UVa11105 - Semi-prime H-numbers(sieve的思想)

This problem is based on an exercise of David Hilbert, who pedagogically suggested that one study the theory of 4n+1 numbers. Here, we do only a bit of that.

An H-number is a positive number which is one more than a multiple of four: 1, 5, 9, 13, 17, 21,... are the H-numbers. For this problem we pretend that these are the only numbers. The H-numbers are closed under multiplication.

As with regular integers, we partition the H-numbers into units, H-primes, andH-composites. 1 is the only unit. An H-number h is H-prime if it is not the unit, and is the product of two H-numbers in only one way: 1 × h. The rest of the numbers are H-composite.

For examples, the first few H-composites are: 5 × 5 = 25, 5 × 9 = 45, 5 × 13 = 65, 9 × 9 = 81, 5 × 17 = 85.

Your task is to count the number of H-semi-primes. An H-semi-prime is an H-number which is the product of exactly two H-primes. The two H-primes may be equal or different. In the example above, all five numbers are H-semi-primes. 125 = 5 × 5 × 5 is not an H-semi-prime, because it's the product of three H-primes.

Each line of input contains an H-number ≤ 1,000,001. The last line of input contains 0 and this line should not be processed.

For each inputted H-number h, print a line stating h and the number of H-semi-primes between 1 and hinclusive, separated by one space in the format shown in the sample.

Sample input

21 857890

Output for sample input

21 085 5789 62

import java.io.FileInputStream;import java.io.BufferedInputStream;import java.io.OutputStreamWriter;import java.io.PrintWriter;import java.util.Scanner;public class Main implements Runnable{private static final boolean DEBUG = false;private static final int N = 1000002;private PrintWriter cout;private Scanner cin;private int h;private int[] vis;private int[] semi;private void init(){try {if (DEBUG) {cin = new Scanner(new BufferedInputStream(new FileInputStream("d:\\OJ\\uva_in.txt")));} else {cin = new Scanner(new BufferedInputStream(System.in));}cout = new PrintWriter(new OutputStreamWriter(System.out));preprocess();} catch (Exception e) {e.printStackTrace();}}private void preprocess(){vis = new int[N];for (int i = 5; i * i < N; i += 4) {if (vis[i] == 0) {for (int j = i + i; j < N; j += i) vis[j] = i;}}semi = new int[N];for (int i = 5; i < N; i += 4) {semi[i] = semi[i - 4];if (vis[i] != 0 && vis[i / vis[i]] == 0) semi[i]++;}}private boolean input(){h = cin.nextInt();if (h == 0) return false;return true;}private void solve(){int ans = semi[h];cout.println(h + " " + ans);cout.flush();}public void run(){init();while (input()) {solve();}}public static void main(String[] args){new Thread(new Main()).start();}}