oj.uz

Submission #172402

# Submission time Handle Problem Language Result Execution time Memory
172402 2020-01-01T13:03:36 Z rama_pang Boat (APIO16_boat) C++14
100 / 100
 635 ms 4476 KB 
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;

int power(int n, int x) {
    if (x == 0) {
        return 1;
    }
    int res = power(n, x / 2);
    res = (1ll * res * res) % MOD;
    if (x & 1) {
        res = (1ll * res * n) % MOD;
    }
    return res;
}

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

    int N;
    cin >> N;

    vector<int> A(N + 1);
    vector<int> B(N + 1);
    vector<int> X;
    vector<int> L;
    vector<int> inv(N + 1); // inv[i] = inverse of integer i
    
    for (int i = 1; i <= N; i++) {
        cin >> A[i] >> B[i];
        X.emplace_back(A[i]);
        X.emplace_back(B[i] + 1);
        inv[i] = power(i, MOD - 2); // Fermatt's Little Theorem for modular multiplicative inverse
    }

    sort(begin(X), end(X));
    X.resize(unique(begin(X), end(X)) - begin(X));

    for (int i = 1; i <= N; i++) {
        A[i] = upper_bound(begin(X), end(X), A[i]) - begin(X);
        B[i] = upper_bound(begin(X), end(X), B[i]) - begin(X);
    }

    L.resize(X.size());
    for (int i = 1; i < X.size(); i++) {
        L[i] = X[i] - X[i - 1];
    }

    vector<vector<int>> DP(N + 1, vector<int>(X.size() + 1, 0));
    vector<vector<int>> Choose(X.size() + 1, vector<int>(N + 1, 0));

    for (int i = 1; i < X.size(); i++) {
        Choose[i][0] = 1;
        for (int j = 1; j <= N; j++) {
            Choose[i][j] = (1ll * Choose[i][j - 1] * (L[i] + j - 1) % MOD) * inv[j] % MOD; // Choose j items from a total of L[i] items, each item can be chosen more than once
        }
    }

    for (int i = 0; i < X.size(); i++) {
        DP[0][i] = 1;
    }

    for (int i = 1; i <= N; i++) {
        DP[i][0] = 1;
        for (int j = 1; j < X.size(); j++) {
            DP[i][j] = DP[i][j - 1];
            for (int k = i, cnt = 0, choose = 0; k > 0; k--) {
                if (A[k] <= j && j <= B[k]) {
                    // Choose[j][cnt] = Same item can be chosen more than once, but it is equal to ignoring duplicate items - thus it is strictly increasing
                    cnt++;
                    DP[i][j] = (1ll * DP[i][j] + (1ll * Choose[j][cnt] * DP[k - 1][j - 1]) % MOD) % MOD;
                }
            }
        }
    }

    cout << (DP[N][X.size() - 1] - 1 + MOD) % MOD << "\n";
    return 0;
}

Compilation message

boat.cpp: In function 'int main()':
boat.cpp:46:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 1; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:53:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 1; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:60:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:66:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int j = 1; j < X.size(); j++) {
                         ~~^~~~~~~~~~
boat.cpp:68:38: warning: unused variable 'choose' [-Wunused-variable]
             for (int k = i, cnt = 0, choose = 0; k > 0; k--) {
                                      ^~~~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 443 ms 4472 KB Output is correct
2 Correct 470 ms 4472 KB Output is correct
3 Correct 454 ms 4344 KB Output is correct
4 Correct 466 ms 4344 KB Output is correct
5 Correct 457 ms 4344 KB Output is correct
6 Correct 180 ms 4472 KB Output is correct
7 Correct 173 ms 4344 KB Output is correct
8 Correct 187 ms 4344 KB Output is correct
9 Correct 185 ms 4344 KB Output is correct
10 Correct 173 ms 4344 KB Output is correct
11 Correct 179 ms 4476 KB Output is correct
12 Correct 175 ms 4344 KB Output is correct
13 Correct 179 ms 4444 KB Output is correct
14 Correct 165 ms 4344 KB Output is correct
15 Correct 184 ms 4472 KB Output is correct
16 Correct 81 ms 1144 KB Output is correct
17 Correct 90 ms 1244 KB Output is correct
18 Correct 83 ms 1148 KB Output is correct
19 Correct 80 ms 1144 KB Output is correct
20 Correct 83 ms 1144 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 443 ms 4472 KB Output is correct
2 Correct 470 ms 4472 KB Output is correct
3 Correct 454 ms 4344 KB Output is correct
4 Correct 466 ms 4344 KB Output is correct
5 Correct 457 ms 4344 KB Output is correct
6 Correct 180 ms 4472 KB Output is correct
7 Correct 173 ms 4344 KB Output is correct
8 Correct 187 ms 4344 KB Output is correct
9 Correct 185 ms 4344 KB Output is correct
10 Correct 173 ms 4344 KB Output is correct
11 Correct 179 ms 4476 KB Output is correct
12 Correct 175 ms 4344 KB Output is correct
13 Correct 179 ms 4444 KB Output is correct
14 Correct 165 ms 4344 KB Output is correct
15 Correct 184 ms 4472 KB Output is correct
16 Correct 81 ms 1144 KB Output is correct
17 Correct 90 ms 1244 KB Output is correct
18 Correct 83 ms 1148 KB Output is correct
19 Correct 80 ms 1144 KB Output is correct
20 Correct 83 ms 1144 KB Output is correct
21 Correct 416 ms 4188 KB Output is correct
22 Correct 457 ms 4344 KB Output is correct
23 Correct 395 ms 3960 KB Output is correct
24 Correct 430 ms 4088 KB Output is correct
25 Correct 429 ms 4088 KB Output is correct
26 Correct 521 ms 3960 KB Output is correct
27 Correct 541 ms 3964 KB Output is correct
28 Correct 530 ms 3960 KB Output is correct
29 Correct 518 ms 3960 KB Output is correct
30 Correct 192 ms 4472 KB Output is correct
31 Correct 173 ms 4344 KB Output is correct
32 Correct 183 ms 4444 KB Output is correct
33 Correct 180 ms 4348 KB Output is correct
34 Correct 180 ms 4372 KB Output is correct
35 Correct 489 ms 4472 KB Output is correct
36 Correct 470 ms 4444 KB Output is correct
37 Correct 471 ms 4344 KB Output is correct
38 Correct 472 ms 4372 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 548 KB Output is correct
2 Correct 6 ms 504 KB Output is correct
3 Correct 6 ms 504 KB Output is correct
4 Correct 6 ms 504 KB Output is correct
5 Correct 6 ms 504 KB Output is correct
6 Correct 7 ms 504 KB Output is correct
7 Correct 7 ms 508 KB Output is correct
8 Correct 7 ms 504 KB Output is correct
9 Correct 7 ms 504 KB Output is correct
10 Correct 7 ms 504 KB Output is correct
11 Correct 7 ms 504 KB Output is correct
12 Correct 6 ms 504 KB Output is correct
13 Correct 6 ms 504 KB Output is correct
14 Correct 7 ms 504 KB Output is correct
15 Correct 6 ms 504 KB Output is correct
16 Correct 5 ms 380 KB Output is correct
17 Correct 5 ms 504 KB Output is correct
18 Correct 5 ms 376 KB Output is correct
19 Correct 5 ms 376 KB Output is correct
20 Correct 5 ms 376 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 443 ms 4472 KB Output is correct
2 Correct 470 ms 4472 KB Output is correct
3 Correct 454 ms 4344 KB Output is correct
4 Correct 466 ms 4344 KB Output is correct
5 Correct 457 ms 4344 KB Output is correct
6 Correct 180 ms 4472 KB Output is correct
7 Correct 173 ms 4344 KB Output is correct
8 Correct 187 ms 4344 KB Output is correct
9 Correct 185 ms 4344 KB Output is correct
10 Correct 173 ms 4344 KB Output is correct
11 Correct 179 ms 4476 KB Output is correct
12 Correct 175 ms 4344 KB Output is correct
13 Correct 179 ms 4444 KB Output is correct
14 Correct 165 ms 4344 KB Output is correct
15 Correct 184 ms 4472 KB Output is correct
16 Correct 81 ms 1144 KB Output is correct
17 Correct 90 ms 1244 KB Output is correct
18 Correct 83 ms 1148 KB Output is correct
19 Correct 80 ms 1144 KB Output is correct
20 Correct 83 ms 1144 KB Output is correct
21 Correct 416 ms 4188 KB Output is correct
22 Correct 457 ms 4344 KB Output is correct
23 Correct 395 ms 3960 KB Output is correct
24 Correct 430 ms 4088 KB Output is correct
25 Correct 429 ms 4088 KB Output is correct
26 Correct 521 ms 3960 KB Output is correct
27 Correct 541 ms 3964 KB Output is correct
28 Correct 530 ms 3960 KB Output is correct
29 Correct 518 ms 3960 KB Output is correct
30 Correct 192 ms 4472 KB Output is correct
31 Correct 173 ms 4344 KB Output is correct
32 Correct 183 ms 4444 KB Output is correct
33 Correct 180 ms 4348 KB Output is correct
34 Correct 180 ms 4372 KB Output is correct
35 Correct 489 ms 4472 KB Output is correct
36 Correct 470 ms 4444 KB Output is correct
37 Correct 471 ms 4344 KB Output is correct
38 Correct 472 ms 4372 KB Output is correct
39 Correct 6 ms 548 KB Output is correct
40 Correct 6 ms 504 KB Output is correct
41 Correct 6 ms 504 KB Output is correct
42 Correct 6 ms 504 KB Output is correct
43 Correct 6 ms 504 KB Output is correct
44 Correct 7 ms 504 KB Output is correct
45 Correct 7 ms 508 KB Output is correct
46 Correct 7 ms 504 KB Output is correct
47 Correct 7 ms 504 KB Output is correct
48 Correct 7 ms 504 KB Output is correct
49 Correct 7 ms 504 KB Output is correct
50 Correct 6 ms 504 KB Output is correct
51 Correct 6 ms 504 KB Output is correct
52 Correct 7 ms 504 KB Output is correct
53 Correct 6 ms 504 KB Output is correct
54 Correct 5 ms 380 KB Output is correct
55 Correct 5 ms 504 KB Output is correct
56 Correct 5 ms 376 KB Output is correct
57 Correct 5 ms 376 KB Output is correct
58 Correct 5 ms 376 KB Output is correct
59 Correct 474 ms 4396 KB Output is correct
60 Correct 459 ms 4388 KB Output is correct
61 Correct 440 ms 4344 KB Output is correct
62 Correct 484 ms 4384 KB Output is correct
63 Correct 476 ms 4396 KB Output is correct
64 Correct 609 ms 4388 KB Output is correct
65 Correct 625 ms 4344 KB Output is correct
66 Correct 615 ms 4404 KB Output is correct
67 Correct 598 ms 4388 KB Output is correct
68 Correct 635 ms 4344 KB Output is correct
69 Correct 470 ms 4384 KB Output is correct
70 Correct 483 ms 4344 KB Output is correct
71 Correct 492 ms 4388 KB Output is correct
72 Correct 503 ms 4472 KB Output is correct
73 Correct 490 ms 4344 KB Output is correct
74 Correct 107 ms 1144 KB Output is correct
75 Correct 110 ms 1148 KB Output is correct
76 Correct 108 ms 1272 KB Output is correct
77 Correct 107 ms 1160 KB Output is correct
78 Correct 105 ms 1016 KB Output is correct