codeforces-230B T-primes
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codeforces-230B T-primes
time limit per test2 seconds memory limit per test256 megabytes
We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we’ll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.
You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.
Input
The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.
Output
Print n lines: the i-th line should contain “YES” (without the quotes), if number xi is Т-prime, and “NO” (without the quotes), if it isn’t.
input
3
4 5 6
output
YES
NO
NO
Note
The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is “YES”. The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is “NO”.
题目大意:找出一个数字,存在3个约数包括1和他本身。
题目思路:这个数只能是另一个数的平方,并且不存在其他约数。
题目链接:230B T-primes
以下是代码:
#include <iostream>#include <cmath>using namespace std;int a[1000100];void isans(){ for (int i = 1; i <= 1000000; i++) a[i] = 1; a[1] = 0; for (int i = 2; i <= 1000000; i++) { if ((long long)i * i <= 1000000 && a[i]) { for (int j = i * i; j <= 1000000; j += i) { a[j] = 0; } } } }int main(){ int n; cin >> n; isans(); while(n--) { long long x; cin >> x; long long num = sqrt(x); if (num * num == x && a[num]) cout << "YES\n"; else cout << "NO\n"; } return 0;}
附上超时的代码:
#include <iostream>#include <cmath>using namespace std;int main(){ int n; cin >> n; while(n--) { long long x; cin >> x; long long num = sqrt(x); int i; for (i = 2;i * i<= num; i++) { if (num % i == 0) { break; } } if (num * num == x && i * i > num && x > 1) cout << "YES\n"; else cout << "NO\n"; } return 0;}
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