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Submission #1092850

# Submission time Handle Problem Language Result Execution time Memory
1092850 2024-09-25T08:52:49 Z alexander707070 Boat (APIO16_boat) C++14
100 / 100
 1941 ms 42080 KB 
#include<bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
 
#define MAXN 5007
using namespace std;
 
struct group{
    int from,to;
}s[2*MAXN];
 
const long long mod=1e9+7;
 
int n,a[MAXN],b[MAXN],m;
vector<int> pos;
 
bool in(group g,int id){
    return g.from>=a[id] and g.to<=b[id];
}
 
long long dp[2][MAXN][507][2];
long long invfact[MAXN];
 
long long cc[507][MAXN];
 
long long comb(int x,int g){
    return cc[x][g];
}
 
long long power(long long a,int b){
    if(b==0)return 1;
    if(b==1)return a;
    if(b==2)return (a*a)%mod;
    if(b%2==0)return power(power(a,b/2),2);
    return (a*power(power(a,b/2),2))%mod;
}
 
 
int main(){
 
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
 
    cin>>n;
 
    for(int i=1;i<=n;i++){
        cin>>a[i]>>b[i];
 
        pos.push_back(a[i]);
        pos.push_back(b[i]);
    }
 
    invfact[0]=1;
    for(long long i=1;i<=n;i++)invfact[i]=(invfact[i-1]*i)%mod;
    for(long long i=1;i<=n;i++)invfact[i]=power(invfact[i],mod-2);
 
    sort(pos.begin(),pos.end());
    
    for(int i=0;i<pos.size()-1;i++){
        if(pos[i]!=pos[i+1]){
            m++; s[m]={pos[i],pos[i]};
            
            if(pos[i]+1<=pos[i+1]-1){
                m++; s[m]={pos[i]+1,pos[i+1]-1};
            }
        }
    }
 
    m++;
    s[m]={pos.back(),pos.back()};
 
    for(int i=1;i<=m;i++){
        cc[0][i]=1;
        for(int f=1;f<=min(n,s[i].to-s[i].from+1);f++){
            cc[f][i]=(long long) cc[f-1][i]*(s[i].to-s[i].from+1-(f-1));
            cc[f][i]%=mod;
        }
 
        for(int f=1;f<=min(n,s[i].to-s[i].from+1);f++){
            cc[f][i]*=invfact[f];
            cc[f][i]%=mod;
        }
    }
 
    for(int i=0;i<=m;i++){
        for(int c=0;c<=n;c++){
            if(i==0)dp[0][i][c][1]=1;
            else dp[0][i][c][1]=comb(c,i);
        }
    }
 
    for(int i=1;i<=n;i++){
        dp[i%2][0][0][1]=1;
 
        for(int f=1;f<=m;f++){
            for(int c=0;c<=n;c++){
                for(int t=0;t<2;t++){
                    
                    dp[i%2][f][c][t]=dp[1-i%2][f][c][0];
                    if(t==1)dp[i%2][f][c][t]+=dp[i%2][f-1][0][1]*comb(c,f);
 
                    if(in(s[f],i) and c+1<=s[f].to-s[f].from+1){
                        dp[i%2][f][c][t]+=dp[1-i%2][f][c+1][1];
                    }
    
                    dp[i%2][f][c][t]%=mod;
                }
            }
        }
    }
    
    cout<<(dp[n%2][m][0][1]-1+mod)%mod<<"\n";
 
    return 0;
}

Compilation message

boat.cpp: In function 'int main()':
boat.cpp:61:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   61 |     for(int i=0;i<pos.size()-1;i++){
      |                 ~^~~~~~~~~~~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 744 ms 22104 KB Output is correct
2 Correct 755 ms 22320 KB Output is correct
3 Correct 719 ms 22316 KB Output is correct
4 Correct 718 ms 22108 KB Output is correct
5 Correct 706 ms 22316 KB Output is correct
6 Correct 720 ms 22316 KB Output is correct
7 Correct 714 ms 22108 KB Output is correct
8 Correct 706 ms 22308 KB Output is correct
9 Correct 704 ms 22316 KB Output is correct
10 Correct 708 ms 22356 KB Output is correct
11 Correct 717 ms 22108 KB Output is correct
12 Correct 740 ms 22104 KB Output is correct
13 Correct 701 ms 22104 KB Output is correct
14 Correct 731 ms 22316 KB Output is correct
15 Correct 736 ms 22312 KB Output is correct
16 Correct 123 ms 5980 KB Output is correct
17 Correct 133 ms 6284 KB Output is correct
18 Correct 126 ms 5980 KB Output is correct
19 Correct 132 ms 6232 KB Output is correct
20 Correct 127 ms 5928 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 744 ms 22104 KB Output is correct
2 Correct 755 ms 22320 KB Output is correct
3 Correct 719 ms 22316 KB Output is correct
4 Correct 718 ms 22108 KB Output is correct
5 Correct 706 ms 22316 KB Output is correct
6 Correct 720 ms 22316 KB Output is correct
7 Correct 714 ms 22108 KB Output is correct
8 Correct 706 ms 22308 KB Output is correct
9 Correct 704 ms 22316 KB Output is correct
10 Correct 708 ms 22356 KB Output is correct
11 Correct 717 ms 22108 KB Output is correct
12 Correct 740 ms 22104 KB Output is correct
13 Correct 701 ms 22104 KB Output is correct
14 Correct 731 ms 22316 KB Output is correct
15 Correct 736 ms 22312 KB Output is correct
16 Correct 123 ms 5980 KB Output is correct
17 Correct 133 ms 6284 KB Output is correct
18 Correct 126 ms 5980 KB Output is correct
19 Correct 132 ms 6232 KB Output is correct
20 Correct 127 ms 5928 KB Output is correct
21 Correct 1290 ms 29276 KB Output is correct
22 Correct 1312 ms 29684 KB Output is correct
23 Correct 1315 ms 29248 KB Output is correct
24 Correct 1291 ms 29276 KB Output is correct
25 Correct 1240 ms 28764 KB Output is correct
26 Correct 1227 ms 27668 KB Output is correct
27 Correct 1286 ms 27740 KB Output is correct
28 Correct 1212 ms 27812 KB Output is correct
29 Correct 1211 ms 27996 KB Output is correct
30 Correct 1911 ms 39260 KB Output is correct
31 Correct 1806 ms 39000 KB Output is correct
32 Correct 1850 ms 38992 KB Output is correct
33 Correct 1876 ms 39168 KB Output is correct
34 Correct 1840 ms 38748 KB Output is correct
35 Correct 728 ms 22316 KB Output is correct
36 Correct 719 ms 22108 KB Output is correct
37 Correct 719 ms 22312 KB Output is correct
38 Correct 710 ms 22272 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 5468 KB Output is correct
2 Correct 15 ms 5676 KB Output is correct
3 Correct 16 ms 5468 KB Output is correct
4 Correct 14 ms 5468 KB Output is correct
5 Correct 15 ms 5468 KB Output is correct
6 Correct 15 ms 5676 KB Output is correct
7 Correct 16 ms 5468 KB Output is correct
8 Correct 15 ms 5676 KB Output is correct
9 Correct 15 ms 5464 KB Output is correct
10 Correct 15 ms 5468 KB Output is correct
11 Correct 16 ms 5680 KB Output is correct
12 Correct 15 ms 5680 KB Output is correct
13 Correct 15 ms 5468 KB Output is correct
14 Correct 15 ms 5468 KB Output is correct
15 Correct 15 ms 5716 KB Output is correct
16 Correct 7 ms 2904 KB Output is correct
17 Correct 7 ms 2908 KB Output is correct
18 Correct 6 ms 2908 KB Output is correct
19 Correct 6 ms 2908 KB Output is correct
20 Correct 7 ms 2928 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 744 ms 22104 KB Output is correct
2 Correct 755 ms 22320 KB Output is correct
3 Correct 719 ms 22316 KB Output is correct
4 Correct 718 ms 22108 KB Output is correct
5 Correct 706 ms 22316 KB Output is correct
6 Correct 720 ms 22316 KB Output is correct
7 Correct 714 ms 22108 KB Output is correct
8 Correct 706 ms 22308 KB Output is correct
9 Correct 704 ms 22316 KB Output is correct
10 Correct 708 ms 22356 KB Output is correct
11 Correct 717 ms 22108 KB Output is correct
12 Correct 740 ms 22104 KB Output is correct
13 Correct 701 ms 22104 KB Output is correct
14 Correct 731 ms 22316 KB Output is correct
15 Correct 736 ms 22312 KB Output is correct
16 Correct 123 ms 5980 KB Output is correct
17 Correct 133 ms 6284 KB Output is correct
18 Correct 126 ms 5980 KB Output is correct
19 Correct 132 ms 6232 KB Output is correct
20 Correct 127 ms 5928 KB Output is correct
21 Correct 1290 ms 29276 KB Output is correct
22 Correct 1312 ms 29684 KB Output is correct
23 Correct 1315 ms 29248 KB Output is correct
24 Correct 1291 ms 29276 KB Output is correct
25 Correct 1240 ms 28764 KB Output is correct
26 Correct 1227 ms 27668 KB Output is correct
27 Correct 1286 ms 27740 KB Output is correct
28 Correct 1212 ms 27812 KB Output is correct
29 Correct 1211 ms 27996 KB Output is correct
30 Correct 1911 ms 39260 KB Output is correct
31 Correct 1806 ms 39000 KB Output is correct
32 Correct 1850 ms 38992 KB Output is correct
33 Correct 1876 ms 39168 KB Output is correct
34 Correct 1840 ms 38748 KB Output is correct
35 Correct 728 ms 22316 KB Output is correct
36 Correct 719 ms 22108 KB Output is correct
37 Correct 719 ms 22312 KB Output is correct
38 Correct 710 ms 22272 KB Output is correct
39 Correct 16 ms 5468 KB Output is correct
40 Correct 15 ms 5676 KB Output is correct
41 Correct 16 ms 5468 KB Output is correct
42 Correct 14 ms 5468 KB Output is correct
43 Correct 15 ms 5468 KB Output is correct
44 Correct 15 ms 5676 KB Output is correct
45 Correct 16 ms 5468 KB Output is correct
46 Correct 15 ms 5676 KB Output is correct
47 Correct 15 ms 5464 KB Output is correct
48 Correct 15 ms 5468 KB Output is correct
49 Correct 16 ms 5680 KB Output is correct
50 Correct 15 ms 5680 KB Output is correct
51 Correct 15 ms 5468 KB Output is correct
52 Correct 15 ms 5468 KB Output is correct
53 Correct 15 ms 5716 KB Output is correct
54 Correct 7 ms 2904 KB Output is correct
55 Correct 7 ms 2908 KB Output is correct
56 Correct 6 ms 2908 KB Output is correct
57 Correct 6 ms 2908 KB Output is correct
58 Correct 7 ms 2928 KB Output is correct
59 Correct 1783 ms 41856 KB Output is correct
60 Correct 1780 ms 42072 KB Output is correct
61 Correct 1800 ms 41976 KB Output is correct
62 Correct 1718 ms 42072 KB Output is correct
63 Correct 1801 ms 42080 KB Output is correct
64 Correct 1833 ms 42072 KB Output is correct
65 Correct 1833 ms 42072 KB Output is correct
66 Correct 1848 ms 42076 KB Output is correct
67 Correct 1772 ms 42076 KB Output is correct
68 Correct 1793 ms 42076 KB Output is correct
69 Correct 1898 ms 42064 KB Output is correct
70 Correct 1941 ms 42064 KB Output is correct
71 Correct 1793 ms 42076 KB Output is correct
72 Correct 1829 ms 42076 KB Output is correct
73 Correct 1860 ms 42076 KB Output is correct
74 Correct 151 ms 6492 KB Output is correct
75 Correct 145 ms 6368 KB Output is correct
76 Correct 146 ms 6492 KB Output is correct
77 Correct 146 ms 6492 KB Output is correct
78 Correct 150 ms 6488 KB Output is correct