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Submission #554700

# Submission time Handle Problem Language Result Execution time Memory
554700 2022-04-29T08:11:49 Z alextodoran Boat (APIO16_boat) C++17
100 / 100
 1804 ms 13288 KB 
/**
 ____ ____ ____ ____ ____
||a |||t |||o |||d |||o ||
||__|||__|||__|||__|||__||
|/__\|/__\|/__\|/__\|/__\|

**/

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N_MAX = 500;
const int M_MAX = N_MAX * 4;

const int MOD = (int) 1e9 + 7;

int pwr (const int &a, const int &b) {
    if (b == 0) {
        return 1;
    } else if (b & 1) {
        return (ll) a * pwr(a, (b ^ 1)) % MOD;
    } else {
        int aux = pwr(a, (b >> 1));
        return (ll) aux * aux % MOD;
    }
}
int inv (const int &a) {
    return pwr(a, MOD - 2);
}

int N;
int a[N_MAX + 2], b[N_MAX + 2];

int M;
int l[M_MAX + 2], r[M_MAX + 2];
void compress () {
    vector <int> v;
    for (int i = 1; i <= N; i++) {
        v.push_back(a[i]);
        v.push_back(b[i]);
    }
    sort(v.begin(), v.end());
    v.resize(unique(v.begin(), v.end()) - v.begin());
    map <int, int> mp;
    for (int i = 0; i < (int) v.size(); i++) {
        if ((i == 0 ? 1 : v[i - 1] + 1) <= v[i] - 1) {
            M++;
            l[M] = (i == 0 ? 1 : v[i - 1] + 1);
            r[M] = v[i] - 1;
        }
        mp[v[i]] = ++M;
        l[M] = r[M] = v[i];
    }
    for (int i = 1; i <= N; i++) {
        a[i] = mp[a[i]];
        b[i] = mp[b[i]];
    }
}

int chooseVals[M_MAX + 2][N_MAX + 2];
int chooseBoxes[N_MAX + 2][N_MAX + 2];
int choose[M_MAX + 2][N_MAX + 2];
void precalc () {
    for (int cnt = 1; cnt <= N; cnt++) {
        chooseBoxes[cnt][1] = 1;
        chooseBoxes[cnt][2] = 1;
        for (int take = 3; take <= cnt; take++) {
            chooseBoxes[cnt][take] = chooseBoxes[cnt - 1][take] + chooseBoxes[cnt - 1][take - 1];
            if (chooseBoxes[cnt][take] >= MOD) {
                chooseBoxes[cnt][take] -= MOD;
            }
        }
    }
    for (int x = 1; x <= M; x++) {
        int from = r[x] - l[x] + 1;
        chooseVals[x][0] = 1;
        for (int take = 1; take <= min(N, from); take++) {
            chooseVals[x][take] = (ll) chooseVals[x][take - 1] * inv(take) % MOD * (from - (take - 1)) % MOD;
        }
        for (int cnt = 1; cnt <= N; cnt++) {
            for (int take = 1 + (cnt > 1); take <= cnt; take++) {
                choose[x][cnt] = (choose[x][cnt] + (ll) chooseVals[x][take] * chooseBoxes[cnt][take]) % MOD;
            }
        }
    }
}

int dp[N_MAX + 2][M_MAX + 2];

int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin >> N;
    for (int i = 1; i <= N; i++) {
        cin >> a[i] >> b[i];
    }
    compress();
    precalc();

    int answer = 0;
    fill(dp[0], dp[0] + M + 1, 1);
    for (int i = 1; i <= N; i++) {
        for (int x = a[i]; x <= b[i]; x++) {
            int cnt = 0;
            for (int j = i; j >= 1; j--) {
                if (a[j] <= x && x <= b[j]) {
                    cnt++;
                    dp[i][x] = (dp[i][x] + (ll) dp[j - 1][x - 1] * choose[x][cnt]) % MOD;
                }
            }
        }
        for (int x = 1; x <= M; x++) {
            dp[i][x] += dp[i][x - 1];
            if (dp[i][x] >= MOD) {
                dp[i][x] -= MOD;
            }
        }
        answer += dp[i][b[i]];
        if (answer >= MOD) {
            answer -= MOD;
        }
        for (int x = 0; x <= M; x++) {
            dp[i][x] += dp[i - 1][x];
            if (dp[i][x] >= MOD) {
                dp[i][x] -= MOD;
            }
        }
    }
    cout << answer << "\n";

    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 620 ms 9272 KB Output is correct
2 Correct 650 ms 9180 KB Output is correct
3 Correct 630 ms 9124 KB Output is correct
4 Correct 635 ms 9160 KB Output is correct
5 Correct 628 ms 9256 KB Output is correct
6 Correct 619 ms 9164 KB Output is correct
7 Correct 634 ms 9200 KB Output is correct
8 Correct 637 ms 9280 KB Output is correct
9 Correct 627 ms 9168 KB Output is correct
10 Correct 608 ms 9180 KB Output is correct
11 Correct 669 ms 9212 KB Output is correct
12 Correct 633 ms 9084 KB Output is correct
13 Correct 628 ms 9392 KB Output is correct
14 Correct 631 ms 9164 KB Output is correct
15 Correct 627 ms 9168 KB Output is correct
16 Correct 112 ms 4432 KB Output is correct
17 Correct 127 ms 4448 KB Output is correct
18 Correct 114 ms 4364 KB Output is correct
19 Correct 118 ms 4424 KB Output is correct
20 Correct 118 ms 4424 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 620 ms 9272 KB Output is correct
2 Correct 650 ms 9180 KB Output is correct
3 Correct 630 ms 9124 KB Output is correct
4 Correct 635 ms 9160 KB Output is correct
5 Correct 628 ms 9256 KB Output is correct
6 Correct 619 ms 9164 KB Output is correct
7 Correct 634 ms 9200 KB Output is correct
8 Correct 637 ms 9280 KB Output is correct
9 Correct 627 ms 9168 KB Output is correct
10 Correct 608 ms 9180 KB Output is correct
11 Correct 669 ms 9212 KB Output is correct
12 Correct 633 ms 9084 KB Output is correct
13 Correct 628 ms 9392 KB Output is correct
14 Correct 631 ms 9164 KB Output is correct
15 Correct 627 ms 9168 KB Output is correct
16 Correct 112 ms 4432 KB Output is correct
17 Correct 127 ms 4448 KB Output is correct
18 Correct 114 ms 4364 KB Output is correct
19 Correct 118 ms 4424 KB Output is correct
20 Correct 118 ms 4424 KB Output is correct
21 Correct 1165 ms 11976 KB Output is correct
22 Correct 1133 ms 11900 KB Output is correct
23 Correct 1105 ms 11852 KB Output is correct
24 Correct 1145 ms 11808 KB Output is correct
25 Correct 1109 ms 11764 KB Output is correct
26 Correct 1315 ms 11532 KB Output is correct
27 Correct 1308 ms 11456 KB Output is correct
28 Correct 1313 ms 11460 KB Output is correct
29 Correct 1319 ms 11596 KB Output is correct
30 Correct 1066 ms 12604 KB Output is correct
31 Correct 1053 ms 12504 KB Output is correct
32 Correct 1057 ms 12552 KB Output is correct
33 Correct 1065 ms 12580 KB Output is correct
34 Correct 1052 ms 12504 KB Output is correct
35 Correct 605 ms 9120 KB Output is correct
36 Correct 605 ms 9296 KB Output is correct
37 Correct 609 ms 9208 KB Output is correct
38 Correct 606 ms 9108 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 2560 KB Output is correct
2 Correct 17 ms 2660 KB Output is correct
3 Correct 18 ms 2668 KB Output is correct
4 Correct 18 ms 2656 KB Output is correct
5 Correct 18 ms 2636 KB Output is correct
6 Correct 21 ms 2656 KB Output is correct
7 Correct 20 ms 2664 KB Output is correct
8 Correct 22 ms 2628 KB Output is correct
9 Correct 20 ms 2644 KB Output is correct
10 Correct 20 ms 2616 KB Output is correct
11 Correct 18 ms 2644 KB Output is correct
12 Correct 18 ms 2592 KB Output is correct
13 Correct 18 ms 2632 KB Output is correct
14 Correct 17 ms 2636 KB Output is correct
15 Correct 18 ms 2644 KB Output is correct
16 Correct 9 ms 1620 KB Output is correct
17 Correct 8 ms 1620 KB Output is correct
18 Correct 9 ms 1604 KB Output is correct
19 Correct 8 ms 1620 KB Output is correct
20 Correct 9 ms 1692 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 620 ms 9272 KB Output is correct
2 Correct 650 ms 9180 KB Output is correct
3 Correct 630 ms 9124 KB Output is correct
4 Correct 635 ms 9160 KB Output is correct
5 Correct 628 ms 9256 KB Output is correct
6 Correct 619 ms 9164 KB Output is correct
7 Correct 634 ms 9200 KB Output is correct
8 Correct 637 ms 9280 KB Output is correct
9 Correct 627 ms 9168 KB Output is correct
10 Correct 608 ms 9180 KB Output is correct
11 Correct 669 ms 9212 KB Output is correct
12 Correct 633 ms 9084 KB Output is correct
13 Correct 628 ms 9392 KB Output is correct
14 Correct 631 ms 9164 KB Output is correct
15 Correct 627 ms 9168 KB Output is correct
16 Correct 112 ms 4432 KB Output is correct
17 Correct 127 ms 4448 KB Output is correct
18 Correct 114 ms 4364 KB Output is correct
19 Correct 118 ms 4424 KB Output is correct
20 Correct 118 ms 4424 KB Output is correct
21 Correct 1165 ms 11976 KB Output is correct
22 Correct 1133 ms 11900 KB Output is correct
23 Correct 1105 ms 11852 KB Output is correct
24 Correct 1145 ms 11808 KB Output is correct
25 Correct 1109 ms 11764 KB Output is correct
26 Correct 1315 ms 11532 KB Output is correct
27 Correct 1308 ms 11456 KB Output is correct
28 Correct 1313 ms 11460 KB Output is correct
29 Correct 1319 ms 11596 KB Output is correct
30 Correct 1066 ms 12604 KB Output is correct
31 Correct 1053 ms 12504 KB Output is correct
32 Correct 1057 ms 12552 KB Output is correct
33 Correct 1065 ms 12580 KB Output is correct
34 Correct 1052 ms 12504 KB Output is correct
35 Correct 605 ms 9120 KB Output is correct
36 Correct 605 ms 9296 KB Output is correct
37 Correct 609 ms 9208 KB Output is correct
38 Correct 606 ms 9108 KB Output is correct
39 Correct 17 ms 2560 KB Output is correct
40 Correct 17 ms 2660 KB Output is correct
41 Correct 18 ms 2668 KB Output is correct
42 Correct 18 ms 2656 KB Output is correct
43 Correct 18 ms 2636 KB Output is correct
44 Correct 21 ms 2656 KB Output is correct
45 Correct 20 ms 2664 KB Output is correct
46 Correct 22 ms 2628 KB Output is correct
47 Correct 20 ms 2644 KB Output is correct
48 Correct 20 ms 2616 KB Output is correct
49 Correct 18 ms 2644 KB Output is correct
50 Correct 18 ms 2592 KB Output is correct
51 Correct 18 ms 2632 KB Output is correct
52 Correct 17 ms 2636 KB Output is correct
53 Correct 18 ms 2644 KB Output is correct
54 Correct 9 ms 1620 KB Output is correct
55 Correct 8 ms 1620 KB Output is correct
56 Correct 9 ms 1604 KB Output is correct
57 Correct 8 ms 1620 KB Output is correct
58 Correct 9 ms 1692 KB Output is correct
59 Correct 1483 ms 13192 KB Output is correct
60 Correct 1442 ms 13288 KB Output is correct
61 Correct 1447 ms 13192 KB Output is correct
62 Correct 1472 ms 13044 KB Output is correct
63 Correct 1479 ms 13172 KB Output is correct
64 Correct 1789 ms 13212 KB Output is correct
65 Correct 1797 ms 13172 KB Output is correct
66 Correct 1794 ms 13096 KB Output is correct
67 Correct 1791 ms 13208 KB Output is correct
68 Correct 1804 ms 13092 KB Output is correct
69 Correct 1431 ms 13140 KB Output is correct
70 Correct 1420 ms 13160 KB Output is correct
71 Correct 1426 ms 13080 KB Output is correct
72 Correct 1451 ms 13164 KB Output is correct
73 Correct 1433 ms 13152 KB Output is correct
74 Correct 155 ms 4476 KB Output is correct
75 Correct 153 ms 4652 KB Output is correct
76 Correct 155 ms 4456 KB Output is correct
77 Correct 153 ms 4556 KB Output is correct
78 Correct 155 ms 4440 KB Output is correct