庞果英雄会 幸运数

题目详情

如果一个数各个数位上的数字之和是质数，并且各个数位上的数字的平方和也是质数，则称它为幸运数。

给定x，y，求x，y之间（ 包含x，y，即闭区间[x,y]）有多少个幸运数。

例如1到20之间有4个幸运数，它们是11,12,14,16，像因为1+1 = 2是质数，1^2 + 1^2 = 2也是质数等等。

给定函数原型，其中1<=x<=y<=1000000000，请完成函数，实现上述功能。

思路：打表

将没次一百万为分解单位， 那么复杂度就变为 max(十亿 / 1000000, 1000000) 的复杂度； 当然可以以十万位分界点， 不过这样打的表就太大了

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>using namespace std;const int PRIME_SIZE = 10000;bool is_prime[PRIME_SIZE];void is_primeime(){    memset(is_prime, true, sizeof(is_prime));    is_prime[1] = false;    is_prime[0] = false;    for(int i = 2; i <= PRIME_SIZE; i++)    {        if(is_prime[i])        {            for(int j = i + i; j <= PRIME_SIZE; j += i)            {                is_prime[j] = false;            }        }    }}int fen(int x, int *f){    int i = 0;    while(x)    {        f[i] = x % 10;        x /= 10;        i++;    }    return i;}int every[] = {91271, 94445, 94442, 90048, 93242, 90507, 85722, 88761, 86192, 82575, 94446, 92681, 90558, 90121, 90298, 89899, 91484, 87734, 87048, 87066, 94443, 90558, 92785, 91861, 89425, 89976, 90882, 91101, 86654, 88236, 90048, 90121, 91861, 87234, 88861, 89530, 85140, 89865, 89860, 84270, 93243, 90298, 89424, 88861, 90778, 89454, 88772, 88304, 87649, 89002, 90507, 89899, 89976, 89530, 89454, 85827, 90143, 87541, 86484, 86946, 85723, 91484, 90882, 85140, 88773, 90143, 86880, 86595, 84358, 80880, 88761, 87734, 91101, 89864, 88304, 87540, 86595, 85632, 85350, 84392, 86192, 87048, 86655, 89860, 87649, 86484, 84358, 85350, 78816, 78805, 82575, 87066, 88236, 84271, 89002, 86946, 80880, 84392, 78805, 76212, 94446, 92681, 90558, 90121, 90298, 89899, 91484, 87734, 87048, 87067, 92681, 89043, 93235, 89625, 87234, 93924, 87946, 86475, 93757, 85378, 90558, 93234, 94860, 87624, 93804, 89514, 89454, 93234, 92235, 89298, 90121, 89625, 87625, 89505, 85748, 86523, 87065, 86100, 87540, 86678, 90298, 87234, 93804, 85748, 88044, 91603, 87697, 83898, 93132, 85632, 89898, 93924, 89514, 86523, 91602, 91722, 88158, 92319, 90180, 84982, 91484, 87946, 89454, 87065, 87697, 88159, 89472, 85084, 86874, 85552, 87734, 86475, 93235, 86100, 83898, 92319, 85084, 83952, 88399, 80883, 87048, 93756, 92235, 87540, 93132, 90180, 86874, 88398, 85956, 81312, 87067, 85377, 89298, 86677, 85632, 84981, 85553, 80883, 81313, 77721, 94443, 90558, 92785, 91861, 89425, 89976, 90882, 91101, 86654, 88237, 90558, 93234, 94860, 87624, 93804, 89514, 89454, 93234, 92235, 89298, 92784, 94860, 89581, 88842, 94734, 88044, 87636, 92517, 86881, 86485, 91861, 87625, 88842, 88794, 87117, 85900, 89348, 88158, 86651, 86838, 89424, 93804, 94734, 87117, 95460, 92133, 91032, 91587, 91734, 86875, 89976, 89514, 88044, 85900, 92133, 85326, 88109, 92532, 84600, 83640, 90882, 89454, 87636, 89348, 91032, 88109, 89296, 87735, 83102, 83854, 91101, 93234, 92517, 88158, 91587, 92532, 87735, 90378, 88569, 81582, 86654, 92235, 86880, 86651, 91734, 84600, 83102, 88569, 78547, 78459, 88236, 89299, 86484, 86838, 86874, 83640, 83854, 81583, 78459, 77352, 90048, 90121, 91861, 87234, 88861, 89530, 85140, 89865, 89860, 84270, 90121, 89625, 87625, 89505, 85748, 86523, 87065, 86100, 87540, 86678, 91861, 87625, 88842, 88794, 87117, 85900, 89348, 88158, 86651, 86838, 87235, 89505, 88794, 84969, 87841, 91404, 85327, 89056, 89340, 83952, 88861, 85748, 87117, 87841, 89200, 88039, 89995, 86578, 87735, 85370, 89530, 86523, 85901, 91404, 88039, 86682, 85536, 88185, 84522, 83150, 85140, 87064, 89348, 85327, 89995, 85536, 84786, 86431, 82829, 78918, 89865, 86100, 88159, 89056, 86578, 88185, 86431, 81798, 83509, 81993, 89860, 87540, 86651, 89340, 87735, 84523, 82829, 83509, 78972, 78142, 84270, 86677, 86838, 83952, 85370, 83150, 78919, 81992, 78142, 72282, 93243, 90298, 89424, 88861, 90778, 89454, 88772, 88304, 87649, 89003, 90298, 87234, 93804, 85748, 88044, 91603, 87697, 83898, 93132, 85632, 89424, 93804, 94734, 87117, 95460, 92133, 91032, 91587, 91734, 86874, 88861, 85748, 87117, 87841, 89200, 88039, 89995, 86578, 87735, 85370, 90778, 88044, 95461, 89200, 87762, 94626, 88492, 84786, 90499, 82825, 89454, 91602, 92133, 88038, 94626, 91962, 87207, 88014, 90303, 83508, 88773, 87697, 91033, 89995, 88492, 87207, 88967, 81992, 82926, 82915, 88304, 83898, 91587, 86578, 84786, 88015, 81992, 80010, 82989, 76742, 87648, 93132, 91734, 87735, 90498, 90303, 82926, 82989, 84168, 77071, 89002, 85632, 86874, 85371, 82825, 83508, 82915, 76742, 77070, 78308, 90507, 89899, 89976, 89530, 89454, 85827, 90143, 87541, 86484, 86946, 89898, 93924, 89514, 86523, 91602, 91722, 88158, 92319, 90180, 84982, 89976, 89514, 88044, 85900, 92133, 85326, 88109, 92532, 84600, 83640, 89530, 86523, 85901, 91404, 88039, 86682, 85536, 88185, 84522, 83150, 89454, 91602, 92133, 88038, 94626, 91962, 87207, 88014, 90303, 83508, 85826, 91722, 85327, 86682, 91962, 81822, 85208, 89172, 80011, 79092, 90143, 88158, 88109, 85536, 87207, 85209, 85841, 82506, 77729, 78104, 87540, 92319, 92532, 88185, 88014, 89172, 82506, 84924, 84720, 76486, 86484, 90180, 84600, 84522, 90303, 80010, 77729, 84720, 74601, 74426, 86946, 84981, 83640, 83150, 83509, 79091, 78104, 76485, 74426, 72687, 85723, 91484, 90882, 85140, 88773, 90143, 86880, 86595, 84358, 80881, 91484, 87946, 89454, 87065, 87697, 88159, 89472, 85084, 86874, 85552, 90882, 89454, 87636, 89348, 91032, 88109, 89296, 87735, 83102, 83854, 85140, 87064, 89348, 85327, 89995, 85536, 84786, 86431, 82829, 78918, 88773, 87697, 91033, 89995, 88492, 87207, 88967, 81992, 82926, 82916, 90143, 88158, 88109, 85536, 87207, 85209, 85841, 82506, 77729, 78104, 86881, 89472, 89296, 84786, 88967, 85841, 78462, 82509, 78136, 74601, 86595, 85084, 87735, 86431, 81992, 82506, 82509, 79404, 75300, 78074, 84358, 86874, 83103, 82829, 82926, 77729, 78136, 75300, 72465, 71200, 80880, 85552, 83854, 78918, 82915, 78104, 74601, 78075, 71200, 70728, 88761, 87734, 91101, 89864, 88304, 87540, 86595, 85632, 85350, 84392, 87734, 86475, 93235, 86100, 83898, 92319, 85084, 83952, 88399, 80883, 91101, 93234, 92517, 88158, 91587, 92532, 87735, 90378, 88569, 81582, 89865, 86100, 88159, 89056, 86578, 88185, 86431, 81798, 83509, 81992, 88304, 83898, 91587, 86578, 84786, 88015, 81992, 80010, 82989, 76742, 87540, 92319, 92532, 88185, 88014, 89172, 82506, 84924, 84720, 76485, 86595, 85084, 87735, 86431, 81992, 82506, 82509, 79404, 75300, 78074, 85632, 83952, 90379, 81798, 80010, 84924, 79404, 73338, 79651, 73927, 85350, 88398, 88569, 83508, 82989, 84720, 75300, 79650, 78933, 72570, 84393, 80883, 81583, 81992, 76742, 76485, 78075, 73927, 72570, 73894, 86192, 87048, 86655, 89860, 87649, 86484, 84358, 85350, 78816, 78805, 87048, 93756, 92235, 87540, 93132, 90180, 86874, 88398, 85956, 81312, 86654, 92235, 86880, 86651, 91734, 84600, 83102, 88569, 78547, 78460, 89860, 87540, 86651, 89340, 87735, 84523, 82829, 83509, 78972, 78142, 87648, 93132, 91734, 87735, 90498, 90303, 82926, 82989, 84168, 77071, 86484, 90180, 84600, 84522, 90303, 80010, 77729, 84720, 74601, 74426, 84358, 86874, 83103, 82829, 82926, 77729, 78136, 75300, 72465, 71200, 85350, 88398, 88569, 83508, 82989, 84720, 75300, 79650, 78933, 72570, 78816, 85956, 78547, 78972, 84168, 74601, 72464, 78933, 69162, 69103, 78805, 81313, 78459, 78142, 77070, 74427, 71200, 72570, 69103, 67634, 82575, 87066, 88236, 84271, 89002, 86946, 80880, 84392, 78805, 76212, 87067, 85377, 89298, 86677, 85632, 84981, 85553, 80883, 81313, 77721, 88236, 89299, 86484, 86838, 86874, 83640, 83854, 81583, 78459, 77352, 84270, 86677, 86838, 83952, 85370, 83150, 78919, 81992, 78142, 72283, 89002, 85632, 86874, 85371, 82825, 83508, 82915, 76742, 77070, 78308, 86946, 84981, 83640, 83150, 83509, 79091, 78104, 76485, 74426, 72687, 80880, 85552, 83854, 78918, 82915, 78104, 74601, 78075, 71200, 70728, 84393, 80883, 81583, 81992, 76742, 76485, 78075, 73927, 72570, 73894, 78805, 81313, 78459, 78142, 77070, 74427, 71200, 72570, 69103, 67634, 76213, 77721, 77352, 72282, 78308, 72687, 70728, 73894, 67634, 68448};int sum[1010];int solve(int x, int y){    int smallCnt = 0;    int *f = new int[20];    long long sig, dou;    int cnt ;    for(int i = x; i <= y; i++)    {        sig = dou = 0;        cnt = fen(i, f);        for(int j = cnt - 1; j >= 0; j--)        {            sig += *(f + j);            dou += (*(f + j)) * (*(f + j));        }        if(is_prime[sig] && is_prime[dou])            smallCnt++;    }    return smallCnt;}int res[10000];int s[10000], e[10000], cnt;void spile(int start, int end, int bud){    for(int i = start; i <= end; i += bud)    {        s[cnt] = i;        e[cnt] = i + bud - 1;        cnt++;    }}int getAns(int x, int y){    int bud = 1000000;    int bud_x = x / bud;    int bud_y = y / bud;    int R = 0;    if(x % bud == 0)    {        if(y % bud == 0)            R = sum[bud_y] - sum[bud_x] + solve(bud_x * bud, bud_x * bud);        else            R = sum[bud_y] + solve(bud_y * bud + 1, y) - sum[bud_x] + solve(bud_x * bud, bud_x * bud);    }    else    {        if(y % bud == 0)            R = sum[bud_y] - sum[bud_x] - solve(bud_x * bud + 1, x - 1);        else            R = sum[bud_y] + solve(bud_y * bud + 1, y) - sum[bud_x] - solve(bud_x * bud + 1, x - 1);    }    return R;}int lucky(int x,int y) {    //freopen("out.txt", "w", stdout);    cnt = 0;    is_primeime();    //spile(1, 1000000000, 1000000);    //long long ans = 0;    //int smallAns;    //for(int i = 0; i < cnt; i++)    //{    //    //is_primeint(s[i]);    //    //is_primeint(e[i]);    //    smallAns = solve(s[i], e[i]);    //    ans += smallAns;    //    //is_primeint(smallAns);    //    //cout << endl;    //    is_primeintf("%d, ", smallAns);    //}    //is_primeint(ans);    for(int i = 0; i <= 1010 && every[i]; i++)        sum[i + 1] = sum[i] + every[i];    int A =  getAns(x, y);    return A;}//start 提示：自动阅卷起始唯一标识，请勿删除或增加。int main(){   lucky(1, 20);return 0;    //main函数方便你自行测试，可不用完成} //end //提示：自动阅卷结束唯一标识，请勿删除或增加。

,