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Submission #849157

# Submission time Handle Problem Language Result Execution time Memory
849157 2023-09-14T07:38:37 Z tch1cherin Boat (APIO16_boat) C++17
100 / 100
 1822 ms 7156 KB 
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2")
#include <bits/stdc++.h>
using namespace std;
 
const int MOD = 1e9 + 7;
 
int inverse(int x) {
  int base = x, power = MOD - 2;
  int result = 1;
  while (power > 0) {
    if (power & 1) {
      result = 1LL * result * base % MOD;
    }
    base = 1LL * base * base % MOD;
    power /= 2;
  }
  return result;
}
 
void norm(int& X) {
  X -= X >= MOD ? MOD : 0;
}
 
int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int N;
  cin >> N;
  vector<int> A(N), B(N);
  vector<int> points;
  for (int i = 0; i < N; i++) {
    cin >> A[i] >> B[i];
    points.push_back(A[i]);
    points.push_back(B[i] + 1);
  }
  sort(points.begin(), points.end());
  points.resize(unique(points.begin(), points.end()) - points.begin());
  vector<int> new_points;
  for (int i = 0; i < (int)points.size(); i++) {
    new_points.push_back(points[i]);
    /*if (i + 1 < (int)points.size() && points[i + 1] - points[i] > 1) {
      new_points.push_back(points[i] + 1);
    }*/
  }
  points = new_points;
  int M = (int)points.size();
  vector<int> weight(M);
  vector<vector<int>> choose_weight(M, vector<int>(N + 1));
  for (int i = 0; i < M; i++) {
    weight[i] = (i == M - 1 ? 1 : points[i + 1] - points[i]);
    choose_weight[i][0] = 1;
    for (int j = 0; j < weight[i] && j < N; j++) {
      int coefficient = 1LL * (weight[i] - j) * inverse(j + 1) % MOD;  
      choose_weight[i][j + 1] = 1LL * choose_weight[i][j] * coefficient % MOD;
    }
  }
  vector<vector<int>> ways(M, vector<int>(N + 1));
  vector<int> pref(M + 1);
  for (int i = 0; i < M; i++) {
    ways[i][0] = 1;
  }
  for (int i = 0; i < N; i++) {
    vector<vector<int>> new_ways(M, vector<int>(N + 1));
    for (int j = 0; j < M; j++) {
      if (A[i] <= points[j] && points[j] <= B[i]) {
        new_ways[j][1] += pref[j];
      }
      for (int k = 0; k < N; k++) {
        norm(new_ways[j][k] += ways[j][k]);
        if (A[i] <= points[j] && points[j] <= B[i]) {
          norm(new_ways[j][k + 1] += ways[j][k]);
        }
      }
    }
    for (int j = 0; j < M; j++) {
      pref[j + 1] = pref[j];
      for (int k = 1; k <= N && k <= weight[j]; k++) {
        pref[j + 1] = (pref[j + 1] + 1LL * new_ways[j][k] * choose_weight[j][k]) % MOD;
      }
    }
    ways = new_ways;
  }
  cout << pref[M] << "\n";
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1173 ms 6844 KB Output is correct
2 Correct 1180 ms 6816 KB Output is correct
3 Correct 1179 ms 6656 KB Output is correct
4 Correct 1189 ms 6516 KB Output is correct
5 Correct 1188 ms 6736 KB Output is correct
6 Correct 1138 ms 6540 KB Output is correct
7 Correct 1134 ms 6896 KB Output is correct
8 Correct 1189 ms 6792 KB Output is correct
9 Correct 1156 ms 6556 KB Output is correct
10 Correct 1144 ms 6756 KB Output is correct
11 Correct 1144 ms 6908 KB Output is correct
12 Correct 1178 ms 6536 KB Output is correct
13 Correct 1157 ms 6972 KB Output is correct
14 Correct 1176 ms 6800 KB Output is correct
15 Correct 1153 ms 6764 KB Output is correct
16 Correct 193 ms 1496 KB Output is correct
17 Correct 223 ms 2200 KB Output is correct
18 Correct 208 ms 1728 KB Output is correct
19 Correct 216 ms 2140 KB Output is correct
20 Correct 210 ms 1624 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1173 ms 6844 KB Output is correct
2 Correct 1180 ms 6816 KB Output is correct
3 Correct 1179 ms 6656 KB Output is correct
4 Correct 1189 ms 6516 KB Output is correct
5 Correct 1188 ms 6736 KB Output is correct
6 Correct 1138 ms 6540 KB Output is correct
7 Correct 1134 ms 6896 KB Output is correct
8 Correct 1189 ms 6792 KB Output is correct
9 Correct 1156 ms 6556 KB Output is correct
10 Correct 1144 ms 6756 KB Output is correct
11 Correct 1144 ms 6908 KB Output is correct
12 Correct 1178 ms 6536 KB Output is correct
13 Correct 1157 ms 6972 KB Output is correct
14 Correct 1176 ms 6800 KB Output is correct
15 Correct 1153 ms 6764 KB Output is correct
16 Correct 193 ms 1496 KB Output is correct
17 Correct 223 ms 2200 KB Output is correct
18 Correct 208 ms 1728 KB Output is correct
19 Correct 216 ms 2140 KB Output is correct
20 Correct 210 ms 1624 KB Output is correct
21 Correct 615 ms 6024 KB Output is correct
22 Correct 627 ms 6332 KB Output is correct
23 Correct 628 ms 6260 KB Output is correct
24 Correct 631 ms 6048 KB Output is correct
25 Correct 638 ms 5884 KB Output is correct
26 Correct 628 ms 5860 KB Output is correct
27 Correct 688 ms 6044 KB Output is correct
28 Correct 638 ms 6380 KB Output is correct
29 Correct 634 ms 5916 KB Output is correct
30 Correct 1111 ms 6496 KB Output is correct
31 Correct 1128 ms 6920 KB Output is correct
32 Correct 1119 ms 6640 KB Output is correct
33 Correct 1139 ms 6604 KB Output is correct
34 Correct 1100 ms 6868 KB Output is correct
35 Correct 1132 ms 6592 KB Output is correct
36 Correct 1130 ms 6796 KB Output is correct
37 Correct 1110 ms 6672 KB Output is correct
38 Correct 1139 ms 6752 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 604 KB Output is correct
2 Correct 15 ms 716 KB Output is correct
3 Correct 15 ms 604 KB Output is correct
4 Correct 15 ms 720 KB Output is correct
5 Correct 15 ms 604 KB Output is correct
6 Correct 15 ms 604 KB Output is correct
7 Correct 16 ms 604 KB Output is correct
8 Correct 16 ms 800 KB Output is correct
9 Correct 17 ms 604 KB Output is correct
10 Correct 17 ms 604 KB Output is correct
11 Correct 15 ms 720 KB Output is correct
12 Correct 15 ms 712 KB Output is correct
13 Correct 15 ms 604 KB Output is correct
14 Correct 15 ms 544 KB Output is correct
15 Correct 16 ms 716 KB Output is correct
16 Correct 8 ms 344 KB Output is correct
17 Correct 8 ms 348 KB Output is correct
18 Correct 8 ms 348 KB Output is correct
19 Correct 7 ms 600 KB Output is correct
20 Correct 8 ms 608 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1173 ms 6844 KB Output is correct
2 Correct 1180 ms 6816 KB Output is correct
3 Correct 1179 ms 6656 KB Output is correct
4 Correct 1189 ms 6516 KB Output is correct
5 Correct 1188 ms 6736 KB Output is correct
6 Correct 1138 ms 6540 KB Output is correct
7 Correct 1134 ms 6896 KB Output is correct
8 Correct 1189 ms 6792 KB Output is correct
9 Correct 1156 ms 6556 KB Output is correct
10 Correct 1144 ms 6756 KB Output is correct
11 Correct 1144 ms 6908 KB Output is correct
12 Correct 1178 ms 6536 KB Output is correct
13 Correct 1157 ms 6972 KB Output is correct
14 Correct 1176 ms 6800 KB Output is correct
15 Correct 1153 ms 6764 KB Output is correct
16 Correct 193 ms 1496 KB Output is correct
17 Correct 223 ms 2200 KB Output is correct
18 Correct 208 ms 1728 KB Output is correct
19 Correct 216 ms 2140 KB Output is correct
20 Correct 210 ms 1624 KB Output is correct
21 Correct 615 ms 6024 KB Output is correct
22 Correct 627 ms 6332 KB Output is correct
23 Correct 628 ms 6260 KB Output is correct
24 Correct 631 ms 6048 KB Output is correct
25 Correct 638 ms 5884 KB Output is correct
26 Correct 628 ms 5860 KB Output is correct
27 Correct 688 ms 6044 KB Output is correct
28 Correct 638 ms 6380 KB Output is correct
29 Correct 634 ms 5916 KB Output is correct
30 Correct 1111 ms 6496 KB Output is correct
31 Correct 1128 ms 6920 KB Output is correct
32 Correct 1119 ms 6640 KB Output is correct
33 Correct 1139 ms 6604 KB Output is correct
34 Correct 1100 ms 6868 KB Output is correct
35 Correct 1132 ms 6592 KB Output is correct
36 Correct 1130 ms 6796 KB Output is correct
37 Correct 1110 ms 6672 KB Output is correct
38 Correct 1139 ms 6752 KB Output is correct
39 Correct 15 ms 604 KB Output is correct
40 Correct 15 ms 716 KB Output is correct
41 Correct 15 ms 604 KB Output is correct
42 Correct 15 ms 720 KB Output is correct
43 Correct 15 ms 604 KB Output is correct
44 Correct 15 ms 604 KB Output is correct
45 Correct 16 ms 604 KB Output is correct
46 Correct 16 ms 800 KB Output is correct
47 Correct 17 ms 604 KB Output is correct
48 Correct 17 ms 604 KB Output is correct
49 Correct 15 ms 720 KB Output is correct
50 Correct 15 ms 712 KB Output is correct
51 Correct 15 ms 604 KB Output is correct
52 Correct 15 ms 544 KB Output is correct
53 Correct 16 ms 716 KB Output is correct
54 Correct 8 ms 344 KB Output is correct
55 Correct 8 ms 348 KB Output is correct
56 Correct 8 ms 348 KB Output is correct
57 Correct 7 ms 600 KB Output is correct
58 Correct 8 ms 608 KB Output is correct
59 Correct 1787 ms 7156 KB Output is correct
60 Correct 1781 ms 6896 KB Output is correct
61 Correct 1774 ms 6596 KB Output is correct
62 Correct 1796 ms 6900 KB Output is correct
63 Correct 1794 ms 7016 KB Output is correct
64 Correct 1814 ms 6688 KB Output is correct
65 Correct 1802 ms 6884 KB Output is correct
66 Correct 1798 ms 6744 KB Output is correct
67 Correct 1822 ms 6732 KB Output is correct
68 Correct 1777 ms 6608 KB Output is correct
69 Correct 1763 ms 7016 KB Output is correct
70 Correct 1757 ms 6864 KB Output is correct
71 Correct 1763 ms 6900 KB Output is correct
72 Correct 1764 ms 6656 KB Output is correct
73 Correct 1751 ms 6888 KB Output is correct
74 Correct 230 ms 1724 KB Output is correct
75 Correct 240 ms 1580 KB Output is correct
76 Correct 220 ms 1824 KB Output is correct
77 Correct 228 ms 1720 KB Output is correct
78 Correct 221 ms 1560 KB Output is correct