oj.uz

Submission #1019303

# Submission time Handle Problem Language Result Execution time Memory
1019303 2024-07-10T17:09:21 Z andrei_iorgulescu Boat (APIO16_boat) C++14
100 / 100
 1354 ms 16588 KB 
#include <bits/stdc++.h>

using namespace std;

#define int long long

int modulo = 1e9 + 7;

int n;
int l[505],r[505];
int dpcur[1005][505], dpant[1005][505],smant[1005];
int fact[1005],invfact[1005];
int f[1005][505],invf[1005][505];

int lgpow(int x,int y)
{
    int z = 1;
    while (y != 0)
    {
        if (y % 2 == 1)
            z = z * x % modulo;
        x = x * x % modulo;
        y /= 2;
    }
    return z;
}

int ways(int x, int y)
{
    if (x < y)
        return 0;
    int rr = 1;
    for (int i = x - y + 1; i <= x; i++)
        rr = rr * i % modulo;
    rr *= invfact[y];
    rr %= modulo;
    return rr;
}

signed main()
{
    fact[0] = invfact[0] = 1;
    for (int i = 1; i <= 1000; i++)
        fact[i] = i * fact[i - 1] % modulo, invfact[i] = lgpow(fact[i],modulo - 2);
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> l[i] >> r[i];
    set<int> timpi;
    for (int i = 1; i <= n; i++)
        timpi.insert(l[i]),timpi.insert(r[i] + 1);
    vector<int> t;
    for (auto it : timpi)
        t.push_back(it);
    vector<pair<int,int>> intv;
    for (int i = 0; i < t.size() - 1; i++)
        intv.push_back({t[i],t[i + 1] - 1});
    for (int j = 0; j < intv.size(); j++)
    {
        for (int q = 1; q <= n; q++)
        {
            f[j][q] = ways(intv[j].second - intv[j].first + 1,q);
            invf[j][q] = lgpow(f[j][q],modulo - 2);
        }
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 0; j < intv.size(); j++)
        {
            for (int q = 1; q <= i; q++)
            {
                dpcur[j][q] = dpant[j][q];
                if (r[i] < intv[j].first or l[i] > intv[j].first)
                    continue;
                if (q != 1)
                {
                    int adg = dpant[j][q - 1] * f[j][q] % modulo * invf[j][q - 1] % modulo;
                    dpcur[j][q] += adg;
                    dpcur[j][q] %= modulo;
                }
                else
                {
                    int cf = intv[j].second - intv[j].first + 1;
                    int sm = 1;///nu mai e nimic inainte
                    for (int jp = 0; jp < j; jp++)
                        sm += smant[jp];
                    sm %= modulo;
                    sm *= cf;
                    sm %= modulo;
                    dpcur[j][q] += sm;
                    dpcur[j][q] %= modulo;
                }
            }
        }
        for (int j = 0; j < intv.size(); j++)
        {
            smant[j] = 0;
            for (int q = 1; q <= i; q++)
                dpant[j][q] = dpcur[j][q],smant[j] += dpcur[j][q];
        }
    }
    int ans = 0;
    for (int j = 0; j < intv.size(); j++)
    {
        for (int q = 1; q <= n; q++)
            ans += dpant[j][q];
    }
    ans %= modulo;
    cout << ans;
    return 0;
}

/**
Exista O(N) intervale relevante de nr barci
dp[i][j][q] = in cate moduri pot lua primii i jucatori, astfel incat ultimul luat sa trimita barci in intervalul j, de fapt q trimitand asa
dp[i][j][q] vine din:
- dp[i - 1][j][q] (omul i sta pe bara), coef = 1
- daca q != 1, dp[i - 1][j][q - 1], coef = ways(q, len[j]) / ways(q - 1, len[j]) unde consider 0 / 0 = 0
- daca q = 1, dp[i - 1][j'][q'], coef = len[j]

Deci pentru majoritatea starilor (tehnic N^3) am o singura tranzitie, pentru N^2 insa am N^2 tranzitii si dau in N^4
Dar tranzitia aia e coef * suma(dp[i - 1][j'][q']) cu j' < j si orice q' (pot chiar sa parcurg j' ca sa nu imi tin sume dubioase ca e N^3)

ways(x, len) = C(len,x)
**/

Compilation message

boat.cpp: In function 'int main()':
boat.cpp:55:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   55 |     for (int i = 0; i < t.size() - 1; i++)
      |                     ~~^~~~~~~~~~~~~~
boat.cpp:57:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   57 |     for (int j = 0; j < intv.size(); j++)
      |                     ~~^~~~~~~~~~~~~
boat.cpp:67:27: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   67 |         for (int j = 0; j < intv.size(); j++)
      |                         ~~^~~~~~~~~~~~~
boat.cpp:94:27: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   94 |         for (int j = 0; j < intv.size(); j++)
      |                         ~~^~~~~~~~~~~~~
boat.cpp:102:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  102 |     for (int j = 0; j < intv.size(); j++)
      |                     ~~^~~~~~~~~~~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 655 ms 16196 KB Output is correct
2 Correct 638 ms 16336 KB Output is correct
3 Correct 694 ms 16488 KB Output is correct
4 Correct 658 ms 16468 KB Output is correct
5 Correct 641 ms 16212 KB Output is correct
6 Correct 667 ms 16212 KB Output is correct
7 Correct 656 ms 16108 KB Output is correct
8 Correct 652 ms 16240 KB Output is correct
9 Correct 665 ms 16208 KB Output is correct
10 Correct 703 ms 16588 KB Output is correct
11 Correct 651 ms 16212 KB Output is correct
12 Correct 650 ms 16180 KB Output is correct
13 Correct 676 ms 16468 KB Output is correct
14 Correct 676 ms 16332 KB Output is correct
15 Correct 662 ms 16116 KB Output is correct
16 Correct 112 ms 3164 KB Output is correct
17 Correct 147 ms 3412 KB Output is correct
18 Correct 117 ms 3152 KB Output is correct
19 Correct 120 ms 3492 KB Output is correct
20 Correct 120 ms 3344 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 655 ms 16196 KB Output is correct
2 Correct 638 ms 16336 KB Output is correct
3 Correct 694 ms 16488 KB Output is correct
4 Correct 658 ms 16468 KB Output is correct
5 Correct 641 ms 16212 KB Output is correct
6 Correct 667 ms 16212 KB Output is correct
7 Correct 656 ms 16108 KB Output is correct
8 Correct 652 ms 16240 KB Output is correct
9 Correct 665 ms 16208 KB Output is correct
10 Correct 703 ms 16588 KB Output is correct
11 Correct 651 ms 16212 KB Output is correct
12 Correct 650 ms 16180 KB Output is correct
13 Correct 676 ms 16468 KB Output is correct
14 Correct 676 ms 16332 KB Output is correct
15 Correct 662 ms 16116 KB Output is correct
16 Correct 112 ms 3164 KB Output is correct
17 Correct 147 ms 3412 KB Output is correct
18 Correct 117 ms 3152 KB Output is correct
19 Correct 120 ms 3492 KB Output is correct
20 Correct 120 ms 3344 KB Output is correct
21 Correct 638 ms 14860 KB Output is correct
22 Correct 614 ms 15136 KB Output is correct
23 Correct 584 ms 14788 KB Output is correct
24 Correct 580 ms 14676 KB Output is correct
25 Correct 621 ms 14672 KB Output is correct
26 Correct 675 ms 14396 KB Output is correct
27 Correct 681 ms 14676 KB Output is correct
28 Correct 648 ms 14164 KB Output is correct
29 Correct 648 ms 14164 KB Output is correct
30 Correct 608 ms 16208 KB Output is correct
31 Correct 615 ms 16140 KB Output is correct
32 Correct 622 ms 16212 KB Output is correct
33 Correct 617 ms 16192 KB Output is correct
34 Correct 615 ms 16212 KB Output is correct
35 Correct 600 ms 16204 KB Output is correct
36 Correct 582 ms 16072 KB Output is correct
37 Correct 594 ms 16084 KB Output is correct
38 Correct 614 ms 16208 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 3420 KB Output is correct
2 Correct 18 ms 3416 KB Output is correct
3 Correct 15 ms 3420 KB Output is correct
4 Correct 15 ms 3420 KB Output is correct
5 Correct 16 ms 3656 KB Output is correct
6 Correct 16 ms 3660 KB Output is correct
7 Correct 20 ms 3664 KB Output is correct
8 Correct 17 ms 3420 KB Output is correct
9 Correct 18 ms 3416 KB Output is correct
10 Correct 16 ms 3420 KB Output is correct
11 Correct 15 ms 3428 KB Output is correct
12 Correct 15 ms 3420 KB Output is correct
13 Correct 15 ms 3596 KB Output is correct
14 Correct 14 ms 3416 KB Output is correct
15 Correct 18 ms 3416 KB Output is correct
16 Correct 9 ms 2140 KB Output is correct
17 Correct 7 ms 2140 KB Output is correct
18 Correct 8 ms 2292 KB Output is correct
19 Correct 9 ms 2136 KB Output is correct
20 Correct 9 ms 2140 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 655 ms 16196 KB Output is correct
2 Correct 638 ms 16336 KB Output is correct
3 Correct 694 ms 16488 KB Output is correct
4 Correct 658 ms 16468 KB Output is correct
5 Correct 641 ms 16212 KB Output is correct
6 Correct 667 ms 16212 KB Output is correct
7 Correct 656 ms 16108 KB Output is correct
8 Correct 652 ms 16240 KB Output is correct
9 Correct 665 ms 16208 KB Output is correct
10 Correct 703 ms 16588 KB Output is correct
11 Correct 651 ms 16212 KB Output is correct
12 Correct 650 ms 16180 KB Output is correct
13 Correct 676 ms 16468 KB Output is correct
14 Correct 676 ms 16332 KB Output is correct
15 Correct 662 ms 16116 KB Output is correct
16 Correct 112 ms 3164 KB Output is correct
17 Correct 147 ms 3412 KB Output is correct
18 Correct 117 ms 3152 KB Output is correct
19 Correct 120 ms 3492 KB Output is correct
20 Correct 120 ms 3344 KB Output is correct
21 Correct 638 ms 14860 KB Output is correct
22 Correct 614 ms 15136 KB Output is correct
23 Correct 584 ms 14788 KB Output is correct
24 Correct 580 ms 14676 KB Output is correct
25 Correct 621 ms 14672 KB Output is correct
26 Correct 675 ms 14396 KB Output is correct
27 Correct 681 ms 14676 KB Output is correct
28 Correct 648 ms 14164 KB Output is correct
29 Correct 648 ms 14164 KB Output is correct
30 Correct 608 ms 16208 KB Output is correct
31 Correct 615 ms 16140 KB Output is correct
32 Correct 622 ms 16212 KB Output is correct
33 Correct 617 ms 16192 KB Output is correct
34 Correct 615 ms 16212 KB Output is correct
35 Correct 600 ms 16204 KB Output is correct
36 Correct 582 ms 16072 KB Output is correct
37 Correct 594 ms 16084 KB Output is correct
38 Correct 614 ms 16208 KB Output is correct
39 Correct 15 ms 3420 KB Output is correct
40 Correct 18 ms 3416 KB Output is correct
41 Correct 15 ms 3420 KB Output is correct
42 Correct 15 ms 3420 KB Output is correct
43 Correct 16 ms 3656 KB Output is correct
44 Correct 16 ms 3660 KB Output is correct
45 Correct 20 ms 3664 KB Output is correct
46 Correct 17 ms 3420 KB Output is correct
47 Correct 18 ms 3416 KB Output is correct
48 Correct 16 ms 3420 KB Output is correct
49 Correct 15 ms 3428 KB Output is correct
50 Correct 15 ms 3420 KB Output is correct
51 Correct 15 ms 3596 KB Output is correct
52 Correct 14 ms 3416 KB Output is correct
53 Correct 18 ms 3416 KB Output is correct
54 Correct 9 ms 2140 KB Output is correct
55 Correct 7 ms 2140 KB Output is correct
56 Correct 8 ms 2292 KB Output is correct
57 Correct 9 ms 2136 KB Output is correct
58 Correct 9 ms 2140 KB Output is correct
59 Correct 1269 ms 16352 KB Output is correct
60 Correct 1275 ms 16496 KB Output is correct
61 Correct 1259 ms 16208 KB Output is correct
62 Correct 1305 ms 16268 KB Output is correct
63 Correct 1256 ms 16100 KB Output is correct
64 Correct 1326 ms 16216 KB Output is correct
65 Correct 1333 ms 16208 KB Output is correct
66 Correct 1323 ms 16208 KB Output is correct
67 Correct 1354 ms 16184 KB Output is correct
68 Correct 1326 ms 16340 KB Output is correct
69 Correct 1046 ms 16208 KB Output is correct
70 Correct 1086 ms 16208 KB Output is correct
71 Correct 1131 ms 16208 KB Output is correct
72 Correct 1095 ms 16208 KB Output is correct
73 Correct 1131 ms 16212 KB Output is correct
74 Correct 166 ms 3152 KB Output is correct
75 Correct 168 ms 3408 KB Output is correct
76 Correct 176 ms 3632 KB Output is correct
77 Correct 168 ms 3172 KB Output is correct
78 Correct 168 ms 3152 KB Output is correct