POJ 2262 Goldbach's Conjecture
Goldbach's Conjecture
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 28913 | Accepted: 11072 |
Description
In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:
For example:
Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.)
Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million.
Every even number greater than 4 can be
written as the sum of two odd prime numbers.
For example:
8 = 3 + 5. Both 3 and 5 are odd prime numbers.
20 = 3 + 17 = 7 + 13.
42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.
Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.)
Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million.
Input
The input will contain one or more test cases.
Each test case consists of one even integer n with 6 <= n < 1000000.
Input will be terminated by a value of 0 for n.
Each test case consists of one even integer n with 6 <= n < 1000000.
Input will be terminated by a value of 0 for n.
Output
For
each test case, print one line of the form n = a + b, where a and b are
odd primes. Numbers and operators should be separated by exactly one
blank like in the sample output below. If there is more than one pair of
odd primes adding up to n, choose the pair where the difference b - a
is maximized. If there is no such pair, print a line saying "Goldbach's
conjecture is wrong."
Sample Input
8
20
42
0
Sample Output
8 = 3 + 5
20 = 3 + 17
42 = 5 + 37
Source
用筛法先筛了1000000以内的素数并且存到prime数组里。
从小端开始测试，并且验证num-prime[i]是否是素数。如果是就打印。
1 #include <iostream>
2 #include <cstdlib>
3 #include <algorithm>
4 #include <cstring>
5 #include <cstdio>
6
7 #define DATASIZE 1000000
8
9 using namespace std;
10
11 bool flag[DATASIZE];
12 int prime[DATASIZE];
13
14 int generate_prime(void)
15 {
16 memset(flag,true,sizeof(bool)*DATASIZE);
17 int current = 0;
18
19 for(int i = 2;i*i <= DATASIZE;++i)
20 if(flag[i])
21 for(int j = 2*i;j <= DATASIZE;j += i)
22 flag[j] = false;
23 for(int i = 2;i != DATASIZE;++i)
24 if(flag[i])
25 prime[current++] = i;
26 return current-1;
27 }
28
29 int main(void)
30 {
31 int primecount = generate_prime();
32
33 int num;
34 while(cin >> num && num)
35 {
36 bool flg = false;
37 for(int i = 0;i != primecount;++i)
38 if(flag[num-prime[i]])
39 {
40 printf("%d = %d + %d\n",num,prime[i],num-prime[i]);
41 flg = true;
42 break;
43 }
44 if(!flg)
45 printf("Goldback's conjecture is wrong.\n");
46 }
47 return 0;
48 }
