[v] = true;
  for (size_t i = 0; i < G[v].size(); i++) {
    edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      int d = dfs(e.to, t, min(f, e.cap));
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}

int max_flow(int s, int t) {
  int flow = 0;
  for (;;) {
    fill(used.begin(), used.end(), false);
    int f = dfs(s, t, numeric_limits<int>::max());
    if (f == 0) return flow;
    flow += f;
  }
}

int main() {
  int V, E;
  cin >> V >> E;
  vector<int> c(E);
  for (int i = 0; i < E; ++i) {
    int from, to, cap;
    cin >> from >> to >> cap;
    add_edge(from, to, cap);
  }
  cout << max_flow(0, V - 1) << endl;
}

Dinic版。これも蟻本の写経。

#include <bits/stdc++.h>

using namespace std;

struct edge {
  int to, cap, rev;
};

const int MAX_V = 101;

vector<vector<edge>> G(MAX_V);
vector<int> level(MAX_V), iter(MAX_V);

void add_edge(int from, int to, int cap) {
  G[from].push_back((edge){to, cap, (int)G[to].size()});
  G[to].push_back((edge){from, 0, (int)G[from].size() - 1});
}

void bfs(int s) {
  fill(level.begin(), level.end(), -1);
  queue<int> que;
  level[s] = 0;
  que.push(s);
  while (!que.empty()) {
    int v = que.front();
    que.pop();
    for (size_t i = 0; i < G[v].size(); i++) {
      edge &e = G[v][i];
      if (e.cap > 0 && level[e.to] < 0) {
        level[e.to] = level[v] + 1;
        que.push(e.to);
      }
    }
  }
}

int dfs(int v, int t, int f) {
  if (v == t) return f;
  for (int &i = iter[v]; i < (int)G[v].size(); i++) {
    edge &e = G[v][i];
    if (e.cap > 0 && level[v] < level[e.to]) {
      int d = dfs(e.to, t, min(f, e.cap));
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}

int max_flow(int s, int t) {
  int flow = 0;
  for (;;) {
    bfs(s);
    if (level[t] < 0) return flow;
    fill(iter.begin(), iter.end(), 0);
    int f;
    while ((f = dfs(s, t, numeric_limits<int>::max())) > 0) {
      flow += f;
    }
  }
}

int main() {
  int V, E;
  cin >> V >> E;
  vector<int> c(E);
  for (int i = 0; i < E; ++i) {
    int from, to, cap;
    cin >> from >> to >> cap;
    add_edge(from, to, cap);
  }
  cout << max_flow(0, V - 1) << endl;
}

http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3307521#1