POJ 3292 Semi-prime H-numbers(打表)
2013-10-18 19:58
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题意大体是:规定如果一个数是由1,5,9,13,17,21、、、这么一个等差数列中的任意两项组成的乘积组成的数称之为H-numbers。然后给你一个数输出比这个数字小的H-numbers有多少个、、、(貌似不能是乘1)。
类似的一个打表,数据范围也不广,可以水过啊、、、
Semi-prime H-numbers
Description
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 theonly numbers. The H-numbers are
closed under multiplication.
As with regular integers, we partition the H-numbers into units, H-primes, and H-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.
Input
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.
Output
For each inputted H-number h, print a line stating h and the number of H-semi-primes between 1 and h inclusive, separated by one space in the format shown in the sample.
Sample Input
Sample Output
类似的一个打表,数据范围也不广,可以水过啊、、、
Semi-prime H-numbers
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 6888 | Accepted: 2943 |
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 theonly numbers. The H-numbers are
closed under multiplication.
As with regular integers, we partition the H-numbers into units, H-primes, and H-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.
Input
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.
Output
For each inputted H-number h, print a line stating h and the number of H-semi-primes between 1 and h inclusive, separated by one space in the format shown in the sample.
Sample Input
21 85 789 0
Sample Output
21 0 85 5 789 62
#include <stdio.h> #include <string.h> #include <cmath> #include <iostream> #include <stdlib.h> #include <map> using namespace std; int f[1001000]; void _printf() { int i, j; memset(f , 0 , sizeof(f)); for(i = 5; i <= 1000; i+= 4) { if(f[i] == 0) { for(j = i; i*j < 1000002; j+=4) { f[i*j] = f[i]+f[j]+1; } } } for(i = 25; i < 1000002; i++) { if(f[i] == 1) f[i] = f[i-1]+1; else f[i] = f[i-1]; } } int main() { int n; _printf(); while(cin >>n) { if(!n) break; cout <<n<<' '<<f <<endl; } return 0; }
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