UVa 670 - The dog task

Accepted date: 2014-06-21
Ranking (as of 2014-06-22): 274 out of 668
Language: C++

/*
  UVa 670 - The dog task

  To build using Visual Studio 2012:
    cl -EHsc -O2 UVa_670_The_dog_task.cpp
*/

#include <iostream>
#include <vector>
#include <queue>
#include <utility>
#include <algorithm>
#include <cmath>
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;
}

struct point {
  int x_, y_;
};

double euclidean_distance(const point& a, const point& b)
{
  double dx = static_cast<double>(a.x_ - b.x_),
    dy = static_cast<double>(a.y_ - b.y_);
  return sqrt(dx * dx + dy * dy);
}

int main()
{
  int l;
  cin >> l;
  while (l--) {
    int n, m;
    cin >> n >> m;
    vector<point> routes(n), places(m);
    for (int i = 0; i < n; i++)
      cin >> routes[i].x_ >> routes[i].y_;
    vector<double> route_distances(n - 1);
    for (int i = 0; i < n - 1; i++)
      route_distances[i] = euclidean_distance(routes[i], routes[i + 1]);
    for (int i = 0; i < m; i++)
      cin >> places[i].x_ >> places[i].y_;

    int nr_vertices = n + m + 2;
    vector< vector<edge> > graph(nr_vertices);
    // indices are:
    // 0 - (m - 1): Ralph's interesting place vertices
    // m - (m + n - 1) : Bob's route vertices, 
    //  i-th vertex represents the path from (x(i), y(i)) to (x(i + 1), y(i + 1))
    // n + m: source vertex, n + m + 1: sink vertex
    int source = n + m, sink = n + m + 1;
    for (int i = 0; i < m; i++) {
      // append the edges between the source and place vertices
      graph[source].push_back(edge(i, 1, 1));
      graph[i].push_back(edge(source, 1, 0));
      for (int j = 0; j < n - 1; j++) {
        // append the edges between place vertices and route vertices
        if (euclidean_distance(places[i], routes[j]) +
          euclidean_distance(places[i], routes[j + 1]) <=
          2.0 * route_distances[j]) {
          graph[i].push_back(edge(m + j, 1, 1));
          graph[m + j].push_back(edge(i, 1, 0));
        }
      }
    }
    for (int i = m; i < m + n; i++) {
      // append the edges between route 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 << n + total_flow(graph, source) << endl;
    for (int i = 0; i < n - 1; i++) {
      if (i)
        cout << ' ';
      cout << routes[i].x_ << ' ' << routes[i].y_;
      const vector<edge>& edges = graph[m + i];
      int j = -1;
      for (size_t k = 0; k < edges.size(); k++)
        if (edges[k].residual && edges[k].v < m) {
          j = edges[k].v; break;
        }
      if (j != -1)
        cout << ' ' << places[j].x_ <<
          ' ' << places[j].y_;
    }
    cout << ' ' << routes[n - 1].x_ <<
      ' ' << routes[n - 1].y_ << endl;
    if (l)
      cout << endl;
  }
  return 0;
}