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Submission #1106736

# Submission time Handle Problem Language Result Execution time Memory
1106736 2024-10-31T02:15:43 Z 12345678 Boat (APIO16_boat) C++17
100 / 100
 765 ms 18368 KB 
#include <bits/stdc++.h>

using namespace std;

#define ll long long

const int nx=505, mod=1e9+7;
ll n, a[nx], b[nx], dp[nx][2*nx], qs[nx][2*nx], sz[2*nx], t, pv, ncr[nx][nx], choose[2*nx][nx], l[nx], r[nx], sm[2*nx][nx];
map<ll, ll> mp;

ll invmod(ll a, ll x)
{
    if (x==0) return 1;
    auto tmp=invmod(a, x/2);
    tmp=(tmp*tmp)%mod;
    if (x%2) return (tmp*a)%mod;
    else return tmp;
}

int main()
{
    cin.tie(NULL)->sync_with_stdio(false);
    cin>>n;
    for (int i=1; i<=n; i++) cin>>a[i]>>b[i], mp[--a[i]]=0, mp[b[i]]=0;
    for (auto &[x, y]:mp) y=t, sz[t]=x-pv, pv=x, t++;
    for (int i=1; i<=n; i++) l[i]=mp[a[i]], r[i]=mp[b[i]];
    ncr[0][0]=1;
    for (int i=1; i<=n; i++)
    {
        for (int j=0; j<=i; j++)
        {
            ncr[i][j]=ncr[i-1][j];
            if (j>0) ncr[i][j]=(ncr[i][j]+ncr[i-1][j-1])%mod;
        }
    }
    for (int i=1; i<t; i++)
    {
        ll tmp=1;
        choose[i][0]=tmp;
        for (int j=1; j<=min(sz[i], n); j++) tmp=(((tmp*(sz[i]-j+1))%mod)*invmod(j, mod-2))%mod, choose[i][j]=tmp;
    }
    for (int i=1; i<t; i++) for (int j=2; j<=n; j++) for (int x=0; x<=j-2; x++) sm[i][j]=(sm[i][j]+choose[i][x+2]*ncr[j-2][x])%mod;
    for (int i=1; i<=n; i++)
    {
        for (int j=1; j<t; j++)
        {
            if (l[i]<j&&j<=r[i])
            {
                dp[i][j]=((qs[i-1][j-1]+1)*sz[j])%mod;
                ll cnt=1;
                for (int k=i-1; k>=1; k--)
                {
                    if (l[k]<j&&j<=r[k]) 
                    {
                        cnt++;
                        if (cnt>=2) dp[i][j]=(dp[i][j]+sm[j][cnt]*(qs[k-1][j-1]+1))%mod;
                    }
                }
            }
            //cout<<"dp "<<i<<' '<<j<<' '<<dp[i][j]<<'\n';
            qs[i][j]=((dp[i][j]+qs[i-1][j]+qs[i][j-1]-qs[i-1][j-1])%mod+mod)%mod;
        }
    }
    cout<<qs[n][t-1];
}

/*
2
1 3
1 3
*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 545 ms 16396 KB Output is correct
2 Correct 545 ms 16392 KB Output is correct
3 Correct 550 ms 16204 KB Output is correct
4 Correct 551 ms 16200 KB Output is correct
5 Correct 549 ms 16196 KB Output is correct
6 Correct 538 ms 16536 KB Output is correct
7 Correct 536 ms 16712 KB Output is correct
8 Correct 535 ms 16712 KB Output is correct
9 Correct 536 ms 16596 KB Output is correct
10 Correct 537 ms 16660 KB Output is correct
11 Correct 538 ms 16712 KB Output is correct
12 Correct 540 ms 16712 KB Output is correct
13 Correct 536 ms 16712 KB Output is correct
14 Correct 538 ms 16712 KB Output is correct
15 Correct 536 ms 16712 KB Output is correct
16 Correct 99 ms 13384 KB Output is correct
17 Correct 107 ms 13508 KB Output is correct
18 Correct 102 ms 13648 KB Output is correct
19 Correct 108 ms 13576 KB Output is correct
20 Correct 107 ms 13640 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 545 ms 16396 KB Output is correct
2 Correct 545 ms 16392 KB Output is correct
3 Correct 550 ms 16204 KB Output is correct
4 Correct 551 ms 16200 KB Output is correct
5 Correct 549 ms 16196 KB Output is correct
6 Correct 538 ms 16536 KB Output is correct
7 Correct 536 ms 16712 KB Output is correct
8 Correct 535 ms 16712 KB Output is correct
9 Correct 536 ms 16596 KB Output is correct
10 Correct 537 ms 16660 KB Output is correct
11 Correct 538 ms 16712 KB Output is correct
12 Correct 540 ms 16712 KB Output is correct
13 Correct 536 ms 16712 KB Output is correct
14 Correct 538 ms 16712 KB Output is correct
15 Correct 536 ms 16712 KB Output is correct
16 Correct 99 ms 13384 KB Output is correct
17 Correct 107 ms 13508 KB Output is correct
18 Correct 102 ms 13648 KB Output is correct
19 Correct 108 ms 13576 KB Output is correct
20 Correct 107 ms 13640 KB Output is correct
21 Correct 537 ms 17416 KB Output is correct
22 Correct 531 ms 17364 KB Output is correct
23 Correct 515 ms 17224 KB Output is correct
24 Correct 530 ms 17264 KB Output is correct
25 Correct 519 ms 17760 KB Output is correct
26 Correct 590 ms 18248 KB Output is correct
27 Correct 601 ms 18248 KB Output is correct
28 Correct 587 ms 18188 KB Output is correct
29 Correct 584 ms 18248 KB Output is correct
30 Correct 534 ms 16456 KB Output is correct
31 Correct 550 ms 16488 KB Output is correct
32 Correct 554 ms 16456 KB Output is correct
33 Correct 556 ms 16456 KB Output is correct
34 Correct 539 ms 16444 KB Output is correct
35 Correct 543 ms 16228 KB Output is correct
36 Correct 543 ms 16328 KB Output is correct
37 Correct 552 ms 16200 KB Output is correct
38 Correct 541 ms 16200 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 8272 KB Output is correct
2 Correct 10 ms 8272 KB Output is correct
3 Correct 10 ms 8272 KB Output is correct
4 Correct 11 ms 8288 KB Output is correct
5 Correct 10 ms 8272 KB Output is correct
6 Correct 11 ms 10064 KB Output is correct
7 Correct 12 ms 10052 KB Output is correct
8 Correct 11 ms 10064 KB Output is correct
9 Correct 12 ms 10064 KB Output is correct
10 Correct 12 ms 8272 KB Output is correct
11 Correct 11 ms 10064 KB Output is correct
12 Correct 10 ms 10064 KB Output is correct
13 Correct 11 ms 8272 KB Output is correct
14 Correct 11 ms 10064 KB Output is correct
15 Correct 11 ms 10064 KB Output is correct
16 Correct 6 ms 8016 KB Output is correct
17 Correct 7 ms 8016 KB Output is correct
18 Correct 7 ms 8016 KB Output is correct
19 Correct 7 ms 8032 KB Output is correct
20 Correct 6 ms 7772 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 545 ms 16396 KB Output is correct
2 Correct 545 ms 16392 KB Output is correct
3 Correct 550 ms 16204 KB Output is correct
4 Correct 551 ms 16200 KB Output is correct
5 Correct 549 ms 16196 KB Output is correct
6 Correct 538 ms 16536 KB Output is correct
7 Correct 536 ms 16712 KB Output is correct
8 Correct 535 ms 16712 KB Output is correct
9 Correct 536 ms 16596 KB Output is correct
10 Correct 537 ms 16660 KB Output is correct
11 Correct 538 ms 16712 KB Output is correct
12 Correct 540 ms 16712 KB Output is correct
13 Correct 536 ms 16712 KB Output is correct
14 Correct 538 ms 16712 KB Output is correct
15 Correct 536 ms 16712 KB Output is correct
16 Correct 99 ms 13384 KB Output is correct
17 Correct 107 ms 13508 KB Output is correct
18 Correct 102 ms 13648 KB Output is correct
19 Correct 108 ms 13576 KB Output is correct
20 Correct 107 ms 13640 KB Output is correct
21 Correct 537 ms 17416 KB Output is correct
22 Correct 531 ms 17364 KB Output is correct
23 Correct 515 ms 17224 KB Output is correct
24 Correct 530 ms 17264 KB Output is correct
25 Correct 519 ms 17760 KB Output is correct
26 Correct 590 ms 18248 KB Output is correct
27 Correct 601 ms 18248 KB Output is correct
28 Correct 587 ms 18188 KB Output is correct
29 Correct 584 ms 18248 KB Output is correct
30 Correct 534 ms 16456 KB Output is correct
31 Correct 550 ms 16488 KB Output is correct
32 Correct 554 ms 16456 KB Output is correct
33 Correct 556 ms 16456 KB Output is correct
34 Correct 539 ms 16444 KB Output is correct
35 Correct 543 ms 16228 KB Output is correct
36 Correct 543 ms 16328 KB Output is correct
37 Correct 552 ms 16200 KB Output is correct
38 Correct 541 ms 16200 KB Output is correct
39 Correct 10 ms 8272 KB Output is correct
40 Correct 10 ms 8272 KB Output is correct
41 Correct 10 ms 8272 KB Output is correct
42 Correct 11 ms 8288 KB Output is correct
43 Correct 10 ms 8272 KB Output is correct
44 Correct 11 ms 10064 KB Output is correct
45 Correct 12 ms 10052 KB Output is correct
46 Correct 11 ms 10064 KB Output is correct
47 Correct 12 ms 10064 KB Output is correct
48 Correct 12 ms 8272 KB Output is correct
49 Correct 11 ms 10064 KB Output is correct
50 Correct 10 ms 10064 KB Output is correct
51 Correct 11 ms 8272 KB Output is correct
52 Correct 11 ms 10064 KB Output is correct
53 Correct 11 ms 10064 KB Output is correct
54 Correct 6 ms 8016 KB Output is correct
55 Correct 7 ms 8016 KB Output is correct
56 Correct 7 ms 8016 KB Output is correct
57 Correct 7 ms 8032 KB Output is correct
58 Correct 6 ms 7772 KB Output is correct
59 Correct 664 ms 17772 KB Output is correct
60 Correct 647 ms 17764 KB Output is correct
61 Correct 644 ms 17224 KB Output is correct
62 Correct 656 ms 17480 KB Output is correct
63 Correct 652 ms 17480 KB Output is correct
64 Correct 760 ms 18248 KB Output is correct
65 Correct 761 ms 18368 KB Output is correct
66 Correct 760 ms 18256 KB Output is correct
67 Correct 765 ms 18284 KB Output is correct
68 Correct 764 ms 18248 KB Output is correct
69 Correct 660 ms 17480 KB Output is correct
70 Correct 649 ms 18036 KB Output is correct
71 Correct 650 ms 17992 KB Output is correct
72 Correct 648 ms 17584 KB Output is correct
73 Correct 652 ms 17684 KB Output is correct
74 Correct 118 ms 13644 KB Output is correct
75 Correct 119 ms 13896 KB Output is correct
76 Correct 118 ms 13884 KB Output is correct
77 Correct 118 ms 13896 KB Output is correct
78 Correct 120 ms 13712 KB Output is correct