Description:
As you can see, calculations of 4 × 3 and 6 × 2 are not necessary. Therefore, we only need to consider factors up to √n because, if n is divisible by some number p, then n = p × q and since p ≤ q, we could derive that p ≤ √n.
Our total runtime has now improved to O(n1.5), which is slightly better. Is there a faster approach?
public int countPrimes(int n) {
int count = 0;
for (int i = 1; i < n; i++) {
if (isPrime(i)) count++;
}
return count;
}
private boolean isPrime(int num) {
if (num <= 1) return false;
// Loop's ending condition is i * i <= num instead of i <= sqrt(num)
// to avoid repeatedly calling an expensive function sqrt().
for (int i = 2; i * i <= num; i++) {
if (num % i == 0) return false;
}
return true;
}
public int countPrimes(int n) {
boolean[] isPrime = new boolean[n];
for (int i = 2; i < n; i++) {
isPrime[i] = true;
}
// Loop's ending condition is i * i < n instead of i < sqrt(n)
// to avoid repeatedly calling an expensive function sqrt().
for (int i = 2; i * i < n; i++) {
if (!isPrime[i]) continue;
for (int j = i * i; j < n; j += i) {
isPrime[j] = false;
}
}
int count = 0;
for (int i = 2; i < n; i++) {
if (isPrime[i]) count++;
}
return count;
}
public int countPrimes(int n) {
boolean[] b = new boolean[n];
// 将非质数标记为true
for (int i = 2; i * i < n; i++) {
if (b[i] == false) {
for (int j = i; i * j < n; j++) {
b[i * j] = true;
}
}
}
// count
int c = 0;
for (int i = 2; i < n; i++) {
if (b[i] == false) {
c++;
}
}
return c;
}
原创声明:本文系作者授权腾讯云开发者社区发表,未经许可,不得转载。
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原创声明:本文系作者授权腾讯云开发者社区发表,未经许可,不得转载。
如有侵权,请联系 cloudcommunity@tencent.com 删除。