Submission #490925

#	Time	Username	Problem	Language	Result	Execution time	Memory
490925		cs142857	Game (IOI13_game)	C++17	100 / 100	3290 ms	49776 KiB

game

// IOI 2013, Game
// Sparse Segment Tree + Treap
// Test: https://www.luogu.com.cn/record/63941489

#include "game.h"
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;

#ifdef DBG
  #define dbg 1
  #define dpf(...) fprintf(stderr, __VA_ARGS__);fflush(stderr);
  #define Dps(...) Dbgs(__VA_ARGS__)
#else
  #define dbg 0
  #define dpf(...) 42
  #define Dps(...) 42
#endif
 
#define SIZE(c) int((c).size())
#define FOR(i,l,r) for(int i = (l); i < (r); ++i)
#define REP(i,c) for(auto &i : (c))
#define ALL(c) (c).begin(),(c).end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
typedef long long i64;
typedef unsigned long long u64;
const double EPS = 1e-12;
const int INF = 1e9 + 10;
typedef vector<int> VI;
typedef vector<string> VS;
typedef pair<int, int> PI;

template <typename T> inline bool UpdateMax(T& x, T v) {
  if(v > x) {x=v; return 1;} else return 0;
}
template <typename T> inline bool UpdateMin(T& x, T v) {
  if(v < x) {x=v; return 1;} else return 0;
}

template <typename T>
using MinPQ = priority_queue<T, vector<T>, greater<T>>;

inline namespace output {
template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& v) {
  return os << "{" << v.first << " " << v.second << "}";
}
}  // namespace output

inline namespace output {  // Only for debug now.
template <class T>
void PrSep(std::ostream& os, string, const T& t) { os << t; }
template <class T, class... U>
void PrSep(std::ostream& os, string sep, const T& t, const U&... u) {
  PrSep(os, sep, t); os << sep; PrSep(os, sep, u...);
}

// Print w/ spaces, end with newline
void Ps() { cout << "\n"; }
template<class ...T> void Ps(const T&... t) { PrSep(cout," ",t...); Ps(); } 
template<class ...T> void Dbgs(const T&... t) { PrSep(cerr," ",t...); cerr << endl; } 
}  // namespace output

long long gcd2(long long X, long long Y) {
    long long tmp;
    while (X != Y && Y != 0) {
        tmp = X;
        X = Y;
        Y = tmp % Y;
    }
    return X;
}

const int MAX_SEG_NODE = 2000000;
const int MAX_INNER_TREE_NODE = 4000000;

// Treap, Split/Merge, without rotation.
// Source: https://cp-algorithms.com/data_structures/treap.html
// Works like map<K, V>, do not allow duplicate key.
template <typename K, typename V>
class Treap {
 public:
  struct TrNode {
    K k;
    V v;
    int pr = rand();
    K min_k, max_k;
    int l = 0, r = 0;
    TrNode() {}
    TrNode(K k, V v) : k(k), v(v) {
      min_k = max_k = k;
    }
  };
  vector<TrNode> a;
  V identity;

  inline virtual void Maintain(int u) {
    if (a[u].l) a[u].min_k = min(a[u].k, a[a[u].l].min_k);
    if (a[u].r) a[u].max_k = max(a[u].k, a[a[u].r].max_k);
  }

  void Init(V identity, int init_capacity = 0) {
    this->identity = identity;
    a.resize(1);
    a[0] = TrNode();
    a[0].v = identity;
    a.reserve(init_capacity + 1);
    empty_idx.clear();
  }

  void Split(int root, K k, int &l, int &r) {
    if (!root) {
      l = r = 0;
    } else if (a[root].k <= k) {
      Split(a[root].r, k, a[root].r, r);
      l = root;
    } else {
      Split(a[root].l, k, l, a[root].l);
      r = root;
    }
    if (l) Maintain(l);
    if (r) Maintain(r);
  }

  // Merges two trees, all values of tree u must less than v.
  // Returns new root.
  int Merge(int l, int r) {
    if (l == 0) return r;
    if (r == 0) return l;
    int u;
    if (a[l].pr > a[r].pr) {
      a[l].r = Merge(a[l].r, r);
      u = l;
    } else {
      a[r].l = Merge(l, a[r].l);
      u = r;
    }
    Maintain(u);
    return u;
  }

  // Returns u that a[u].k == k, or 0 not found.
  int Find(int root, K k) {
    int u = root;
    while (u) {
      if (a[u].k == k) return u;
      if (a[u].k > k)
        u = a[u].l;
      else 
        u = a[u].r;
    }
    return 0;
  }

  // If the key already exists, returns {the existing node, false}.
  // Otherwise, returns {the newly inserted node, true}, the value of the
  // newly inserted node will be `identity`.
  pair<int, bool> Insert(int& root, K k) {
    int u = Find(root, k);
    if (u) return {u, false};
    u = NewNodeIdx();
    a[u] = TrNode(k, identity);
    int l, r;
    Split(root, k, l, r);
    root = Merge(Merge(l, u), r);
    return {u, true};
  }

  void MaintainFromRoot(int root, int u) {
    if (a[u].k < a[root].k)
      MaintainFromRoot(a[root].l, u);
    else if (a[u].k > a[root].k)
      MaintainFromRoot(a[root].r, u);
    Maintain(root);
  }

  friend std::ostream& operator<<(std::ostream& os, const Treap<K, V>& t) {
    for (int i = 1; i < SIZE(t.a); ++i) {
      os << i << ": {" << t.a[i].k << " " << t.a[i].v << "} " << t.a[i].pr
         << " {" << t.a[i].l << " " << t.a[i].r << "}\n";
    }
    return os;
  }

 private:
  VI empty_idx;

  int NewNodeIdx() {
    int u;
    if (!empty_idx.empty()) {
      u = empty_idx.back();
      empty_idx.pop_back();
    } else {
      u = SIZE(a);
      a.emplace_back();
    }
    return u;
  }
};

// Treap, with weight and weight GCD-merge of sub-tree.
class TreapWithWeight : public Treap<int, pair<i64, i64>> {
 public:
  using K = int;
  using T = pair<i64, i64>;
  using Base = Treap<K, T>;
  using TrNode = typename Base::TrNode;

  void Init() {
    Base::Init({0, 0}, MAX_INNER_TREE_NODE);
  }

  inline virtual void Maintain(int u) {
    Base::Maintain(u);
    a[u].v.second = gcd2(gcd2(a[a[u].l].v.second, a[a[u].r].v.second),
                         a[u].v.first);
  }

  void Set(int& root, K k, i64 w) {
    int u = Base::Insert(root, k).first;
    a[u].v.first = w;
    Base::MaintainFromRoot(root, u);
  }

  i64 RangeQuery(int root, K min_k, K max_k) {
    i64 res = 0;
    if (!root || a[root].max_k < min_k || a[root].min_k > max_k)
      ;
    else if (a[root].min_k >= min_k && a[root].max_k <= max_k)
      res = a[root].v.second;
    else {
      if (a[root].k >= min_k && a[root].k <= max_k) res = a[root].v.first;
      res = gcd2(res, RangeQuery(a[root].l, min_k, max_k));
      res = gcd2(res, RangeQuery(a[root].r, min_k, max_k));
    }
    return res;
  }
};

template <typename T>
class BaseDySegTree {
 public:
  struct Node {
    int l = -1, r = -1;
    T v;
  };
  int max_idx;
  vector<Node> a;

  inline virtual T default_value() const = 0;

  void Init(int max_idx) {
    assert(max_idx >= -1);
    this->max_idx = max_idx;
    a.clear();
    a.reserve(MAX_SEG_NODE);
  }

  int NewNode() {
    int res = SIZE(a);
    a.emplace_back();
    a.back().v = default_value();
    return res;
  }
};

template <typename T>
class DySegTree2D : public BaseDySegTree<int> {
 public:
  int max_y;
  TreapWithWeight tree;

  inline virtual int default_value() const { return 0; }

  void Init(int max_x, int max_y) {
    BaseDySegTree<int>::Init(max_x);
    this->max_y = max_y;
    tree.Init();
  }

  int Update(int x, int y, T v, int p) { return Update(x, y, v, p, 0, this->max_idx); }

  T Query(int qlx, int qrx, int qly, int qry, int p) {
    return Query(qlx, qrx, qly, qry, p, 0, this->max_idx);
  }

 private:
  inline void NewLeft(int p) {
    if (a[p].l < 0) a[p].l = NewNode();
  }
  inline void NewRight(int p) {
    if (a[p].r < 0) a[p].r = NewNode();
  }

  T Update(int x, int y, T v, int p, int li, int ri) {
    T res;
    if (li == ri) {
      res = v;
    } else {
      int m = (li + ri) >> 1;
      if (x <= m) {
        NewLeft(p);
        res = Update(x, y, v, a[p].l, li, m);
        if (a[p].r >= 0) res = gcd2(res, QueryY(a[a[p].r].v, y, y));
      } else {
        NewRight(p);
        res = Update(x, y, v, a[p].r, m + 1, ri);
        if (a[p].l >= 0) res = gcd2(res, QueryY(a[a[p].l].v, y, y));
      }
    }
    tree.Set(a[p].v, y, res);
    return res;
  }

  T Query(int qlx, int qrx, int qly, int qry, int p, int lx, int rx) {
    if (p < 0 || qlx > rx || qrx < lx) return 0;
    T res;
    if (qlx <= lx && qrx >= rx) {
      res = QueryY(a[p].v, qly, qry);
    } else {
      int m = (lx + rx) >> 1;
      res = gcd2(Query(qlx, qrx, qly, qry, this->a[p].l, lx, m),
                 Query(qlx, qrx, qly, qry, this->a[p].r, m + 1, rx));
    }
    return res;
  }

  T QueryY(int root, int qly, int qry) {
    return tree.RangeQuery(root, qly, qry);
  }
};

DySegTree2D<i64> st;
int root;

void init(int R, int C) {
  st.Init(R - 1, C - 1);
  root = st.NewNode();
}

void update(int x, int y, i64 w) {
  st.Update(x, y, w, root);
}

i64 calculate(int lx, int ly, int rx, int ry) {
  return st.Query(lx, rx, ly, ry, root);
}

• Subtask 1: 10 / 10
• Subtask 2: 27 / 27
• Subtask 3: 26 / 26
• Subtask 4: 17 / 17
• Subtask 5: 20 / 20