HackerEarth Alice and wheel-graph problem solution

In this HackerEarth Alice and wheel-graph problem solution Alice has a wheel-graph: an undirected graph with n + 1 nodes and 2 . n edges. In wheel-graph there are edges between n + 1 and i for each integer i : 1 <= i <= n and edges between i and i mod n + 1 for each integer i : 1 <= i <= n (see examples to understand it better). Undirected graphs are quite boring for Alice so she made a directed wheel-graph and now each edge has a direction.

Alice wants performs two types of queries:

• 1 a b - change orientation between nodes a and b. Now orientation is from a to b (before this query in graph was a edge from node b to node a).
• 2 a b - check if is b reachable from a.

Help her.

HackerEarth Alice and wheel-graph problem solution.

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
#include <cmath>
#include <ctime>
#include <functional>
#include <sstream>
#include <fstream>
#include <valarray>
#include <complex>
#include <queue>
#include <cassert>
#include <bitset>
using namespace std;

#ifdef LOCAL
#define debug_flag 1
#else
#define debug_flag 0
#endif

  template <class T1, class T2 >
std::ostream& operator << (std::ostream& os, const pair<T1, T2> &p) 
{
  os << "[" << p.first << ", " << p.second << "]";
  return os;
}

  template <class T >
std::ostream& operator << (std::ostream& os, const std::vector<T>& v) 
{
  os << "[";
  bool first = true;
  for (typename std::vector<T>::const_iterator it = v.begin(); it != v.end(); ++it)
  {
    if (!first)
      os << ", ";
    first = false;
    os << *it;
  }
  os << "]";
  return os;
}

  template <class T >
std::ostream& operator << (std::ostream& os, const std::set<T>& v) 
{
  os << "[";
  bool first = true;
  for (typename std::set<T>::const_iterator it = v.begin(); it != v.end(); ++it)
  {
    if (!first)
      os << ", ";
    first = false;
    os << *it;
  }
  os << "]";
  return os;
}

#define dbg(args...) { if (debug_flag) { _print(_split(#args, ',').begin(), args); cerr << endl; } else { void(0);} }

vector<string> _split(const string& s, char c) {
  vector<string> v;
  stringstream ss(s);
  string x;
  while (getline(ss, x, c))
    v.emplace_back(x);
  return v;
}

void _print(vector<string>::iterator) {}
template<typename T, typename... Args>
void _print(vector<string>::iterator it, T a, Args... args) {
  string name = it -> substr((*it)[0] == ' ', it -> length());
  if (isalpha(name[0]))
    cerr << name  << " = " << a << " ";
  else
    cerr << name << " ";
  _print(++it, args...);
}

typedef long long int int64;

struct Graph
{
  int n;

  set<int> no_right_s;
  set<int> no_left_s;
  set<int> to_center_s;
  vector<pair<int, int> > segments;

  Graph(int new_n = 0)
  {
    n = new_n;
  }

  void change_edge(int a, int b)
  {
    if (a == n)
    {
      to_center_s.erase(b);
    }
    else if (b == n)
    {
      to_center_s.insert(a);
    }
    else if ((a + 1) % n == b)
    {
      no_right_s.erase(a);
      no_left_s.insert(b);
    }
    else
    {
      no_left_s.erase(a);
      no_right_s.insert(b);
    }
  }

  bool can_reach_center(int a)
  {
    if (a == n)
      return true;

    segments.clear();
    add_reachable_to_right(a);
    add_reachable_to_left(a);

    for (pair<int, int> segment : segments)
    {
      int l = segment.first;
      int r = segment.second;
      auto it = to_center_s.lower_bound(l);
      if (it != to_center_s.end() && *it <= r)
        return true;
    }

    return false;
  }

  void add_reachable_to_right(int a)
  {
    if (no_right_s.empty())
    {
      segments.clear();
      segments.emplace_back(0, n - 1);
      return;
    }

    auto it = no_right_s.lower_bound(a);
    if (it != no_right_s.end())
    {
      segments.emplace_back(a, *it);
      return;
    }

    segments.emplace_back(a, n - 1);

    if (no_right_s.count(n - 1) == 1 || a == 0)
      return;

    it = no_right_s.lower_bound(0);
    if (it == no_right_s.end())
      segments.emplace_back(0, a - 1);
    else
      segments.emplace_back(0, *it);
  }

  void add_reachable_to_left(int a)
  {
    if (no_left_s.empty())
    {
      segments.clear();
      segments.emplace_back(0, n - 1);
      return;
    }

    auto it = no_left_s.upper_bound(a);
    if (it != no_left_s.begin())
    {
      it--;
      segments.emplace_back(*it, a);
      return;
    }

    segments.emplace_back(0, a);

    if (no_left_s.count(0) == 1 || a == n - 1)
      return;

    it = no_left_s.end();
    it--;
    segments.emplace_back(*it, n - 1);
  }
};

int n;
Graph graph, reverse_graph;

bool can_reach(int a, int b)
{
  bool can_reach_center_b = reverse_graph.can_reach_center(b);

  if (a == n)
    return can_reach_center_b; 
  
  bool can_reach_center_a = graph.can_reach_center(a);

  if (b == n)
    return can_reach_center_a;

  if (can_reach_center_a && can_reach_center_b)
    return true;

  for (pair<int, int> segment : graph.segments)
  {
    int l = segment.first;
    int r = segment.second;
    if (l <= b && b <= r)
      return true;
  }

  return false;
}

int main()
{
#ifdef LOCAL
  freopen ("input.txt", "r", stdin);
#endif

  scanf("%d", &n);

  graph = Graph(n);
  reverse_graph = Graph(n);

  for (int i = 0; i < 2 * n; i++)
  {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    graph.change_edge(a, b);
    reverse_graph.change_edge(b, a);
  }

  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; i++)
  {
    int type, a, b;
    scanf("%d%d%d", &type, &a, &b);
    a--;
    b--;

    if (type == 1)
    {
      graph.change_edge(a, b);
      reverse_graph.change_edge(b, a);
    }
    else
    {
      bool res = can_reach(a, b);
      printf("%s\n", res ? "Yes" : "No");
    }
  }

  return 0;
}