oj.uz

답안 #490925

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
490925 2021-11-29T20:01:39 Z cs142857 게임 (IOI13_game) C++17
100 / 100
 3290 ms 49776 KB 
// 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
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 316 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 296 KB Output is correct

Subtask #2
27.0 / 27.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 649 ms 10752 KB Output is correct
5 Correct 269 ms 10552 KB Output is correct
6 Correct 666 ms 8032 KB Output is correct
7 Correct 727 ms 7712 KB Output is correct
8 Correct 433 ms 7148 KB Output is correct
9 Correct 723 ms 7792 KB Output is correct
10 Correct 682 ms 7504 KB Output is correct
11 Correct 1 ms 204 KB Output is correct

Subtask #3
26.0 / 26.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 2 ms 316 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 316 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 849 ms 12100 KB Output is correct
13 Correct 1539 ms 7048 KB Output is correct
14 Correct 218 ms 5464 KB Output is correct
15 Correct 1561 ms 8188 KB Output is correct
16 Correct 255 ms 9688 KB Output is correct
17 Correct 881 ms 9020 KB Output is correct
18 Correct 1473 ms 11188 KB Output is correct
19 Correct 1265 ms 11332 KB Output is correct
20 Correct 1258 ms 10796 KB Output is correct
21 Correct 0 ms 332 KB Output is correct

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 1 ms 292 KB Output is correct
12 Correct 636 ms 10784 KB Output is correct
13 Correct 262 ms 10556 KB Output is correct
14 Correct 662 ms 7988 KB Output is correct
15 Correct 733 ms 7744 KB Output is correct
16 Correct 435 ms 7120 KB Output is correct
17 Correct 725 ms 7848 KB Output is correct
18 Correct 691 ms 7620 KB Output is correct
19 Correct 847 ms 12024 KB Output is correct
20 Correct 1557 ms 6936 KB Output is correct
21 Correct 227 ms 5496 KB Output is correct
22 Correct 1551 ms 8044 KB Output is correct
23 Correct 257 ms 9696 KB Output is correct
24 Correct 871 ms 8856 KB Output is correct
25 Correct 1494 ms 11284 KB Output is correct
26 Correct 1314 ms 11284 KB Output is correct
27 Correct 1266 ms 10676 KB Output is correct
28 Correct 383 ms 27972 KB Output is correct
29 Correct 1469 ms 30628 KB Output is correct
30 Correct 1908 ms 22084 KB Output is correct
31 Correct 1690 ms 18672 KB Output is correct
32 Correct 325 ms 10116 KB Output is correct
33 Correct 477 ms 10312 KB Output is correct
34 Correct 355 ms 24328 KB Output is correct
35 Correct 1030 ms 19648 KB Output is correct
36 Correct 2238 ms 28452 KB Output is correct
37 Correct 1778 ms 28660 KB Output is correct
38 Correct 1802 ms 27988 KB Output is correct
39 Correct 1405 ms 24344 KB Output is correct
40 Correct 1 ms 204 KB Output is correct

Subtask #5
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 288 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 264 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 646 ms 10712 KB Output is correct
13 Correct 260 ms 10572 KB Output is correct
14 Correct 661 ms 7992 KB Output is correct
15 Correct 727 ms 7764 KB Output is correct
16 Correct 437 ms 7132 KB Output is correct
17 Correct 710 ms 8080 KB Output is correct
18 Correct 686 ms 7536 KB Output is correct
19 Correct 842 ms 12068 KB Output is correct
20 Correct 1529 ms 6844 KB Output is correct
21 Correct 219 ms 5580 KB Output is correct
22 Correct 1538 ms 8056 KB Output is correct
23 Correct 259 ms 9820 KB Output is correct
24 Correct 865 ms 9056 KB Output is correct
25 Correct 1461 ms 11348 KB Output is correct
26 Correct 1265 ms 11284 KB Output is correct
27 Correct 1253 ms 10760 KB Output is correct
28 Correct 392 ms 27972 KB Output is correct
29 Correct 1466 ms 30716 KB Output is correct
30 Correct 1904 ms 22012 KB Output is correct
31 Correct 1667 ms 18560 KB Output is correct
32 Correct 323 ms 10116 KB Output is correct
33 Correct 476 ms 10308 KB Output is correct
34 Correct 357 ms 24356 KB Output is correct
35 Correct 1031 ms 19636 KB Output is correct
36 Correct 2217 ms 28508 KB Output is correct
37 Correct 1710 ms 28636 KB Output is correct
38 Correct 1760 ms 28292 KB Output is correct
39 Correct 596 ms 47656 KB Output is correct
40 Correct 2643 ms 49776 KB Output is correct
41 Correct 3027 ms 38680 KB Output is correct
42 Correct 2669 ms 31048 KB Output is correct
43 Correct 801 ms 44584 KB Output is correct
44 Correct 423 ms 10432 KB Output is correct
45 Correct 1446 ms 24492 KB Output is correct
46 Correct 3290 ms 48504 KB Output is correct
47 Correct 3273 ms 48640 KB Output is correct
48 Correct 3208 ms 48216 KB Output is correct
49 Correct 0 ms 204 KB Output is correct