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Cod sursa(job #960329)
#include <algorithm>
#include <fstream>
#include <iostream>
#include <queue>
#include <set>
#include <vector>
using namespace std;
ifstream fin("maxflow.in");
ofstream fout("maxflow.out");
const int MAX_N = 1005;
const int INF = 1 << 30;
int source, sink;
int N, M;
vector<int> graph[MAX_N];
int capacity[MAX_N][MAX_N];
int flow[MAX_N][MAX_N];
int excess[MAX_N];
int height[MAX_N];
int height_frequency[2 * MAX_N];
queue<int> q;
set<int> gaps;
void read_input();
int push_relabel();
void initialize_preflow();
void discharge(int u);
void push(int u, int v);
inline int cf(int u, int v);
int main() {
read_input();
fout << push_relabel();
return 0;
}
void read_input() {
fin >> N >> M;
for (int i = 1, a, b, c; i <= M; ++i) {
fin >> a >> b >> c;
graph[a].push_back(b);
graph[b].push_back(a);
capacity[a][b] = c;
}
source = 1;
sink = N;
}
int push_relabel() {
initialize_preflow();
while (!q.empty()) {
int u = q.front();
discharge(u);
q.pop();
}
return -excess[source];
}
void initialize_preflow() {
height[source] = N;
for (auto v : graph[source]) {
flow[source][v] = excess[v] = capacity[source][v];
excess[source] += (flow[v][source] = -capacity[source][v]);
if (v != sink) {
q.push(v);
}
}
height_frequency[0] = N - 1;
height_frequency[N] = 1;
}
void discharge(int u) {
//magic gap heuristic that reduces the running time
if (!gaps.empty()) {
int min_gap = *gaps.begin();
if (height[u] > min_gap) {
height[u] = max(height[u], height[source] + 1);
}
}
//remove if unnecessary
while (excess[u] > 0) {
int min_height = INF;
for (auto v : graph[u]) {
if (cf(u, v) > 0) {
if (height[u] == height[v] + 1) {
push(u, v);
if (v != source && v != sink) {
q.push(v);
}
} else {
min_height = min(min_height, height[v]);
}
}
}
if (excess[u] > 0) {
int old_height = height[u];
int new_height = min_height + 1;
height[u] = new_height;
//also needed for gap heuristic
height_frequency[old_height] -= 1;
height_frequency[new_height] += 1;
if (height_frequency[old_height] == 0 &&
0 < old_height && old_height < N) {
gaps.insert(old_height);
}
if (height_frequency[new_height] == 1) {
gaps.erase(new_height);
}
//cut here
}
}
}
inline void push(int u, int v) {
int quantity = min(excess[u], cf(u, v));
flow[u][v] += quantity;
flow[v][u] -= quantity;
excess[u] -= quantity;
excess[v] += quantity;
}
inline int cf(int u, int v) {
return capacity[u][v] - flow[u][v];
}