Submission #625926

#	Time	Username	Problem	Language	Result	Execution time	Memory
625926		Benq	Radio Towers (IOI22_towers)	C++17	100 / 100	1762 ms	256916 KiB

towers

#include "towers.h"

#include <vector>

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python! 

// pairs
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
#define mp make_pair
#define f first
#define s second

#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;

// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()

#define lb lower_bound
#define ub upper_bound
tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }
tcT> int upb(V<T>& a, const T& b) { return int(ub(all(a),b)-bg(a)); }

// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1,0,-1,0}, dy[4]{0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;

// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
  return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x)) 
constexpr int p2(int x) { return 1<<x; }
constexpr int msk2(int x) { return p2(x)-1; }

ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0; } // set a = max(a,b)

tcTU> T fstTrue(T lo, T hi, U f) {
  ++hi; assert(lo <= hi); // assuming f is increasing
  while (lo < hi) { // find first index such that f is true 
    T mid = lo+(hi-lo)/2;
    f(mid) ? hi = mid : lo = mid+1; 
  } 
  return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
  --lo; assert(lo <= hi); // assuming f is decreasing
  while (lo < hi) { // find first index such that f is true 
    T mid = lo+(hi-lo+1)/2;
    f(mid) ? lo = mid : hi = mid-1;
  } 
  return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
  sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
  auto it = t.find(u); assert(it != end(t));
  t.erase(it); } // element that doesn't exist from (multi)set

#define tcTUU tcT, class ...U

inline namespace Helpers {
  //////////// is_iterable
  // https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
  // this gets used only when we can call begin() and end() on that type
  tcT, class = void> struct is_iterable : false_type {};
  tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
                                    decltype(end(declval<T>()))
                                   >
                         > : true_type {};
  tcT> constexpr bool is_iterable_v = is_iterable<T>::value;

  //////////// is_readable
  tcT, class = void> struct is_readable : false_type {};
  tcT> struct is_readable<T,
          typename std::enable_if_t<
              is_same_v<decltype(cin >> declval<T&>()), istream&>
          >
      > : true_type {};
  tcT> constexpr bool is_readable_v = is_readable<T>::value;

  //////////// is_printable
  // // https://nafe.es/posts/2020-02-29-is-printable/
  tcT, class = void> struct is_printable : false_type {};
  tcT> struct is_printable<T,
          typename std::enable_if_t<
              is_same_v<decltype(cout << declval<T>()), ostream&>
          >
      > : true_type {};
  tcT> constexpr bool is_printable_v = is_printable<T>::value;
}

inline namespace Input {
  tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
  tcTUU> void re(T& t, U&... u);
  tcTU> void re(pair<T,U>& p); // pairs

  // re: read
  tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
  tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
  tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
  tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
  tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
    each(x,i) re(x); }
  tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple

  // rv: resize and read vectors
  void rv(size_t) {}
  tcTUU> void rv(size_t N, V<T>& t, U&... u);
  template<class...U> void rv(size_t, size_t N2, U&... u);
  tcTUU> void rv(size_t N, V<T>& t, U&... u) {
    t.rsz(N); re(t);
    rv(N,u...); }
  template<class...U> void rv(size_t, size_t N2, U&... u) {
    rv(N2,u...); }

  // dumb shortcuts to read in ints
  void decrement() {} // subtract one from each
  tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
  #define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
  #define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
}

inline namespace ToString {
  tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;

  // ts: string representation to print
  tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
    stringstream ss; ss << fixed << setprecision(15) << v;
    return ss.str(); } // default
  tcT> str bit_vec(T t) { // bit vector to string
    str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
    res += "}"; return res; }
  str ts(V<bool> v) { return bit_vec(v); }
  template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
  tcTU> str ts(pair<T,U> p); // pairs
  tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
  tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
  tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
    // convert container to string w/ separator sep
    bool fst = 1; str res = "";
    for (const auto& x: v) {
      if (!fst) res += sep;
      fst = 0; res += ts(x);
    }
    return res;
  }
  tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
    return "{"+ts_sep(v,", ")+"}"; }

  // for nested DS
  template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type 
    ts_lev(const T& v) { return {ts(v)}; }
  template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type 
    ts_lev(const T& v) {
    if (lev == 0 || !sz(v)) return {ts(v)};
    vs res;
    for (const auto& t: v) {
      if (sz(res)) res.bk += ",";
      vs tmp = ts_lev<lev-1>(t);
      res.ins(end(res),all(tmp));
    }
    F0R(i,sz(res)) {
      str bef = " "; if (i == 0) bef = "{";
      res[i] = bef+res[i];
    }
    res.bk += "}";
    return res;
  }
}

inline namespace Output {
  template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
  template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
    pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
  // print w/ no spaces
  template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); } 
  // print w/ spaces, end with newline
  void ps() { cout << "\n"; }
  template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); } 
  // debug to cerr
  template<class ...T> void dbg_out(const T&... t) {
    pr_sep(cerr," | ",t...); cerr << endl; }
  void loc_info(int line, str names) {
    cerr << "Line(" << line << ") -> [" << names << "]: "; }
  template<int lev, class T> void dbgl_out(const T& t) {
    cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
  #ifdef LOCAL
    #define dbg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
    #define dbgl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
  #else // don't actually submit with this
    #define dbg(...) 0
    #define dbgl(lev,x) 0
  #endif

  const clock_t beg = clock();
  #define dbg_time() dbg((db)(clock()-beg)/CLOCKS_PER_SEC)
}

inline namespace FileIO {
  void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
  void setOut(str s) { freopen(s.c_str(),"w",stdout); }
  void setIO(str s = "") {
    cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
    // cin.exceptions(cin.failbit);
    // throws exception when do smth illegal
    // ex. try to read letter into int
    if (sz(s)) setIn(s+".in"), setOut(s+".out"); // for old USACO
  }
}

/**
 * Description: 1D range minimum query. Can also do queries 
   * for any associative operation in $O(1)$ with D\&C
 * Source: KACTL
 * Verification: 
  * https://cses.fi/problemset/stats/1647/
  * http://wcipeg.com/problem/ioi1223
  * https://pastebin.com/ChpniVZL
 * Memory: O(N\log N)
 * Time: O(1)
 */

tcT> struct RMQ {
  int level(int x) { return 31-__builtin_clz(x); }
  V<vi> jmp;
  void init(const V<T>& _v) {
    jmp = {_v};
    for (int j = 1; 1<<j <= sz(_v); ++j) {
      jmp.pb(vi(sz(_v)-(1<<j)+1));
      F0R(i,sz(jmp[j])) jmp[j][i] = min(jmp[j-1][i],
        jmp[j-1][i+(1<<(j-1))]);
    }
  }
  int query(int l, int r) {
    assert(l <= r); int d = level(r-l+1);
    return min(jmp[d][l],jmp[d][r-(1<<d)+1]); }
};

struct PSeg {
  // Either globally or in a single class:
  static char buf[450 << 20];
  void* operator new(size_t s) {
    static size_t i = sizeof buf;
    assert(s < i);
    return (void*)&buf[i -= s];
  }
  void operator delete(void*) {}

  int N;
  struct Node {
    int sum = 0;
    Node *l = nullptr, *r = nullptr;
    Node* upd(int L, int R, int pos, int inc) {
      if (L == R) {
        return new Node{this->sum+inc};
      }
      int M = (L+R)/2;
      if (pos <= M) {
        auto l = this->l->upd(L, M, pos, inc);
        return new Node{l->sum+this->r->sum, l, this->r};
      } else {
        auto r = this->r->upd(M+1, R, pos, inc);
        return new Node{this->l->sum+r->sum, this->l, r};
      }
    }
    int query(int L, int R, int up) {
      if (R <= up) return sum;
      if (up < L) return 0;
      int M = (L+R)/2;
      return l->query(L, M, up) + r->query(M+1, R, up);
    }
  };
  V<Node*> stor;
  Node* build(int L, int R) {
    if (L == R) return new Node{};
    int M = (L+R)/2;
    auto l = build(L, M), r = build(M+1, R);
    return new Node{0,l,r};
  }
  void inc(int pos, int inc) {
    stor.pb(stor.bk->upd(0, N-1, pos, inc));
  }
  int query(int it, int up) {
    return stor.at(it)->query(0, N-1, up);
  }
  void init(int N_) {
    N = N_;
    stor.pb(build(0, N-1));
  }
};


RMQ<int> pos, neg;
vi H, lef, rig;

int qmin(int l, int r) {
  return pos.query(l, r);
}

int qmax(int l, int r) {
  return -neg.query(l, r);
}

V<AR<int,4>> ev;
PSeg a, b;

void init(int N, std::vector<int> H_) {
  H = H_;
  pos.init(H_);
  each(t,H_) t *= -1;
  neg.init(H_);
  lef.rsz(N), rig.rsz(N);
  {
    vi stk{-1};
    F0R(i,N) {
      while (stk.bk != -1 && H[stk.bk] <= H[i]) stk.pop_back();
      lef[i] = stk.bk+1;
      stk.pb(i);
    }
  }
  {
    vi stk{N};
    R0F(i,N) {
      while (stk.bk != N && H[stk.bk] < H[i]) stk.pop_back();
      rig[i] = stk.bk-1;
      stk.pb(i);
    }
  }
  F0R(i,N) if (lef[i] < i) {
    int mn = qmin(lef[i], i);
    int lo = qmax(lef[i], i-1), hi = H[i];
    lo -= mn, hi -= mn;
    assert(lo <= hi);
    if (lo < hi) {
      // dbg("PUSHING L", lef[i], i, lo, hi);
      ev.pb({lo, 1, lef[i], i});
      ev.pb({hi, 0, lef[i], i});
    }
  }
  F0R(i,N) if (rig[i] > i) {
    int mn = qmin(i, rig[i]);
    int lo = qmax(i+1, rig[i]), hi = H[i];
    lo -= mn, hi -= mn;
    assert(lo <= hi);
    if (lo < hi) {
      // dbg("PUSHING R", i, rig[i], lo, hi);
      ev.pb({lo, 1, i, rig[i]});
      ev.pb({hi, 0, i, rig[i]});
    }
  }
  sor(ev);
  a.init(N), b.init(N);
  each(t, ev) {
    a.inc(t[2], (t[1] == 1 ? 1 : -1));
    b.inc(t[3], (t[1] == 1 ? 1 : -1));
  }
}
// # with right <= R - # with

int max_towers(int L, int R, int D) {
  // dbg("MAX TOWERS", L, R, D);
  auto small_interval = [&](int l, int r) {
    // dbg("TESTING", l, r);
    return l <= r && qmax(l, r) - qmin(l, r) < D;
  };
  if (small_interval(L, R)) return 1;
  int ans = 0;
  {
    int M = fstTrue(L, R, [&](int i) { return qmax(L, i) - qmin(L, i) >= D; } );
    if (M <= R && lef.at(M) < L) ++ans;
  }
  {
    int M = lstTrue(L, R, [&](int i) { return qmax(i, R) - qmin(i, R) >= D; });
    if (M >= L && rig.at(M) > R) ++ans;
  }
  // dbg(ev, L, R, D);
  // dbg("BEFORE", ans);
  int it = lwb(ev, {D, 0, 0, 0});
  ans += b.query(it, R) - a.query(it, L-1);
  return ans;
}

Compilation message (stderr)

towers.cpp: In function 'void FileIO::setIn(str)':
towers.cpp:248:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  248 |   void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
      |                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
towers.cpp: In function 'void FileIO::setOut(str)':
towers.cpp:249:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  249 |   void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 4 / 4
• Subtask 2: 11 / 11
• Subtask 3: 12 / 12
• Subtask 4: 14 / 14
• Subtask 5: 17 / 17
• Subtask 6: 19 / 19
• Subtask 7: 23 / 23