Problem p00998 (C++)

Buggy submission (status: Time Limit Exceeded):
#define NDEBUG 1
#include <bits/stdc++.h>

using key_type = int;

enum { L, R };

struct node {
  key_type key;
  std::array<node *, 2> ch;
  int size;
  int height;

  int min;

  static node *const nil;

  node() : node(-1) {}
  node(key_type key) : node(key, nil, nil, 1, 1, key) {}
  node(const key_type key, node *left, node *right, int size, int height,
       key_type min)
      : key(key), ch({{left, right}}), size(size), height(height), min(min) {}

  void *operator new(size_t) {
    static int p = 0;
    static node pool[1000000];
    return pool + p++;
  }
};

node *const node::nil = new node(key_type(), nullptr, nullptr, 0, 0, 1e9);
node *const nil = node::nil;
namespace trush {
auto ___ = []() { return nil->ch = {{nil, nil}}; };
};

using np = node *;
using cnp = const node *;

// ok
np update(np n) {
  n->size = n->ch[L]->size + 1 + n->ch[R]->size;
  n->height = std::max(n->ch[L]->height, n->ch[R]->height) + 1;

  n->min = std::min({n->ch[L]->min, n->key, n->ch[R]->min});
  return n;
}

// ok
template <int dir> np rotate(np n) {
  assert(n->ch[!dir] != nil);
  np root = n->ch[!dir];
  n->ch[!dir] = root->ch[dir];
  root->ch[dir] = n;
  update(n);
  update(root);
  return root;
}

// ok
int bfactor(np n) {
  assert(n != nil);
  return n->ch[R]->height - n->ch[L]->height;
}

// ok
np balance(np n) {
  assert(abs(bfactor(n)) <= 2);
  if (bfactor(n) == +2) {
    if (bfactor(n->ch[R]) < 0)
      n->ch[R] = rotate<R>(n->ch[R]);
    return rotate<L>(n);
  } else if (bfactor(n) == -2) {
    if (bfactor(n->ch[L]) > 0)
      n->ch[L] = rotate<L>(n->ch[L]);
    return rotate<R>(n);
  } else {
    return n;
  }
}

// ok
np insert_at(np n, int k, key_type x) {
  assert(0 <= k && k <= n->size);
  if (n == nil)
    return new node(x);
  int sl = n->ch[L]->size;
  if (k <= sl)
    n->ch[L] = insert_at(n->ch[L], k, x);
  else
    n->ch[R] = insert_at(n->ch[R], k - sl - 1, x);
  return balance(update(n));
}

// ok
template <int dir> std::pair<np, np> remove_most(np n) {
  assert(n != nil);
  if (n->ch[dir] != nil) {
    np most;
    std::tie(n->ch[dir], most) = remove_most<dir>(n->ch[dir]);
    return {balance(update(n)), most};
  } else {
    np res = n->ch[!dir];
    n->ch[!dir] = nil;
    return {res, update(n)};
  }
}

// ok
std::pair<np, key_type> remove_at(np n, int k) {
  assert(n != nil);
  int sl = n->ch[L]->size;
  if (k < sl) {
    key_type most;
    std::tie(n->ch[L], most) = remove_at(n->ch[L], k);
    return {balance(update(n)), most};
  }
  if (k == sl) {
    if (n->ch[R] == nil) {
      return {n->ch[L], n->key};
    } else {
      np most;
      std::tie(n->ch[R], most) = remove_most<L>(n->ch[R]);
      most->ch = n->ch;
      // delete n;
      return {balance(update(most)), n->key};
    }
  } else {
    key_type most;
    std::tie(n->ch[R], most) = remove_at(n->ch[R], k - sl - 1);
    return {balance(update(n)), most};
  }
}

// ok
np merge_with_root(np l, np root, np r) {
  // Members of `root` except root->key may not be valid for performance.
  if (abs(l->height - r->height) <= 1) {
    root->ch = {{l, r}};
    return update(root);
  } else if (l->height > r->height) {
    l->ch[R] = merge_with_root(l->ch[R], root, r);
    return balance(update(l));
  } else {
    r->ch[L] = merge_with_root(l, root, r->ch[L]);
    return balance(update(r));
  }
}

// ok
np merge(np l, np r) {
  if (l == nil)
    return r;
  if (r == nil)
    return l;
  np m;
  if (l->height > r->height)
    std::tie(r, m) = remove_most<L>(r);
  else
    std::tie(l, m) = remove_most<R>(l);
  return merge_with_root(l, m, r);
}

template <typename Iterator> np build(Iterator left, Iterator right) {
  int n = right - left;
  Iterator mid = left + n / 2;
  if (n == 0)
    return nil;
  np l = build(left, mid);
  np r = build(mid + 1, right);
  np m = new node(*mid);
  m->ch = {{l, r}};
  return update(m);
}

// ok
std::pair<np, np> split_at(np n, int k) {
  assert(0 <= k && k <= n->size);
  if (n == nil)
    return {nil, nil};
  int sl = n->ch[L]->size;
  np l = n->ch[L];
  np r = n->ch[R];
  n->ch[L] = n->ch[R] = nil;
  // Members of node passed to `merge` must be valid,
  // but ones for `merge_with_root` doesn't have to.
  np nl, nr;
  if (k < sl) {
    std::tie(nl, nr) = split_at(l, k);
    return {nl, merge_with_root(nr, n, r)};
  } else if (k == sl) {
    update(n);
    return {l, merge(n, r)};
  } else {
    std::tie(nl, nr) = split_at(r, k - sl - 1);
    return {merge_with_root(l, n, nl), nr};
  }
}

void update_at(np n, int k, key_type x) {
  assert(0 <= k && k <= n->size - 1);
  int sl = n->ch[L]->size;
  if (k < sl) {
    update_at(n->ch[L], k, x);
  } else if (k == sl) {
    n->key = x;
  } else {
    update_at(n->ch[R], k - sl - 1, x);
  }
  update(n);
}

key_type range_min(np n, int l, int r) {
  assert(n != nil);
  assert(0 <= l && l <= r);
  assert(l <= r && r <= n->size);
  if (l == 0 && r == n->size) {
    return n->min;
  }
  int sl = n->ch[L]->size;
  key_type res = 1e9;
  if (l < sl) {
    res = std::min(res, range_min(n->ch[L], l, std::min(r, sl)));
  }
  if (l <= sl && sl < r) {
    res = std::min(res, n->key);
  }
  if (sl + 1 < r) {
    res =
        std::min(res, range_min(n->ch[R], std::max(0, l - sl - 1), r - sl - 1));
  }
  return res;
}

namespace test {

int real_height(np n) {
  if (n == nil)
    return 0;
  return 1 + std::max(real_height(n->ch[L]), real_height(n->ch[R]));
}

int real_size(np n) {
  if (n == nil)
    return 0;
  return 1 + real_size(n->ch[L]) + real_size(n->ch[R]);
}

int real_min(np n) {
  if (n == nil)
    return 1e9;
  return std::min({real_min(n->ch[L]), n->key, real_min(n->ch[R])});
}

bool verify(np n) {
  if (n == nil) {
    if (n->ch[L] != nil)
      return false;
    if (n->ch[R] != nil)
      return false;
    return true;
  }
  np l = n->ch[L];
  np r = n->ch[R];

  if (n->size != real_size(n))
    return false;
  if (n->height != real_height(n))
    return false;
  if (n->min != real_min(n))
    return false;

  if (n->size != l->size + 1 + r->size)
    return false;
  if (n->height != std::max(l->height, r->height) + 1)
    return false;
  if (n->min != std::min({n->ch[L]->min, n->key, n->ch[R]->min}))
    return false;

  if (abs(bfactor(n)) >= 2)
    return false;
  return true;
}
} // namespace test

void to_a(np n, std::vector<int> &v) {
  if (n == nil)
    return;
  to_a(n->ch[L], v);
  v.push_back(n->key);
  to_a(n->ch[R], v);
}

std::vector<int> to_a(np n) {
  std::vector<int> res;
  to_a(n, res);
  return res;
}

using namespace std;

mt19937 mt(100);

int randint(int l, int r) {
  uniform_int_distribution<int> dist(l, r);
  return dist(mt);
}

void show(const vector<int> &x) {
  for (auto &e : x)
    cout << e << ' ';
  cout << endl;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n, q;
  while (cin >> n >> q) {
    vector<int> a(n);
    for (int i = 0; i < n; ++i)
      cin >> a[i];
    np root = build(a.begin(), a.end());
    for (int i = 0; i < q; ++i) {
      int t, x, y;
      cin >> t >> x >> y;
      if (t == 0) {
        int t;
        tie(root, t) = remove_at(root, y);
        root = insert_at(root, x, t);
      } else if (t == 1) {
        ++y;
        cout << range_min(root, x, y) << '\n';
        // np l, m, r;
        // tie(m, r) = split_at(root, y);
        // tie(l, m) = split_at(m, x);
        // cout << m->min << '\n';
        // root = merge(l, merge(m, r));
      } else {
        update_at(root, x, y);
      }
      test::verify(root);
    }
  }

  // for (int _ = 0; _ < 10000; ++_) {
  //     int N = randint(1, 2000);
  //     np root = nil;
  //     vector<int> v(N);
  //     for (int i = 0; i < N; ++i) {
  //         v[i] = randint(0, 100);
  //         root = insert_at(root, i, v[i]);
  //     }
  //     int k = randint(0, N);
  //     np l, r;
  //     tie(l, r) = split_at(root, k);
  //     test::verify(l);
  //     test::verify(r);
  //     vector<int> vl(v.begin(), v.begin() + k), vr(v.begin() + k, v.end());
  //     assert(to_a(l) == vl);
  //     assert(to_a(r) == vr);
  //     root = merge(l, r);
  //     test::verify(root);
  //     for (auto &x : vr) vl.push_back(x);
  //     assert(to_a(root) == vl);
  // }

  // for (int _ = 0; _ < 10000; ++_) {
  //     int N = randint(1, 2000);
  //     np root = nil;
  //     // vector<int> v;
  //     for (int i = 0; i < N; ++i) {
  //         if (root->size && randint(0, 3) == 0) {
  //             int k = randint(0, root->size - 1);
  //             // v.erase(v.begin() + k);
  //             root = remove_at(root, k);
  //         } else {
  //             int k = randint(0, root->size);
  //             int x = randint(0, 100);
  //             // v.insert(v.begin() + k, x);
  //             root = insert_at(root, k, x);
  //         }
  //         // vector<int> a = to_a(root);
  //         // assert(verify(root));
  //         // assert(a == v);
  //     }
  //     assert(test::verify(root));
  //     // vector<int> a = to_a(root);
  //     // assert(a == v);
  // }
}

Fixed submission:
#define NDEBUG 1
#include <bits/stdc++.h>

using key_type = int;

enum { L, R };

struct node {
  key_type key;
  std::array<node *, 2> ch;
  int size;
  int height;

  int min;

  static node *const nil;

  node() : node(-1) {}
  node(key_type key) : node(key, nil, nil, 1, 1, key) {}
  node(const key_type key, node *left, node *right, int size, int height,
       key_type min)
      : key(key), ch({{left, right}}), size(size), height(height), min(min) {}

  void *operator new(size_t) {
    static int p = 0;
    static node pool[1000000];
    return pool + p++;
  }
};

node *const node::nil = new node(key_type(), nullptr, nullptr, 0, 0, 1e9);
node *const nil = node::nil;
namespace trush {
auto ___ = []() { return nil->ch = {{nil, nil}}; };
};

using np = node *;
using cnp = const node *;

// ok
np update(np n) {
  n->size = n->ch[L]->size + 1 + n->ch[R]->size;
  n->height = std::max(n->ch[L]->height, n->ch[R]->height) + 1;

  n->min = std::min({n->ch[L]->min, n->key, n->ch[R]->min});
  return n;
}

// ok
template <int dir> np rotate(np n) {
  assert(n->ch[!dir] != nil);
  np root = n->ch[!dir];
  n->ch[!dir] = root->ch[dir];
  root->ch[dir] = n;
  update(n);
  update(root);
  return root;
}

// ok
int bfactor(np n) {
  assert(n != nil);
  return n->ch[R]->height - n->ch[L]->height;
}

// ok
np balance(np n) {
  assert(abs(bfactor(n)) <= 2);
  if (bfactor(n) == +2) {
    if (bfactor(n->ch[R]) < 0)
      n->ch[R] = rotate<R>(n->ch[R]);
    return rotate<L>(n);
  } else if (bfactor(n) == -2) {
    if (bfactor(n->ch[L]) > 0)
      n->ch[L] = rotate<L>(n->ch[L]);
    return rotate<R>(n);
  } else {
    return n;
  }
}

// ok
np insert_at(np n, int k, key_type x) {
  assert(0 <= k && k <= n->size);
  if (n == nil)
    return new node(x);
  int sl = n->ch[L]->size;
  if (k <= sl)
    n->ch[L] = insert_at(n->ch[L], k, x);
  else
    n->ch[R] = insert_at(n->ch[R], k - sl - 1, x);
  return balance(update(n));
}

// ok
template <int dir> std::pair<np, np> remove_most(np n) {
  assert(n != nil);
  if (n->ch[dir] != nil) {
    np most;
    std::tie(n->ch[dir], most) = remove_most<dir>(n->ch[dir]);
    return {balance(update(n)), most};
  } else {
    np res = n->ch[!dir];
    n->ch[!dir] = nil;
    return {res, update(n)};
  }
}

// ok
std::pair<np, key_type> remove_at(np n, int k) {
  assert(n != nil);
  int sl = n->ch[L]->size;
  if (k < sl) {
    key_type most;
    std::tie(n->ch[L], most) = remove_at(n->ch[L], k);
    return {balance(update(n)), most};
  }
  if (k == sl) {
    if (n->ch[R] == nil) {
      return {n->ch[L], n->key};
    } else {
      np most;
      std::tie(n->ch[R], most) = remove_most<L>(n->ch[R]);
      most->ch = n->ch;
      // delete n;
      return {balance(update(most)), n->key};
    }
  } else {
    key_type most;
    std::tie(n->ch[R], most) = remove_at(n->ch[R], k - sl - 1);
    return {balance(update(n)), most};
  }
}

// ok
np merge_with_root(np l, np root, np r) {
  // Members of `root` except root->key may not be valid for performance.
  if (abs(l->height - r->height) <= 1) {
    root->ch = {{l, r}};
    return update(root);
  } else if (l->height > r->height) {
    l->ch[R] = merge_with_root(l->ch[R], root, r);
    return balance(update(l));
  } else {
    r->ch[L] = merge_with_root(l, root, r->ch[L]);
    return balance(update(r));
  }
}

// ok
np merge(np l, np r) {
  if (l == nil)
    return r;
  if (r == nil)
    return l;
  np m;
  if (l->height > r->height)
    std::tie(r, m) = remove_most<L>(r);
  else
    std::tie(l, m) = remove_most<R>(l);
  return merge_with_root(l, m, r);
}

template <typename Iterator> np build(Iterator left, Iterator right) {
  int n = right - left;
  Iterator mid = left + n / 2;
  if (n == 0)
    return nil;
  np l = build(left, mid);
  np r = build(mid + 1, right);
  np m = new node(*mid);
  m->ch = {{l, r}};
  return update(m);
}

// ok
std::pair<np, np> split_at(np n, int k) {
  assert(0 <= k && k <= n->size);
  if (n == nil)
    return {nil, nil};
  int sl = n->ch[L]->size;
  np l = n->ch[L];
  np r = n->ch[R];
  n->ch[L] = n->ch[R] = nil;
  // Members of node passed to `merge` must be valid,
  // but ones for `merge_with_root` doesn't have to.
  np nl, nr;
  if (k < sl) {
    std::tie(nl, nr) = split_at(l, k);
    return {nl, merge_with_root(nr, n, r)};
  } else if (k == sl) {
    update(n);
    return {l, merge(n, r)};
  } else {
    std::tie(nl, nr) = split_at(r, k - sl - 1);
    return {merge_with_root(l, n, nl), nr};
  }
}

void update_at(np n, int k, key_type x) {
  assert(0 <= k && k <= n->size - 1);
  int sl = n->ch[L]->size;
  if (k < sl) {
    update_at(n->ch[L], k, x);
  } else if (k == sl) {
    n->key = x;
  } else {
    update_at(n->ch[R], k - sl - 1, x);
  }
  update(n);
}

key_type range_min(np n, int l, int r) {
  assert(n != nil);
  assert(0 <= l && l <= r);
  assert(l <= r && r <= n->size);
  if (l == 0 && r == n->size) {
    return n->min;
  }
  int sl = n->ch[L]->size;
  key_type res = 1e9;
  if (l < sl) {
    res = std::min(res, range_min(n->ch[L], l, std::min(r, sl)));
  }
  if (l <= sl && sl < r) {
    res = std::min(res, n->key);
  }
  if (sl + 1 < r) {
    res =
        std::min(res, range_min(n->ch[R], std::max(0, l - sl - 1), r - sl - 1));
  }
  return res;
}

namespace test {

int real_height(np n) {
  if (n == nil)
    return 0;
  return 1 + std::max(real_height(n->ch[L]), real_height(n->ch[R]));
}

int real_size(np n) {
  if (n == nil)
    return 0;
  return 1 + real_size(n->ch[L]) + real_size(n->ch[R]);
}

int real_min(np n) {
  if (n == nil)
    return 1e9;
  return std::min({real_min(n->ch[L]), n->key, real_min(n->ch[R])});
}

bool verify(np n) {
  if (n == nil) {
    if (n->ch[L] != nil)
      return false;
    if (n->ch[R] != nil)
      return false;
    return true;
  }
  np l = n->ch[L];
  np r = n->ch[R];

  if (n->size != real_size(n))
    return false;
  if (n->height != real_height(n))
    return false;
  if (n->min != real_min(n))
    return false;

  if (n->size != l->size + 1 + r->size)
    return false;
  if (n->height != std::max(l->height, r->height) + 1)
    return false;
  if (n->min != std::min({n->ch[L]->min, n->key, n->ch[R]->min}))
    return false;

  if (abs(bfactor(n)) >= 2)
    return false;
  return true;
}
} // namespace test

void to_a(np n, std::vector<int> &v) {
  if (n == nil)
    return;
  to_a(n->ch[L], v);
  v.push_back(n->key);
  to_a(n->ch[R], v);
}

std::vector<int> to_a(np n) {
  std::vector<int> res;
  to_a(n, res);
  return res;
}

using namespace std;

mt19937 mt(100);

int randint(int l, int r) {
  uniform_int_distribution<int> dist(l, r);
  return dist(mt);
}

void show(const vector<int> &x) {
  for (auto &e : x)
    cout << e << ' ';
  cout << endl;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n, q;
  while (cin >> n >> q) {
    vector<int> a(n);
    for (int i = 0; i < n; ++i)
      cin >> a[i];
    np root = build(a.begin(), a.end());
    for (int i = 0; i < q; ++i) {
      int t, x, y;
      cin >> t >> x >> y;
      if (t == 0) {
        int t;
        tie(root, t) = remove_at(root, y);
        root = insert_at(root, x, t);
      } else if (t == 1) {
        ++y;
        cout << range_min(root, x, y) << '\n';
        // np l, m, r;
        // tie(m, r) = split_at(root, y);
        // tie(l, m) = split_at(m, x);
        // cout << m->min << '\n';
        // root = merge(l, merge(m, r));
      } else {
        update_at(root, x, y);
      }
      // test::verify(root);
    }
  }

  // for (int _ = 0; _ < 10000; ++_) {
  //     int N = randint(1, 2000);
  //     np root = nil;
  //     vector<int> v(N);
  //     for (int i = 0; i < N; ++i) {
  //         v[i] = randint(0, 100);
  //         root = insert_at(root, i, v[i]);
  //     }
  //     int k = randint(0, N);
  //     np l, r;
  //     tie(l, r) = split_at(root, k);
  //     test::verify(l);
  //     test::verify(r);
  //     vector<int> vl(v.begin(), v.begin() + k), vr(v.begin() + k, v.end());
  //     assert(to_a(l) == vl);
  //     assert(to_a(r) == vr);
  //     root = merge(l, r);
  //     test::verify(root);
  //     for (auto &x : vr) vl.push_back(x);
  //     assert(to_a(root) == vl);
  // }

  // for (int _ = 0; _ < 10000; ++_) {
  //     int N = randint(1, 2000);
  //     np root = nil;
  //     // vector<int> v;
  //     for (int i = 0; i < N; ++i) {
  //         if (root->size && randint(0, 3) == 0) {
  //             int k = randint(0, root->size - 1);
  //             // v.erase(v.begin() + k);
  //             root = remove_at(root, k);
  //         } else {
  //             int k = randint(0, root->size);
  //             int x = randint(0, 100);
  //             // v.insert(v.begin() + k, x);
  //             root = insert_at(root, k, x);
  //         }
  //         // vector<int> a = to_a(root);
  //         // assert(verify(root));
  //         // assert(a == v);
  //     }
  //     assert(test::verify(root));
  //     // vector<int> a = to_a(root);
  //     // assert(a == v);
  // }
}