(Hdu step 2.1.2) How many prime numbers (determine whether a number is a prime number)

(Hdu step 2.1.2) How many prime numbers (determine whether a number is a prime number)

Question:

How many prime numbers

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Total Submission (s): 8513 Accepted Submission (s): 2716

Problem DescriptionGive you a lot of positive integers, just to find out how many prime numbers there are.

InputThere are a lot of cases. in each case, there is an integer N representing the number of integers to find. each integer won't exceed 32-bit signed integer, and each of them won't be less than 2.

Output For each case, print the number of prime numbers you have found out.

Sample Input 32 3 4

Sample Output 2

Authorwangye

SourceHDU 2007-11 Programming Contest_WarmUp

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Question Analysis:

Determine whether a number is a prime number. This question can be done in many ways: the definition method, the Euler's sieve method, and the Elatos sieve method. Use this question

Definition method.

Some knowledge points about prime numbers:

First, for a natural number N, as long as it can be divisible by a non-1 Non-its own number, it is certainly not a prime number, so no
Other numbers must be removed.
Second, for N, you only need to remove the prime number less than N. For example, if N can be divisible by 15, the actual
3 and 5 can be divisible. If N cannot be divisible by 3 and 5, N will never be divisible by 15.
Third, for N, do not have to remove all prime numbers from 2 to N-1, just remove all prime numbers less than or equal to √ N (root N. This can be proved by the reverse proof:
If N is a combination, there must be integers d1 and d2 greater than 1 and less than N, so that N = d1 × d2.
If d1 and d2 are greater than √ N, there are: N = d1 × d2> √ N × √ N = N.
This is not possible. Therefore, one of d1 and d2 must be less than or equal to √ N.

The Code is as follows:

/** B. cpp ** Created on: January 30, 2015 * Author: Administrator */# include
 
  
# Include
  
   
# Include
   
    
Using namespace std;/*** determine whether a number is a prime number */bool isPrime (int n) {if (n = 1 | n = 0) {// 0 and 1 are neither sum nor Prime return false;} int I; for (I = 2; I <= sqrt (n * 1.0); ++ I) {// to determine whether a number is a prime number, you only need to go to the <= root number n. if n is obtained from the upper bound, TLEif (n % I = 0) {// if it can integer one of the factors return false; // It indicates that it is not a prime number} return true;} int main () {int n; while (scanf ("% d", & n )! = EOF) {int ans = 0; int I; for (I = 0; I <n; ++ I) {int temp; scanf ("% d ", & temp); if (isPrime (temp) = true) {ans ++ ;}} printf ("% d \ n", ans);} return 0 ;}