UVa 10080 - Gopher II

Accepted date: 2012-10-15
Ranking (as of 2013-01-27): 486
Language: C++

/*
  UVa 10080 - Gopher II

  To build using Visual Studio 2008:
    cl -EHsc -O2 gopher_II.cpp
*/

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

const int nr_gophers_max = 100, nr_holes_max = 100;

pair<double, double> gophers[nr_gophers_max], holes[nr_holes_max];

double euclidean_distance(const pair<double, double>& p,
  const pair<double, double>& q)
{
  double dx = p.first - q.first, dy = p.second - q.second;
  return sqrt(dx * dx + dy * dy);
}

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 nr_gophers, nr_holes;
  double seconds, velocity;
  while (cin >> nr_gophers >> nr_holes >>
    seconds >> velocity) {
    for (int i = 0; i < nr_gophers; i++)
      cin >> gophers[i].first >> gophers[i].second;
    for (int i = 0; i < nr_holes; i++)
      cin >> holes[i].first >> holes[i].second;
    int nr_vertices = nr_gophers + nr_holes + 2;
    vector< vector<edge> > graph(nr_vertices);
    // indices are:
    //  0 - (nr_gophers - 1): gopher vertices,
    //  nr_gophers - (nr_gophers + nr_holes - 1): hole vertices,
    //  (nr_gophers + nr_holes): source vertex,
    // (nr_gophers + nr_holes + 1): sink vertex
    int source = nr_gophers + nr_holes, sink = nr_gophers + nr_holes + 1;
    double d = velocity * seconds;
    for (int i = 0; i < nr_gophers; i++) {
      // append the edges between the source and gopher vertices
      graph[source].push_back(edge(i, 1, 1));
      graph[i].push_back(edge(source, 1, 0));
      for (int j = 0; j < nr_holes; j++)
        if (euclidean_distance(gophers[i], holes[j]) <= d) {
          // append the edges between gopher vertices and hole vertices
          // if a gopher can reach the hole in the specified time
          graph[i].push_back(edge(nr_gophers + j, 1, 1));
          graph[nr_gophers + j].push_back(edge(i, 1, 0));
        }
    }
    for (int i = nr_gophers; i < nr_gophers + nr_holes; i++) {
      // append the edges between hole vertices and the sink
      graph[i].push_back(edge(sink, 1, 1));
      graph[sink].push_back(edge(i, 1, 0));
    }
    netflow(graph, source, sink);
      // apply Ford-Fulkerson's augmenting path algorithm
    cout << nr_gophers - total_flow(graph, source) << endl;
  }
  return 0;
}