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Submission #523175

# Submission time Handle Problem Language Result Execution time Memory
523175 2022-02-07T07:17:34 Z blue Boat (APIO16_boat) C++17
100 / 100
 1979 ms 12268 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++)
    {   
        for(int j = 0; j <= ct; j++)
            for(int k = 0; k <= N; k++)
                DP[i][j][k] = 0;

        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 = 1;

                        for(int j2 = 1; j2 < j; j2++)
                            curr = ad(curr, DPsum[i-1][j2]);

                        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 990 ms 12268 KB Output is correct
2 Correct 988 ms 12256 KB Output is correct
3 Correct 993 ms 12252 KB Output is correct
4 Correct 991 ms 12248 KB Output is correct
5 Correct 971 ms 12236 KB Output is correct
6 Correct 1020 ms 12248 KB Output is correct
7 Correct 961 ms 12252 KB Output is correct
8 Correct 991 ms 12248 KB Output is correct
9 Correct 1006 ms 12248 KB Output is correct
10 Correct 1014 ms 12256 KB Output is correct
11 Correct 1010 ms 12252 KB Output is correct
12 Correct 992 ms 12252 KB Output is correct
13 Correct 964 ms 12244 KB Output is correct
14 Correct 995 ms 12248 KB Output is correct
15 Correct 992 ms 12256 KB Output is correct
16 Correct 164 ms 2380 KB Output is correct
17 Correct 162 ms 2520 KB Output is correct
18 Correct 164 ms 2524 KB Output is correct
19 Correct 194 ms 2636 KB Output is correct
20 Correct 156 ms 2552 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 990 ms 12268 KB Output is correct
2 Correct 988 ms 12256 KB Output is correct
3 Correct 993 ms 12252 KB Output is correct
4 Correct 991 ms 12248 KB Output is correct
5 Correct 971 ms 12236 KB Output is correct
6 Correct 1020 ms 12248 KB Output is correct
7 Correct 961 ms 12252 KB Output is correct
8 Correct 991 ms 12248 KB Output is correct
9 Correct 1006 ms 12248 KB Output is correct
10 Correct 1014 ms 12256 KB Output is correct
11 Correct 1010 ms 12252 KB Output is correct
12 Correct 992 ms 12252 KB Output is correct
13 Correct 964 ms 12244 KB Output is correct
14 Correct 995 ms 12248 KB Output is correct
15 Correct 992 ms 12256 KB Output is correct
16 Correct 164 ms 2380 KB Output is correct
17 Correct 162 ms 2520 KB Output is correct
18 Correct 164 ms 2524 KB Output is correct
19 Correct 194 ms 2636 KB Output is correct
20 Correct 156 ms 2552 KB Output is correct
21 Correct 1209 ms 11200 KB Output is correct
22 Correct 1180 ms 11340 KB Output is correct
23 Correct 1178 ms 11136 KB Output is correct
24 Correct 1186 ms 11060 KB Output is correct
25 Correct 1180 ms 11108 KB Output is correct
26 Correct 1286 ms 10820 KB Output is correct
27 Correct 1320 ms 10984 KB Output is correct
28 Correct 1268 ms 10792 KB Output is correct
29 Correct 1293 ms 10744 KB Output is correct
30 Correct 985 ms 12212 KB Output is correct
31 Correct 999 ms 12236 KB Output is correct
32 Correct 987 ms 12208 KB Output is correct
33 Correct 991 ms 12236 KB Output is correct
34 Correct 1070 ms 12200 KB Output is correct
35 Correct 1051 ms 12212 KB Output is correct
36 Correct 1071 ms 12216 KB Output is correct
37 Correct 1016 ms 12220 KB Output is correct
38 Correct 984 ms 12192 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 716 KB Output is correct
2 Correct 13 ms 816 KB Output is correct
3 Correct 13 ms 716 KB Output is correct
4 Correct 15 ms 784 KB Output is correct
5 Correct 13 ms 716 KB Output is correct
6 Correct 17 ms 716 KB Output is correct
7 Correct 14 ms 776 KB Output is correct
8 Correct 14 ms 788 KB Output is correct
9 Correct 13 ms 780 KB Output is correct
10 Correct 15 ms 780 KB Output is correct
11 Correct 12 ms 776 KB Output is correct
12 Correct 12 ms 776 KB Output is correct
13 Correct 15 ms 784 KB Output is correct
14 Correct 14 ms 716 KB Output is correct
15 Correct 13 ms 716 KB Output is correct
16 Correct 7 ms 608 KB Output is correct
17 Correct 7 ms 608 KB Output is correct
18 Correct 6 ms 588 KB Output is correct
19 Correct 6 ms 596 KB Output is correct
20 Correct 6 ms 600 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 990 ms 12268 KB Output is correct
2 Correct 988 ms 12256 KB Output is correct
3 Correct 993 ms 12252 KB Output is correct
4 Correct 991 ms 12248 KB Output is correct
5 Correct 971 ms 12236 KB Output is correct
6 Correct 1020 ms 12248 KB Output is correct
7 Correct 961 ms 12252 KB Output is correct
8 Correct 991 ms 12248 KB Output is correct
9 Correct 1006 ms 12248 KB Output is correct
10 Correct 1014 ms 12256 KB Output is correct
11 Correct 1010 ms 12252 KB Output is correct
12 Correct 992 ms 12252 KB Output is correct
13 Correct 964 ms 12244 KB Output is correct
14 Correct 995 ms 12248 KB Output is correct
15 Correct 992 ms 12256 KB Output is correct
16 Correct 164 ms 2380 KB Output is correct
17 Correct 162 ms 2520 KB Output is correct
18 Correct 164 ms 2524 KB Output is correct
19 Correct 194 ms 2636 KB Output is correct
20 Correct 156 ms 2552 KB Output is correct
21 Correct 1209 ms 11200 KB Output is correct
22 Correct 1180 ms 11340 KB Output is correct
23 Correct 1178 ms 11136 KB Output is correct
24 Correct 1186 ms 11060 KB Output is correct
25 Correct 1180 ms 11108 KB Output is correct
26 Correct 1286 ms 10820 KB Output is correct
27 Correct 1320 ms 10984 KB Output is correct
28 Correct 1268 ms 10792 KB Output is correct
29 Correct 1293 ms 10744 KB Output is correct
30 Correct 985 ms 12212 KB Output is correct
31 Correct 999 ms 12236 KB Output is correct
32 Correct 987 ms 12208 KB Output is correct
33 Correct 991 ms 12236 KB Output is correct
34 Correct 1070 ms 12200 KB Output is correct
35 Correct 1051 ms 12212 KB Output is correct
36 Correct 1071 ms 12216 KB Output is correct
37 Correct 1016 ms 12220 KB Output is correct
38 Correct 984 ms 12192 KB Output is correct
39 Correct 12 ms 716 KB Output is correct
40 Correct 13 ms 816 KB Output is correct
41 Correct 13 ms 716 KB Output is correct
42 Correct 15 ms 784 KB Output is correct
43 Correct 13 ms 716 KB Output is correct
44 Correct 17 ms 716 KB Output is correct
45 Correct 14 ms 776 KB Output is correct
46 Correct 14 ms 788 KB Output is correct
47 Correct 13 ms 780 KB Output is correct
48 Correct 15 ms 780 KB Output is correct
49 Correct 12 ms 776 KB Output is correct
50 Correct 12 ms 776 KB Output is correct
51 Correct 15 ms 784 KB Output is correct
52 Correct 14 ms 716 KB Output is correct
53 Correct 13 ms 716 KB Output is correct
54 Correct 7 ms 608 KB Output is correct
55 Correct 7 ms 608 KB Output is correct
56 Correct 6 ms 588 KB Output is correct
57 Correct 6 ms 596 KB Output is correct
58 Correct 6 ms 600 KB Output is correct
59 Correct 1628 ms 12248 KB Output is correct
60 Correct 1546 ms 12256 KB Output is correct
61 Correct 1605 ms 12252 KB Output is correct
62 Correct 1670 ms 12256 KB Output is correct
63 Correct 1700 ms 12260 KB Output is correct
64 Correct 1934 ms 12256 KB Output is correct
65 Correct 1910 ms 12252 KB Output is correct
66 Correct 1979 ms 12252 KB Output is correct
67 Correct 1912 ms 12252 KB Output is correct
68 Correct 1945 ms 12252 KB Output is correct
69 Correct 1549 ms 12252 KB Output is correct
70 Correct 1481 ms 12252 KB Output is correct
71 Correct 1447 ms 12256 KB Output is correct
72 Correct 1519 ms 12252 KB Output is correct
73 Correct 1464 ms 12252 KB Output is correct
74 Correct 202 ms 2508 KB Output is correct
75 Correct 199 ms 2508 KB Output is correct
76 Correct 194 ms 2548 KB Output is correct
77 Correct 208 ms 2536 KB Output is correct
78 Correct 190 ms 2508 KB Output is correct