Submission #558860

#	Time	Username	Problem	Language	Result	Execution time	Memory
558860		Sweezy	Boat (APIO16_boat)	C++17	9 / 100	1162 ms	13556 KiB

boat

#include <bits/stdc++.h>
 
using namespace std;
#define int long long
 
template <typename A, typename B>
string to_string(pair<A, B> p);
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
 
string to_string(const string& s) {
  return '"' + s + '"';
}
 
string to_string(const char* s) {
  return to_string((string) s);
}
 
string to_string(bool b) {
  return (b ? "true" : "false");
}
 
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
 
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
  
void debug_out() { cerr << endl; }
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
 
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
 
#define all(a) (a).begin(), (a).end()
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define reps(i, s, n) for (int i = s; i < (n); ++i)
#define pb push_back
#define sz(a) (int) (a.size())
 
const int mod = 1e9 + 7;

void solve() {
  int n;
  cin >> n;
  vector<int> a(n), b(n), cs;
  rep(i, n) {
    cin >> a[i] >> b[i];
    cs.pb(a[i]);
    cs.pb(b[i]);
  }
 
  sort(all(cs));
  cs.erase(unique(all(cs)), cs.end());
  map<int, int> mp;
  vector<int> l, r;
  rep(i, sz(cs)) {
    if ((i == 0 ? 0 : cs[i - 1]) + 1 <= cs[i] - 1) {
      l.pb((i == 0 ? 0 : cs[i - 1]) + 1);
      r.pb(cs[i] - 1);
    }
    mp[cs[i]] = sz(l);
    l.pb(cs[i]);
    r.pb(cs[i]);
  }
  rep(i, n) {
    a[i] = mp[a[i]];
    b[i] = mp[b[i]];
    // debug(a[i], b[i]);
  }

  auto add = [&] (int &a, int b) -> void {
    (a += b) %= mod;
  };
 
  auto mul = [&] (int a, int b) -> int {
    return a * b % mod;
  };
 
  auto binpow = [&] (int a, int n) -> int {
    int res = 1;
    while (n) {
      if (n % 2) {
        res = mul(res, a);
      }
      a = mul(a, a);
      n /= 2;
    }
    return res;
  };
 
  auto inv = [&] (int val) {
    return binpow(val, mod - 2);
  };
 
  vector<int> f(n + 1), rf(n + 1);
  f[0] = rf[0] = 1;
  reps(i, 1, n + 1) {
    f[i] = mul(f[i - 1], i);
    rf[i] = inv(f[i]);
  }
 
  auto choose = [&] (int n, int k) {
    int res = 1;
    reps(i, 1, k + 1) {
      res = mul(res, n - k + i);
    }
    return mul(res, rf[k]);
  };

  // [i]: 1
  // 0 0 0 0 0 1 7 1 3 1 0 0 
  // [i]: 2
  // 0 0 0 1 53 1 35 9 33 13 42 14 
  // [i]: 3
  // 0 1 24 1 1484 55 497 99 0 0 0 0 

  // [i, x, j, cnt]: 3 6 3 1
  // [dp[i][x]]: 399
  // [i, x, j, cnt]: 3 6 2 2
  // [dp[i][x]]: 441
  // [i, x, j, cnt]: 3 6 1 3
  // [dp[i][x]]: 497

  int segs = sz(l);
  vector<vector<int>> C(segs, vector<int> (n + 1));
  rep(seg, segs) {
    rep(i, n + 1) {
      C[seg][i] = choose(r[seg] - l[seg] + 1, i);
    }
    reps(i, 3, n + 1) {
      add(C[seg][i], C[seg][i - 1]);
    }
  }
 
  int answer = 0;
  vector<vector<int>> dp(n, vector<int> (segs));
  rep(i, n) {
    reps(seg, a[i], b[i] + 1) {
      int len = r[seg] - l[seg] + 1;
      int cnt = 0;
      for (int j = i; j >= 0; j--) {
        if (a[j] <= seg && seg <= b[j]) {
          cnt++;
          if (cnt > len) break;
          // debug(i, seg, j, len, cnt, C[seg][cnt], choose(len, cnt));
          if (j == 0 || seg == 0) {
            add(dp[i][seg], C[seg][cnt]);
          } else {
            add(dp[i][seg], mul(dp[j - 1][seg - 1], C[seg][cnt]));
          }
          // debug(dp[i][seg]);
        }
      }
    }
    // debug(i, dp[i]);
    reps(j, 1, segs) {
      add(dp[i][j], dp[i][j - 1]);
    }
    add(answer, dp[i][b[i]]);
    rep(j, segs) {
      add(dp[i][j], (i ? dp[i - 1][j] : 1));
    }
  }

  cout << answer;
}
 
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
  return 0;
}

• Subtask 1: 9 / 9
• Subtask 2: 0 / 22
• Subtask 3: 0 / 27
• Subtask 4: 0 / 42