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Submission #1076386

# Submission time Handle Problem Language Result Execution time Memory
1076386 2024-08-26T13:29:03 Z alexdd Boat (APIO16_boat) C++17
100 / 100
 1202 ms 8504 KB 
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1e9+7;
const int MAXV = 2000;
int put(int a, int exp)
{
    if(exp==0)
        return 1;
    if(exp%2==0)
        return put(a*a%MOD,exp/2);
    else
        return put(a*a%MOD,exp/2)*a%MOD;
}
int n,cate;
int le[505],ri[505];
map<int,int> mp,nrm;
int invnrm[MAXV+5],nr[MAXV+5];
int dp[MAXV+5][505];
int sumdp[MAXV+5];
int prec_inv[505];
signed main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        cin>>le[i]>>ri[i];
        mp[le[i]]++;
        mp[ri[i]]++;
        prec_inv[i] = put(i,MOD-2);
    }
    for(auto it:mp)
    {
        if(it.second)
        {
            nrm[it.first]=++cate;
            invnrm[cate]=it.first;

            cate++;
        }
    }
    for(int i=1;i<=cate;i+=2)
    {
        nr[i]=1;
        nr[i+1]=invnrm[i+2]-invnrm[i]-1;
    }
    dp[0][0]=1;
    sumdp[0]=1;
    for(int ult=1;ult<cate;ult++)
        sumdp[ult] = sumdp[ult-1];
    for(int i=1;i<=n;i++)
    {
        le[i] = nrm[le[i]];
        ri[i] = nrm[ri[i]];
        for(int ult=ri[i];ult>=le[i];ult--)
        {
            for(int cnt=min(i,nr[ult]);cnt>1;cnt--)
            {
                dp[ult][cnt]= (dp[ult][cnt] + dp[ult][cnt-1] * (nr[ult]-cnt+1)%MOD * prec_inv[cnt])%MOD;
            }
            dp[ult][1] = (dp[ult][1] + sumdp[ult-1]*nr[ult])%MOD;
            /*for(int j=0;j<ult;j++)
                for(int orice=0;orice<i;orice++)
                    dp[ult][1] = (dp[ult][1] + dp[j][orice]*nr[ult])%MOD;*/
        }
        sumdp[0]=1;
        for(int ult=1;ult<cate;ult++)
        {
            sumdp[ult] = sumdp[ult-1];
            for(int cnt=1;cnt<=i;cnt++)
                sumdp[ult] = (sumdp[ult] + dp[ult][cnt])%MOD;
        }
    }
    int rez=0;
    for(int ult=1;ult<=cate;ult++)
        for(int cnt=1;cnt<=n;cnt++)
            rez = (rez + dp[ult][cnt])%MOD;
    cout<<rez;
    return 0;
}
/**

impartim intervalul [1,1e9] in intervale relevante, o sa avem maxim 1000 intervale relevante

dp[i][ult][cnt] = in cate moduri pot primele i scoli barci, a.i. ultimele cnt numere sa fie aflate in intervalul ult

daca i poate sa aleaga intervalul ult

dp[i][ult][1] = dp[i-1][ult][1] + sum(dp[i-1][orice<ult][orice])*nr[ult]
pt cnt>=2  dp[i][ult][cnt] = dp[i-1][ult][cnt] + dp[i-1][ult][cnt-1] / comb(nr[ult],cnt-1) * comb(nr[ult],cnt)
pt cnt>=2  dp[i][ult][cnt] = dp[i-1][ult][cnt] + dp[i-1][ult][cnt-1] * (nr[ult]-cnt+1) / cnt

(nr[ult]-cnt+1) / cnt

*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 497 ms 2456 KB Output is correct
2 Correct 499 ms 2384 KB Output is correct
3 Correct 496 ms 2388 KB Output is correct
4 Correct 496 ms 2388 KB Output is correct
5 Correct 497 ms 2612 KB Output is correct
6 Correct 496 ms 2388 KB Output is correct
7 Correct 495 ms 2388 KB Output is correct
8 Correct 495 ms 2384 KB Output is correct
9 Correct 494 ms 2468 KB Output is correct
10 Correct 499 ms 2384 KB Output is correct
11 Correct 495 ms 2388 KB Output is correct
12 Correct 495 ms 2348 KB Output is correct
13 Correct 497 ms 2492 KB Output is correct
14 Correct 501 ms 2488 KB Output is correct
15 Correct 499 ms 2464 KB Output is correct
16 Correct 87 ms 800 KB Output is correct
17 Correct 94 ms 816 KB Output is correct
18 Correct 90 ms 820 KB Output is correct
19 Correct 94 ms 848 KB Output is correct
20 Correct 91 ms 836 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 497 ms 2456 KB Output is correct
2 Correct 499 ms 2384 KB Output is correct
3 Correct 496 ms 2388 KB Output is correct
4 Correct 496 ms 2388 KB Output is correct
5 Correct 497 ms 2612 KB Output is correct
6 Correct 496 ms 2388 KB Output is correct
7 Correct 495 ms 2388 KB Output is correct
8 Correct 495 ms 2384 KB Output is correct
9 Correct 494 ms 2468 KB Output is correct
10 Correct 499 ms 2384 KB Output is correct
11 Correct 495 ms 2388 KB Output is correct
12 Correct 495 ms 2348 KB Output is correct
13 Correct 497 ms 2492 KB Output is correct
14 Correct 501 ms 2488 KB Output is correct
15 Correct 499 ms 2464 KB Output is correct
16 Correct 87 ms 800 KB Output is correct
17 Correct 94 ms 816 KB Output is correct
18 Correct 90 ms 820 KB Output is correct
19 Correct 94 ms 848 KB Output is correct
20 Correct 91 ms 836 KB Output is correct
21 Correct 915 ms 7876 KB Output is correct
22 Correct 916 ms 7832 KB Output is correct
23 Correct 899 ms 7692 KB Output is correct
24 Correct 914 ms 7776 KB Output is correct
25 Correct 898 ms 7668 KB Output is correct
26 Correct 875 ms 7508 KB Output is correct
27 Correct 887 ms 7444 KB Output is correct
28 Correct 873 ms 7324 KB Output is correct
29 Correct 873 ms 7248 KB Output is correct
30 Correct 949 ms 8016 KB Output is correct
31 Correct 948 ms 7864 KB Output is correct
32 Correct 939 ms 8016 KB Output is correct
33 Correct 953 ms 8016 KB Output is correct
34 Correct 934 ms 8016 KB Output is correct
35 Correct 502 ms 4440 KB Output is correct
36 Correct 507 ms 4304 KB Output is correct
37 Correct 502 ms 4688 KB Output is correct
38 Correct 498 ms 4436 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 1880 KB Output is correct
2 Correct 10 ms 1884 KB Output is correct
3 Correct 10 ms 1884 KB Output is correct
4 Correct 10 ms 1884 KB Output is correct
5 Correct 10 ms 1884 KB Output is correct
6 Correct 11 ms 1880 KB Output is correct
7 Correct 11 ms 1884 KB Output is correct
8 Correct 11 ms 2032 KB Output is correct
9 Correct 11 ms 1884 KB Output is correct
10 Correct 11 ms 2036 KB Output is correct
11 Correct 10 ms 1884 KB Output is correct
12 Correct 10 ms 2072 KB Output is correct
13 Correct 11 ms 1880 KB Output is correct
14 Correct 11 ms 2064 KB Output is correct
15 Correct 10 ms 1884 KB Output is correct
16 Correct 5 ms 1116 KB Output is correct
17 Correct 4 ms 1116 KB Output is correct
18 Correct 5 ms 1116 KB Output is correct
19 Correct 5 ms 1160 KB Output is correct
20 Correct 5 ms 1116 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 497 ms 2456 KB Output is correct
2 Correct 499 ms 2384 KB Output is correct
3 Correct 496 ms 2388 KB Output is correct
4 Correct 496 ms 2388 KB Output is correct
5 Correct 497 ms 2612 KB Output is correct
6 Correct 496 ms 2388 KB Output is correct
7 Correct 495 ms 2388 KB Output is correct
8 Correct 495 ms 2384 KB Output is correct
9 Correct 494 ms 2468 KB Output is correct
10 Correct 499 ms 2384 KB Output is correct
11 Correct 495 ms 2388 KB Output is correct
12 Correct 495 ms 2348 KB Output is correct
13 Correct 497 ms 2492 KB Output is correct
14 Correct 501 ms 2488 KB Output is correct
15 Correct 499 ms 2464 KB Output is correct
16 Correct 87 ms 800 KB Output is correct
17 Correct 94 ms 816 KB Output is correct
18 Correct 90 ms 820 KB Output is correct
19 Correct 94 ms 848 KB Output is correct
20 Correct 91 ms 836 KB Output is correct
21 Correct 915 ms 7876 KB Output is correct
22 Correct 916 ms 7832 KB Output is correct
23 Correct 899 ms 7692 KB Output is correct
24 Correct 914 ms 7776 KB Output is correct
25 Correct 898 ms 7668 KB Output is correct
26 Correct 875 ms 7508 KB Output is correct
27 Correct 887 ms 7444 KB Output is correct
28 Correct 873 ms 7324 KB Output is correct
29 Correct 873 ms 7248 KB Output is correct
30 Correct 949 ms 8016 KB Output is correct
31 Correct 948 ms 7864 KB Output is correct
32 Correct 939 ms 8016 KB Output is correct
33 Correct 953 ms 8016 KB Output is correct
34 Correct 934 ms 8016 KB Output is correct
35 Correct 502 ms 4440 KB Output is correct
36 Correct 507 ms 4304 KB Output is correct
37 Correct 502 ms 4688 KB Output is correct
38 Correct 498 ms 4436 KB Output is correct
39 Correct 10 ms 1880 KB Output is correct
40 Correct 10 ms 1884 KB Output is correct
41 Correct 10 ms 1884 KB Output is correct
42 Correct 10 ms 1884 KB Output is correct
43 Correct 10 ms 1884 KB Output is correct
44 Correct 11 ms 1880 KB Output is correct
45 Correct 11 ms 1884 KB Output is correct
46 Correct 11 ms 2032 KB Output is correct
47 Correct 11 ms 1884 KB Output is correct
48 Correct 11 ms 2036 KB Output is correct
49 Correct 10 ms 1884 KB Output is correct
50 Correct 10 ms 2072 KB Output is correct
51 Correct 11 ms 1880 KB Output is correct
52 Correct 11 ms 2064 KB Output is correct
53 Correct 10 ms 1884 KB Output is correct
54 Correct 5 ms 1116 KB Output is correct
55 Correct 4 ms 1116 KB Output is correct
56 Correct 5 ms 1116 KB Output is correct
57 Correct 5 ms 1160 KB Output is correct
58 Correct 5 ms 1116 KB Output is correct
59 Correct 1131 ms 8504 KB Output is correct
60 Correct 1118 ms 8504 KB Output is correct
61 Correct 1122 ms 8500 KB Output is correct
62 Correct 1135 ms 8284 KB Output is correct
63 Correct 1140 ms 8484 KB Output is correct
64 Correct 1188 ms 8272 KB Output is correct
65 Correct 1194 ms 8276 KB Output is correct
66 Correct 1188 ms 8264 KB Output is correct
67 Correct 1182 ms 8500 KB Output is correct
68 Correct 1202 ms 8420 KB Output is correct
69 Correct 1097 ms 8280 KB Output is correct
70 Correct 1094 ms 8280 KB Output is correct
71 Correct 1097 ms 8284 KB Output is correct
72 Correct 1099 ms 8276 KB Output is correct
73 Correct 1099 ms 8504 KB Output is correct
74 Correct 114 ms 1116 KB Output is correct
75 Correct 114 ms 1116 KB Output is correct
76 Correct 114 ms 1116 KB Output is correct
77 Correct 113 ms 1116 KB Output is correct
78 Correct 113 ms 1116 KB Output is correct