Prime screening method (ordinary sieve and linear sieve) __ algorithm

Title: Given an n, find all prime numbers of 1~n.

Here are two methods for selecting prime numbers:

The first type: ordinary Sieve method.

Time complexity is O (Nloglogn), and the disadvantage is that a composite number may be filtered multiple times.

Code:

void Prime ()
{
	memset (tag,0,sizeof (tag));
	Tag[0]=tag[1]=1;
	for (int i=2; i*i <= N; i++)
		if (tag[i]==0) {
			prime[ct++]=i;
			for (int j=i+i;j<=n;j+=i)
				tag[j]=1
		}
}

The second type: linear sieve.

The time complexity is O (n), because each composite is guaranteed to be filtered only by its smallest mass factor. The key code in the 10th, 11 lines, because if I can complete out of prime[j], then I must be a composite, and I have the quality factor is certainly less than prime[j], so this can stop, because the back of the prime[] than I small of that quality factor to be larger.

Code:

void Prime () {
	memset (tag,0,sizeof (tag));
	int cnt=0;
	Tag[0]=tag[1]=1;
	for (int i = 2; i<n; i++) {
		if (!tag[i])
			prime[cnt++]=i;
		for (int j=0;j<cnt && prime[j]*i<n; j + +) {
			Tag[i*prime[j]] = 1;
			if (i% prime[j]==0) break;}}