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Submission #523179

# Submission time Handle Problem Language Result Execution time Memory
523179 2022-02-07T07:22:03 Z blue Boat (APIO16_boat) C++17
100 / 100
 1033 ms 12356 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
using namespace std;

using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
#define sz(x) int(x.size())

const ll mod = 1'000'000'007;

ll mul(ll a, ll b)
{
    return (a*b) % mod;
}

ll ad(ll a, ll b)
{
    return (a+b) % mod;
}

ll sq(ll a)
{
    return mul(a,a);
}

ll pow(ll b, ll e)
{
    if(e == 0) return 1;
    else if(e % 2 == 1) return mul(b, pow(b, e-1));
    else return sq(pow(b, e/2));
}

ll get_inv(ll a)
{
    return pow(a, mod-2);
}

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

    int N;
    cin >> N;

    ll a[1+N], b[1+N];


    map<ll, ll> values;

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

        values[a[i]] = 0;
        values[b[i]] = 0;
    }

    values[0] = 0;
    values[1] = 0;


    vll ep;

    for(auto& z : values) ep.push_back(z.first);

    int ct = sz(ep) - 1;

    vll blocksize(1+ct);
    blocksize[0] = 0;
    for(int i = 1; i <= ct; i++)
        blocksize[i] = ep[i] - ep[i-1];

    
    int x[1+N], y[1+N];


    // for(int i = 0; i <= ct; i++) cerr << i << " : " << ep[i] << ' ' << blocksize[i] << '\n';

    for(int i = 1; i <= N; i++)
    {
        x[i] = 0;
        int lo = 1, hi = ct;
        while(lo != hi)
        {
            int mid = (lo+hi)/2 + 1;
            if(ep[mid] <= a[i])
                lo = mid;
            else
                hi = mid-1;
        }
        x[i] = lo + 1;

        y[i] = 0;
        lo = 1, hi = ct;
        while(lo != hi)
        {
            int mid = (lo+hi)/2+1;
            if(ep[mid] <= b[i])
                lo = mid;
            else
                hi = mid-1;
        }
        y[i] = lo;
    }


    ll*** DP = new ll**[1+N];
    for(int i = 0; i <= N; i++)
    {
        if(i <= 1)
        {
            DP[i] = new ll*[1+ct];
            for(int j = 0; j <= ct; j++)
            {
                DP[i][j] = new ll[1+N];
                for(int k = 0; k <= N; k++) DP[i][j][k] = 0;
            }
        }
        else DP[i] = DP[i-2]; 
    }


    ll inv[1+N];
    for(int i = 1; i <= N; i++) inv[i] = get_inv(i);

    vvll DPsum(1+N, vll(1+ct, 0)); 

    // cerr << "!" <<  x[1] << ' ' << y[1] << '\n';
    for(int j = x[1]; j <= y[1]; j++)
    {
        DPsum[1][j] = ad(DPsum[1][j], blocksize[j]);
        DP[1][j][1] = blocksize[j];   
    }


    for(int i = 2; i <= N; i++)
    {   
        ll ds[1+ct];
        ds[0] = 0;
        for(int j = 1; j <= ct; j++) ds[j] = ad(ds[j-1], DPsum[i-1][j]);

        for(int j = 1; j <= ct; j++)
        {
            for(int k = 1; k <= i; k++)
            {
                DP[i][j][k] = DP[i-1][j][k];

                if(x[i] <= j && j <= y[i])
                {
                    if(j == 1 && k == 1)
                    {
                        ;//DP[i][1][1] = blocksize[j] * 
                    }
                    else if(j == 1)
                    {
                        ;
                    }
                    else if(k == 1)
                    {
                        ll curr = ad(1, ds[j-1]);

                        DP[i][j][1] = ad(DP[i][j][1], mul(curr, blocksize[j]));
                    }
                    else
                    {
                        if(k <= blocksize[j])
                            DP[i][j][k] = ad(DP[i][j][k], mul(DP[i-1][j][k-1], mul(blocksize[j] - k + 1, inv[k])));
                    }
                }

                DPsum[i][j] = ad(DPsum[i][j], DP[i][j][k]);
            }
        }
    }

    ll res = 0;
    for(int j = 1; j <= ct; j++)
        res = ad(res, DPsum[N][j]);

    cout << res << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 780 ms 12252 KB Output is correct
2 Correct 787 ms 12244 KB Output is correct
3 Correct 788 ms 12356 KB Output is correct
4 Correct 797 ms 12264 KB Output is correct
5 Correct 799 ms 12244 KB Output is correct
6 Correct 798 ms 12248 KB Output is correct
7 Correct 825 ms 12252 KB Output is correct
8 Correct 798 ms 12288 KB Output is correct
9 Correct 794 ms 12356 KB Output is correct
10 Correct 806 ms 12252 KB Output is correct
11 Correct 803 ms 12248 KB Output is correct
12 Correct 786 ms 12248 KB Output is correct
13 Correct 782 ms 12244 KB Output is correct
14 Correct 803 ms 12248 KB Output is correct
15 Correct 814 ms 12244 KB Output is correct
16 Correct 140 ms 2504 KB Output is correct
17 Correct 153 ms 2508 KB Output is correct
18 Correct 143 ms 2516 KB Output is correct
19 Correct 152 ms 2616 KB Output is correct
20 Correct 147 ms 2540 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 780 ms 12252 KB Output is correct
2 Correct 787 ms 12244 KB Output is correct
3 Correct 788 ms 12356 KB Output is correct
4 Correct 797 ms 12264 KB Output is correct
5 Correct 799 ms 12244 KB Output is correct
6 Correct 798 ms 12248 KB Output is correct
7 Correct 825 ms 12252 KB Output is correct
8 Correct 798 ms 12288 KB Output is correct
9 Correct 794 ms 12356 KB Output is correct
10 Correct 806 ms 12252 KB Output is correct
11 Correct 803 ms 12248 KB Output is correct
12 Correct 786 ms 12248 KB Output is correct
13 Correct 782 ms 12244 KB Output is correct
14 Correct 803 ms 12248 KB Output is correct
15 Correct 814 ms 12244 KB Output is correct
16 Correct 140 ms 2504 KB Output is correct
17 Correct 153 ms 2508 KB Output is correct
18 Correct 143 ms 2516 KB Output is correct
19 Correct 152 ms 2616 KB Output is correct
20 Correct 147 ms 2540 KB Output is correct
21 Correct 726 ms 11212 KB Output is correct
22 Correct 742 ms 11340 KB Output is correct
23 Correct 737 ms 11136 KB Output is correct
24 Correct 733 ms 11068 KB Output is correct
25 Correct 722 ms 11116 KB Output is correct
26 Correct 704 ms 10828 KB Output is correct
27 Correct 706 ms 10996 KB Output is correct
28 Correct 697 ms 10792 KB Output is correct
29 Correct 700 ms 10748 KB Output is correct
30 Correct 789 ms 12108 KB Output is correct
31 Correct 799 ms 12356 KB Output is correct
32 Correct 802 ms 12208 KB Output is correct
33 Correct 792 ms 12236 KB Output is correct
34 Correct 797 ms 12204 KB Output is correct
35 Correct 790 ms 12204 KB Output is correct
36 Correct 803 ms 12204 KB Output is correct
37 Correct 815 ms 12208 KB Output is correct
38 Correct 845 ms 12196 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 716 KB Output is correct
2 Correct 8 ms 812 KB Output is correct
3 Correct 7 ms 716 KB Output is correct
4 Correct 8 ms 716 KB Output is correct
5 Correct 8 ms 780 KB Output is correct
6 Correct 9 ms 716 KB Output is correct
7 Correct 8 ms 716 KB Output is correct
8 Correct 10 ms 784 KB Output is correct
9 Correct 8 ms 716 KB Output is correct
10 Correct 8 ms 716 KB Output is correct
11 Correct 9 ms 816 KB Output is correct
12 Correct 8 ms 716 KB Output is correct
13 Correct 10 ms 716 KB Output is correct
14 Correct 9 ms 776 KB Output is correct
15 Correct 8 ms 716 KB Output is correct
16 Correct 5 ms 604 KB Output is correct
17 Correct 5 ms 600 KB Output is correct
18 Correct 6 ms 588 KB Output is correct
19 Correct 4 ms 588 KB Output is correct
20 Correct 5 ms 588 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 780 ms 12252 KB Output is correct
2 Correct 787 ms 12244 KB Output is correct
3 Correct 788 ms 12356 KB Output is correct
4 Correct 797 ms 12264 KB Output is correct
5 Correct 799 ms 12244 KB Output is correct
6 Correct 798 ms 12248 KB Output is correct
7 Correct 825 ms 12252 KB Output is correct
8 Correct 798 ms 12288 KB Output is correct
9 Correct 794 ms 12356 KB Output is correct
10 Correct 806 ms 12252 KB Output is correct
11 Correct 803 ms 12248 KB Output is correct
12 Correct 786 ms 12248 KB Output is correct
13 Correct 782 ms 12244 KB Output is correct
14 Correct 803 ms 12248 KB Output is correct
15 Correct 814 ms 12244 KB Output is correct
16 Correct 140 ms 2504 KB Output is correct
17 Correct 153 ms 2508 KB Output is correct
18 Correct 143 ms 2516 KB Output is correct
19 Correct 152 ms 2616 KB Output is correct
20 Correct 147 ms 2540 KB Output is correct
21 Correct 726 ms 11212 KB Output is correct
22 Correct 742 ms 11340 KB Output is correct
23 Correct 737 ms 11136 KB Output is correct
24 Correct 733 ms 11068 KB Output is correct
25 Correct 722 ms 11116 KB Output is correct
26 Correct 704 ms 10828 KB Output is correct
27 Correct 706 ms 10996 KB Output is correct
28 Correct 697 ms 10792 KB Output is correct
29 Correct 700 ms 10748 KB Output is correct
30 Correct 789 ms 12108 KB Output is correct
31 Correct 799 ms 12356 KB Output is correct
32 Correct 802 ms 12208 KB Output is correct
33 Correct 792 ms 12236 KB Output is correct
34 Correct 797 ms 12204 KB Output is correct
35 Correct 790 ms 12204 KB Output is correct
36 Correct 803 ms 12204 KB Output is correct
37 Correct 815 ms 12208 KB Output is correct
38 Correct 845 ms 12196 KB Output is correct
39 Correct 7 ms 716 KB Output is correct
40 Correct 8 ms 812 KB Output is correct
41 Correct 7 ms 716 KB Output is correct
42 Correct 8 ms 716 KB Output is correct
43 Correct 8 ms 780 KB Output is correct
44 Correct 9 ms 716 KB Output is correct
45 Correct 8 ms 716 KB Output is correct
46 Correct 10 ms 784 KB Output is correct
47 Correct 8 ms 716 KB Output is correct
48 Correct 8 ms 716 KB Output is correct
49 Correct 9 ms 816 KB Output is correct
50 Correct 8 ms 716 KB Output is correct
51 Correct 10 ms 716 KB Output is correct
52 Correct 9 ms 776 KB Output is correct
53 Correct 8 ms 716 KB Output is correct
54 Correct 5 ms 604 KB Output is correct
55 Correct 5 ms 600 KB Output is correct
56 Correct 6 ms 588 KB Output is correct
57 Correct 4 ms 588 KB Output is correct
58 Correct 5 ms 588 KB Output is correct
59 Correct 993 ms 12248 KB Output is correct
60 Correct 1033 ms 12244 KB Output is correct
61 Correct 970 ms 12244 KB Output is correct
62 Correct 1018 ms 12248 KB Output is correct
63 Correct 1008 ms 12248 KB Output is correct
64 Correct 1000 ms 12248 KB Output is correct
65 Correct 980 ms 12244 KB Output is correct
66 Correct 972 ms 12244 KB Output is correct
67 Correct 978 ms 12356 KB Output is correct
68 Correct 978 ms 12244 KB Output is correct
69 Correct 896 ms 12236 KB Output is correct
70 Correct 880 ms 12244 KB Output is correct
71 Correct 882 ms 12260 KB Output is correct
72 Correct 916 ms 12248 KB Output is correct
73 Correct 918 ms 12240 KB Output is correct
74 Correct 158 ms 2488 KB Output is correct
75 Correct 159 ms 2508 KB Output is correct
76 Correct 156 ms 2544 KB Output is correct
77 Correct 158 ms 2524 KB Output is correct
78 Correct 156 ms 2508 KB Output is correct