00-自测2. 素数对猜想 (20)

</pre></div></div></div><div id="problemInfo" class="rfloat" style="margin: 0px; padding: 2px; border: 1px solid rgb(221, 221, 221); font-family: 'Droid Sans', Verdana, 'Microsoft YaHei', Tahoma, sans-serif; font-size: 12px; line-height: 18px; vertical-align: baseline; float: right; text-align: center; color: rgb(51, 51, 51); background-color: rgb(250, 250, 250);"><div class="limit" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><div class="key" style="margin: 0px; padding: 0px 20px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline; background-color: rgb(221, 221, 221);">时间限制</div><div class="value" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">400 ms</div></div><div class="limit" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><div class="key" style="margin: 0px; padding: 0px 20px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline; background-color: rgb(221, 221, 221);">内存限制</div><div class="value" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">65536 kB</div></div><div class="limit" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><div class="key" style="margin: 0px; padding: 0px 20px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline; background-color: rgb(221, 221, 221);">代码长度限制</div><div class="value" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">8000 B</div></div><div class="checker" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><div class="key" style="margin: 0px; padding: 0px 20px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline; background-color: rgb(221, 221, 221);">判题程序</div><div class="value" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><span title="纯文本对比" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">Standard</span></div></div><div class="key" style="margin: 0px; padding: 0px 20px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline; background-color: rgb(221, 221, 221);">作者</div><div class="value" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">CHEN, Yue</div></div><div id="problemContent" style="margin: 0px; padding: 0px; border: 0px; font-family: 'Droid Sans', Verdana, 'Microsoft YaHei', Tahoma, sans-serif; font-size: 12px; line-height: 18px; vertical-align: baseline; color: rgb(51, 51, 51); background-color: rgb(250, 250, 250);"><p style="margin-top: 0px; margin-bottom: 1.5em; padding-top: 0px; padding-bottom: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">让我们定义 d<sub style="line-height: 0;">n</sub> 为：d<sub style="line-height: 0;">n</sub> = p<sub style="line-height: 0;">n+1</sub> - p<sub style="line-height: 0;">n</sub>，其中 p<sub style="line-height: 0;">i</sub> 是第i个素数。显然有 d<sub style="line-height: 0;">1</sub>=1 且对于n>1有 d<sub style="line-height: 0;">n</sub> 是偶数。“素数对猜想”认为“存在无穷多对相邻且差为2的素数”。</p><p style="margin-top: 0px; margin-bottom: 1.5em; padding-top: 0px; padding-bottom: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;">现给定任意正整数N (< 10<sup style="line-height: 0;">5</sup>)，请计算不超过N的满足猜想的素数对的个数。</p><p style="margin-top: 0px; margin-bottom: 1.5em; padding-top: 0px; padding-bottom: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><strong>输入格式：</strong>每个测试输入包含1个测试用例，给出正整数N。</p><p style="margin-top: 0px; margin-bottom: 1.5em; padding-top: 0px; padding-bottom: 0px; border: 0px; font-family: inherit;font-size:undefined; font-style: inherit; font-variant: inherit; line-height: inherit; vertical-align: baseline;"><strong>输出格式：</strong>每个测试用例的输出占一行，不超过N的满足猜想的素数对的个数。</p><strong>输入样例：</strong><pre style="margin-top: 1.5em; margin-bottom: 1.5em; padding: 0px; border: 0px; font-family: 'Droid Sans Mono', Consolas, 'Courier New', monospace; font-size: 1em; line-height: 1.5; vertical-align: baseline; overflow: auto;">20

输出样例：

4

#include <iostream>#include <math.h>#define MAX 100000using namespace std;bool isPrime(int n){    if(n==2||n==3)        return true;   for(int i=2;i<=sqrt(n);i++)    if(n%i==0)        return false;   return true;}int a[10001];int main(){    int i,j=1,N;    a[0]=2;a[1]=3;    cin>>N;    int sum=0;    for(i=3;i<=N-2;)    {        if(isPrime(i)&&isPrime(i+2))        {            sum++;        }        i+=2;    }    cout<<sum<<endl;    return 0;}