UVa 10330 - Power Transmission

Accepted date: 2014-08-01
Ranking (as of 2014-08-02): 606 out of 1470
Language: C++

/*
  UVa 10330 - Power Transmission

  To build using Visucal Studio 2012:
    cl -EHsc UVa_10330_Power_Transmission.cpp
*/

#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;

struct edge {
  int v; // neighboring vertex
  int capacity; // capacity of edge
  int flow; // flow through edge
  int residual; // residual capacity of edge

  edge(int _v, int _capacity, int _residual)
    : v(_v), capacity(_capacity), flow(0), residual(_residual) {}
};

struct vertex_state {
  bool discovered;
  int parent;

  vertex_state() : discovered(false), parent(-1) {}
};

void bfs(const vector< vector<edge> >& graph,
  int start, vector<vertex_state>& states)
{
  queue<int> q;
  states[start].discovered = true;
  q.push(start);
  while (!q.empty()) {
    int u = q.front(); q.pop();
    for (int i = 0; i < graph[u].size(); i++) {
      const edge& e = graph[u][i];
      if (e.residual > 0 && !states[e.v].discovered) {
        states[e.v].discovered = true;
        states[e.v].parent = u;
        q.push(e.v);
      }
    }
  }
}

edge& find_edge(vector< vector<edge> >& graph, int u, int v)
{
  int i;
  for (i = 0; i < graph[u].size(); i++)
    if (graph[u][i].v == v)
      break;
  return graph[u][i];
}

int path_volume(vector< vector<edge> >& graph,
  int start, int end, const vector<vertex_state>& states)
{
  if (states[end].parent == -1)
    return 0;
  edge& e = find_edge(graph, states[end].parent, end);
  if (start == states[end].parent)
    return e.residual;
  else
    return min(path_volume(graph, start, states[end].parent, states),
      e.residual);
}

void augment_path(vector< vector<edge> >& graph,
  int start, int end, const vector<vertex_state>& states, int volume)
{
  if (start == end)
    return;
  edge& e = find_edge(graph, states[end].parent, end);
  if (e.flow < e.capacity)
    e.flow += volume;
  if (e.residual)
    e.residual -= volume;
  edge& r= find_edge(graph, end, states[end].parent);
  if (r.flow)
    r.flow -= volume;
  if (r.residual < r.capacity)
    r.residual += volume;
  augment_path(graph, start, states[end].parent, states, volume);
}

void netflow(vector< vector<edge> >& graph, int source, int sink)
{
  while (true) {
    vector<vertex_state> states(graph.size());
    bfs(graph, source, states);
    int volume = path_volume(graph, source, sink, states);
      // calculate the volume of augmenting path
    if (volume > 0)
      augment_path(graph, source, sink, states, volume);
    else
      break;
  }
}

int total_flow(const vector< vector<edge> >& graph, int source)
{
  int flow = 0;
  const vector<edge>& edges = graph[source];
  for (int i = 0, e = edges.size(); i < e; i++)
    flow += edges[i].flow;
  return flow;
}

int main()
{
  int n;
  while (cin >> n) {
    int nr_vertices = 2 * n + 2;
    vector< vector<edge> > graph(nr_vertices);
    // indices are:
    // 0 - (2 * n - 1): regulator vertices, 2 * n: source vertex, 
    // 2 * n + 1: sink vertex
    // Note that each regulators are treated as a pair of vertices.
    int source = 2 * n, sink = 2 * n + 1;
    vector<int> rcs(n); // regulator capacities
    for (int i = 0; i < n; i++) {
      // append the edges between each pair of regulator vertices
      cin >> rcs[i];
      graph[2 * i].push_back(edge(2 * i + 1, rcs[i], rcs[i]));
      graph[2 * i + 1].push_back(edge(2 * i, rcs[i], 0));
    }
    int m;
    cin >> m;
    while (m--) { // append the edges between regulators
      int i, j, c;
      cin >> i >> j >> c;
      i--; j--;
      graph[2 * i + 1].push_back(edge(2 * j, c, c));
      graph[2 * j].push_back(edge(2 * i + 1, c , 0));
    }
    int b, d;
    cin >> b >> d;
    while (b--) { // append the edges from the source to regulators
      int i;
      cin >> i;
      i--;
      graph[source].push_back(edge(2 * i, rcs[i], rcs[i]));
      graph[2 * i].push_back(edge(source, rcs[i], 0));
    }
    while (d--) { // append the edges from regulators to the sink
      int i;
      cin >> i;
      i--;
      graph[2 * i + 1].push_back(edge(sink, rcs[i], rcs[i]));
      graph[sink].push_back(edge(2 * i + 1, rcs[i], 0));
    }
    netflow(graph, source, sink);
    cout << total_flow(graph, source) << endl;
  }
  return 0;
}