[Luogu 3383] [TEMPLATE] linear sieve prime number, luogu3383 sieve Prime Number

[Luogu 3383] [TEMPLATE] linear sieve prime number, luogu3383 sieve Prime Number
Description

For example, given a range of N, You need to query whether M is a prime number (each number is within the range of 1-N)

Input/Output Format

Input Format:

The first line contains two positive integers N and M, indicating the query range and the number of queries respectively.

Each row in the next M row contains an integer not less than 1 and not greater than N, that is, whether the approximate number is a prime number.

Output Format:

The output contains M rows. Each row is Yes or No, which is the result of each query in sequence.

Input and Output sample input sample #1:

100 52349197

Output sample #1:

YesYesNoNoYes

Description

Time-Space limit: 500 ms 128 M

Data scale:

For 30% of data: N <= 10000, M <= 10000

For 100% of data: N <= 10000000, M <= 100000

Example:

N = 100, indicating that the number of subsequent queries is not greater than 100 and greater than 1.

Therefore, 2, 3, and 97 are prime numbers, and 4 and 91 are non-prime numbers.

Therefore, Yes, Yes, No, No, and Yes are output in sequence.

Normal screening method:

 1 #include<cstdio> 2 #include<cstring> 3 #include<algorithm> 4 #include<iostream> 5 using namespace std; 6 bool is_prime(int x){ 7     if(x==1) return false; 8     for(int i=2;i*i<=x;i++){ 9         if(x%i==0) return false;    10     }11     return true;12 }13 int n,m;14 int main(){15     scanf("%d%d",&n,&m);16     for(int i=1;i<=m;i++){17         int x;scanf("%d",&x);18         if(is_prime(x)) puts("Yes");19         else puts("No");20     }21     return 0;22 }

AI screening method:

 1 #include<cstdio> 2 #include<cstring> 3 #include<iostream> 4 #include<algorithm> 5 #include<cmath>  6 using namespace std; 7 int n,m,q;bool is_prime[10000005]; 8 void eratos(int n){ 9     memset(is_prime,true,sizeof(is_prime));10     is_prime[1]=false;11     for(int i=2;i<=sqrt(n);i++){12         if(is_prime[i]){13             int j=i*2;14             while(j<=n){15                 is_prime[j]=false;16                 j=j+i;17             }18         }19     }20 }21 int main(){22     scanf("%d%d",&n,&m);23     eratos(n);24     for(int i=1;i<=m;i++){25         scanf("%d",&q);26         if(is_prime[q]) printf("Yes\n");27         else printf("No\n");28     }29     return 0;30 }

European screening method (linear screening method ):

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<cmath> 6 using namespace std; 7 bool is_prime[10000005]; 8 int prime[5000005],cnt=0,n,m,a;  9 void getlist(int n){10     memset(is_prime,true,sizeof(is_prime));11     is_prime[1]=false;12     for(int i=2;i<=n/2;i++){13         if(is_prime[i])prime[++cnt]=i;14         for(int j=1;j<=cnt&&i*prime[j]<=n;j++){15             is_prime[i*prime[j]]=false;16             if(i%prime[j]==0) break;17         }18     }19 }20 int main(){21     scanf("%d%d",&n,&m);22     getlist(n);23     for(int i=1;i<=m;i++){24         scanf("%d",&a);25         if(is_prime[a]) printf("Yes\n");26         else printf("No\n");27     }28     return 0;29 }