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max_flow_ford_fulkerson.cpp
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//
// max-flow (Ford-Fulkerson's algorithm)
//
// verified
// AOJ Course GRL_6_A Network Flow - Maximum Flow
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_A&lang=jp
//
// AtCoder Library Practice Contest D - Maxflow
// https://atcoder.jp/contests/practice2/tasks/practice2_d
//
#include <bits/stdc++.h>
using namespace std;
// edge class (for network-flow)
template<class FLOWTYPE> struct FlowEdge {
// core members
int rev, from, to;
FLOWTYPE cap, icap, flow;
// constructor
FlowEdge(int r, int f, int t, FLOWTYPE c)
: rev(r), from(f), to(t), cap(c), icap(c), flow(0) {}
void reset() { cap = icap, flow = 0; }
// debug
friend ostream& operator << (ostream& s, const FlowEdge& E) {
return s << E.from << "->" << E.to << '(' << E.flow << '/' << E.icap << ')';
}
};
// graph class (for network-flow)
template<class FLOWTYPE> struct FlowGraph {
// core members
vector<vector<FlowEdge<FLOWTYPE>>> list;
vector<pair<int,int>> pos; // pos[i] := {vertex, order of list[vertex]} of i-th edge
// constructor
FlowGraph(int n = 0) : list(n) { }
void init(int n = 0) {
list.assign(n, FlowEdge<FLOWTYPE>());
pos.clear();
}
// getter
vector<FlowEdge<FLOWTYPE>> &operator [] (int i) {
return list[i];
}
const vector<FlowEdge<FLOWTYPE>> &operator [] (int i) const {
return list[i];
}
size_t size() const {
return list.size();
}
FlowEdge<FLOWTYPE> &get_rev_edge(const FlowEdge<FLOWTYPE> &e) {
if (e.from != e.to) return list[e.to][e.rev];
else return list[e.to][e.rev + 1];
}
FlowEdge<FLOWTYPE> &get_edge(int i) {
return list[pos[i].first][pos[i].second];
}
const FlowEdge<FLOWTYPE> &get_edge(int i) const {
return list[pos[i].first][pos[i].second];
}
vector<FlowEdge<FLOWTYPE>> get_edges() const {
vector<FlowEdge<FLOWTYPE>> edges;
for (int i = 0; i < (int)pos.size(); ++i) {
edges.push_back(get_edge(i));
}
return edges;
}
// change edges
void reset() {
for (int i = 0; i < (int)list.size(); ++i) {
for (FlowEdge<FLOWTYPE> &e : list[i]) e.reset();
}
}
void change_edge(FlowEdge<FLOWTYPE> &e, FLOWTYPE new_cap, FLOWTYPE new_flow) {
FlowEdge<FLOWTYPE> &re = get_rev_edge(e);
e.cap = new_cap - new_flow, e.icap = new_cap, e.flow = new_flow;
re.cap = new_flow;
}
// add_edge
void add_edge(int from, int to, FLOWTYPE cap) {
pos.emplace_back(from, (int)list[from].size());
list[from].push_back(FlowEdge<FLOWTYPE>((int)list[to].size(), from, to, cap));
list[to].push_back(FlowEdge<FLOWTYPE>((int)list[from].size() - 1, to, from, 0));
}
// debug
friend ostream& operator << (ostream& s, const FlowGraph &G) {
const auto &edges = G.get_edges();
for (const auto &e : edges) s << e << endl;
return s;
}
};
// Ford-Fulkerson
template<class FLOWTYPE> FLOWTYPE FordFulkerson
(FlowGraph<FLOWTYPE> &G, int s, int t, FLOWTYPE limit_flow)
{
FLOWTYPE current_flow = 0;
// DFS
vector<bool> used((int)G.size(), false);
auto dfs = [&](auto self, int v, FLOWTYPE up_flow) {
if (v == t) return up_flow;
FLOWTYPE res_flow = 0;
used[v] = true;
for (FlowEdge<FLOWTYPE> &e : G[v]) {
if (used[e.to] || e.cap == 0) continue;
FLOWTYPE flow = self(self, e.to, min(up_flow - res_flow, e.cap));
FlowEdge<FLOWTYPE> &re = G.get_rev_edge(e);
if (flow <= 0) continue;
res_flow += flow;
e.cap -= flow, e.flow += flow;
re.cap += flow, re.flow -= flow;
if (res_flow == up_flow) break;
}
return res_flow;
};
// flow
while (current_flow < limit_flow) {
used.assign((int)G.size(), false);
FLOWTYPE flow = dfs(dfs, s, limit_flow - current_flow);
if (!flow) break;
current_flow += flow;
}
return current_flow;
};
template<class FLOWTYPE> FLOWTYPE FordFulkerson(FlowGraph<FLOWTYPE> &G, int s, int t) {
return FordFulkerson(G, s, t, numeric_limits<FLOWTYPE>::max());
}
//------------------------------//
// Examples
//------------------------------//
// AOJ
void AOJ_Course_GRL_6_A() {
int V, E;
cin >> V >> E;
FlowGraph<int> G(V);
for (int i = 0; i < E; ++i) {
int u, v, c;
cin >> u >> v >> c;
G.add_edge(u, v, c);
}
int res = FordFulkerson(G, 0, V-1);
cout << res << endl;
}
// ACL practice D
void ACL_practice_D() {
// 上下左右を表すベクトル
const vector<int> DX = {1, 0, -1, 0};
const vector<int> DY = {0, 1, 0, -1};
// 入力受け取り
int N, M;
cin >> N >> M;
vector<string> grid(N);
for (int i = 0; i < N; ++i) cin >> grid[i];
// フローネットワークを作る
// 各マスの番号を 0, 1, ..., NM-1 とし、超頂点の番号を S = NM, T = NM+1 とする
FlowGraph<int> G(N * M + 2);
int S = N * M, T = N * M + 1;
// マス (i, j) の頂点番号を返す関数
auto index = [&](int i, int j) -> int { return i * M + j; };
// 黒色マスと白色マスを結ぶ (黒色:i + j が偶数、白色:i + j が奇数)
for (int i = 0; i < N; ++i) {
for (int j = 0; j < M; ++j) {
// 黒色マスならば、上下左右の 4 マスと辺を結んでいく
if ((i + j) % 2 == 0 && grid[i][j] == '.') {
for (int dir = 0; dir < 4; ++dir) {
int i2 = i + DX[dir], j2 = j + DY[dir];
if (i2 < 0 || i2 >= N || j2 < 0 || j2 >= M) continue;
// どちらも空マスならば、ドミノを置けるので、辺を結ぶ
if (grid[i2][j2] == '.') {
G.add_edge(index(i, j), index(i2, j2), 1);
}
}
}
// 超頂点 S から黒色マスへの辺を結ぶ
if ((i + j) % 2 == 0 && grid[i][j] == '.') {
G.add_edge(S, index(i, j), 1);
}
// 白色マスから超頂点 T への辺を結ぶ
if ((i + j) % 2 == 1 && grid[i][j] == '.') {
G.add_edge(index(i, j), T, 1);
}
}
}
// 最大流を流す
int max_flow = FordFulkerson(G, S, T);
// フロー値が 1 となった辺を特定して、ドミノタイリングを復元する
const auto &edges = G.get_edges();
for (const auto &e : edges) {
// 辺 e が超頂点に接続するものや、フロー値が 0 であるものはスキップ
if (e.from == S || e.to == T || e.flow == 0) continue;
// 辺 e の両端点に対応するマス
int ifrom = e.from / M, jfrom = e.from % M;
int ito = e.to / M, jto = e.to % M;
// ドミノを置く
if (ifrom == ito) {
// ドミノを横に配置する場合
if (jfrom > jto) swap(jfrom, jto);
grid[ifrom][jfrom] = '>';
grid[ito][jto] = '<';
} else if (jfrom == jto) {
// ドミノを縦に配置する場合
if (ifrom > ito) swap(ifrom, ito);
grid[ifrom][jfrom] = 'v';
grid[ito][jto] = '^';
}
}
// 出力
cout << max_flow << endl;
for (int i = 0; i < N; ++i) cout << grid[i] << endl;
}
int main() {
//AOJ_Course_GRL_6_A();
ACL_practice_D();
}