Submission #1092850

#	Time	Username	Problem	Language	Result	Execution time	Memory
1092850		alexander707070	Boat (APIO16_boat)	C++14	100 / 100	1941 ms	42080 KiB

boat

#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 (stderr)

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 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 42 / 42