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  • Acwing-196-质数距离(素数区间筛法)

    链接:

    https://www.acwing.com/problem/content/198/

    题意:

    给定两个整数L和U,你需要在闭区间[L,U]内找到距离最接近的两个相邻质数C1和C2(即C2-C1是最小的),如果存在相同距离的其他相邻质数对,则输出第一对。

    同时,你还需要找到距离最远的两个相邻质数D1和D2(即D1-D2是最大的),如果存在相同距离的其他相邻质数对,则输出第一对。

    思路:

    筛除,l-r中的素数, 使用区间筛法, 先筛出1-sqrt(r), 再筛l-r.
    记录l-r的素数,挨个判断.

    代码:

    #include <bits/stdc++.h>
    using namespace std;
    typedef long long LL;
    
    const int MAXN = 1e6+10;
    int IsPri1[MAXN], IsPri2[MAXN];
    LL Pri[MAXN], Res[MAXN];
    LL l, r;
    int pos;
    
    void Euler()
    {
        memset(IsPri1, 0, sizeof(IsPri1));
        memset(IsPri2, 0, sizeof(IsPri2));
        pos = 0;
        for (int i = 2;i <= sqrt(r);i++)
        {
            if (IsPri1[i] == 0)
                Pri[++pos] = i;
            for (int j = 1;j <= pos && Pri[j]*i <= sqrt(r);j++)
            {
                IsPri1[Pri[j]*i] = 1;
                if (i%Pri[j] == 0)
                    break;
            }
        }
        for (int i = 1;i <= pos;i++)
        {
            for (LL j = max(2LL, (0LL+l+Pri[i]-1)/Pri[i])*Pri[i];j <= r;j += Pri[i])
                IsPri2[j-l+1] = 1;
        }
    }
    
    int main()
    {
        while (~scanf("%lld%lld", &l, &r))
        {
            Euler();
            int cnt = 0;
            int sl, sr, bl, br;
            int sv = 1e9, bv = 0;
            if (l == 1)
                IsPri2[l] = 1;
            for (int i = 1;i <= r-l+1;i++)
            {
                if (IsPri2[i] == 0)
                    Res[++cnt] = i+l-1;
            }
            if (cnt < 2)
                printf("There are no adjacent primes.
    ");
            else
            {
                for (int i = 1;i < cnt;i++)
                {
                    if (Res[i+1]-Res[i] < sv)
                    {
                        sv = Res[i+1]-Res[i];
                        sl = Res[i], sr = Res[i+1];
                    }
                    if (Res[i+1]-Res[i] > bv)
                    {
                        bv = Res[i+1]-Res[i];
                        bl = Res[i], br = Res[i+1];
                    }
                }
                printf("%d,%d are closest, %d,%d are most distant.
    ", sl, sr, bl, br);
            }
        }
    
        return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/YDDDD/p/11553482.html
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