"Algorithm" general method and the method of filtering to find prime number

Prime number refers to the factor is only 1 and its own numbers (1 is not prime), the solution of prime numbers in mathematics is widely used, and the solution of the prime number within N is also our programming often encountered problems, in this problem, the screening method to solve the prime numbers are executed quickly. The following first describes how to infer a is not a prime number, and then introduce the ordinary method to find the prime number within N, followed by the filtering method to find the prime number of N, and finally the execution time of the two algorithms is relatively

Infer whether a number is prime

Algorithm thought: inferred that the sum of the squares of less than or equal to a number of all integers greater than 1 is divisible by this number, assuming that the number is not prime;

//infer whether a number is prime  bool  isplain (int  value )    {int  m = sqrt (value ); if  (value  < 2 ) return     false ; for  (int  i = 2 ; I <= m; i++) {if  ((value %i) ==0        ) {return  false ; }} return  true ;}  

Common method for solving primes within n

Algorithm idea: Declare an n-size bool array. The initial value is false, and then starts from 2 to infer whether a number is prime. If. Then the Boolean value is set to True

//普通法求素数bool* putong(int n){    boolvaluenewbool[n];    for (int0; i < n; i++)        valuefalse;    for (int2; i < n; i++){        if (isPlain(i)){            valuetrue;        }    }    returnvalue;}

The number of primes within n is calculated by filtering method

Algorithm idea: Find the prime number of the radical that is less than or equal to N. Then the multiples of all these primes in n are removed, the remaining numbers are primes, and are implemented by Boolean arrays

//filter method for prime numbersBOOL* Shuaixuan (intN) {BOOL*value=New BOOL[n]; for(inti =0; i<n; i++)value[I] =true;value[0] =false;value[1] =false; for(inti =2; I <= sqrt (n); i++) {if(value[i] && isplain (i)) {intc =2;intj = i*c; while(J < N) {value[j] =false;            j = i*c++; }        }    }return value;}

Complete code and execution results

The following code calls the normal method and the filter method, can loop input n (by CTRL + C end), for different data test, followed by a test to carry out a result diagram

#include <iostream>usingnamespace Std;#include <ctime>#include <math.h>#include <conio.h>//Infer whether a number is primeBOOLIsplain (int value){intm = sqrt (value);if(value<2)return false; for(inti =2; I <= m; i++) {if((value%i) = =0){return false; }    }return true;}//Common law seeking prime numbersBOOL* Putong (intN) {BOOL*value=New BOOL[n]; for(inti =0; I < n; i++)value[I] =false; for(inti =2; I < n; i++) {if(Isplain (i)) {value[I] =true; }    }return value;}//filter method for prime numbersBOOL* Shuaixuan (intN) {BOOL*value=New BOOL[n]; for(inti =0; i<n; i++)value[I] =true;value[0] =false;value[1] =false; for(inti =2; I <= sqrt (n); i++) {if(value[i] && isplain (i)) {intc =2;intj = i*c; while(J < N) {value[j] =false;            j = i*c++; }        }    }return value;}intMain () {intN while(CIN >> N) {intstart = Clock ();BOOL* value1 = Putong (n);intend = Clock (); cout <<"Normal method:"<< End-start << Endl; start = Clock ();BOOL* value2 = Shuaixuan (n);        end = Clock (); cout <<"Screening method:"<< End-start << Endl;        Delete[] value1;        value1 = NULL;        Delete[] value2;    value2 = NULL; } _getch ();}

It can be seen that the greater the N. The better the performance of the filter method is for the normal method.

"Algorithm" general method and the method of filtering to find prime number