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。
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