【題解】LightOJ1259 Goldbach`s Conjecture 線性篩
Description
Goldbach’s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:
Every even integer, greater than 2, can be expressed as the sum of two primes [1].
Now your task is to check whether this conjecture holds for integers up to 107.
Input
Input starts with an integer T (≤ 300), denoting the number of test cases.
Each case starts with a line containing an integer n (4 ≤ n ≤ 107, n is even).
Output
For each case, print the case number and the number of ways you can express n as sum of two primes. To be more specific, we want to find the number of (a, b) where
1) Both a and b are prime
2) a + b = n
3) a ≤ b
Sample Input
2
6
4
Sample Output
Case 1: 1
Case 2: 1
Note
1.An integer is said to be prime, if it is divisible by exactly two different integers. First few primes are 2, 3, 5, 7, 11, 13, …
我居然能想到n²的列舉……真是為我智商捉急
#include<cstdio>
const int N=1e7+10;
int t,prime[N/2],p,n,ca;
bool iscomp[N];
void primetable()
{
for(int i=2;i<N;i++)
{
if(!iscomp[i])prime[p++]=i;
for(int j=0;j<p&&prime[j]*i<N;j++)
{
iscomp[i*prime[j]]=1;
if(i%prime[j]==0)break;
}
}
}
int main()
{
//freopen("in.txt","r",stdin);
primetable();
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
int cnt=0;
for(int i=0;prime[i]<=n/2;i++)
if(!iscomp[n-prime[i]])cnt++;
printf("Case %d: %d\n",++ca,cnt);
}
return 0;
}
總結
線性篩出素數之後直接暴力就好