How to optimize dynamic programming?
- by Chan
Problem A number is called lucky if the sum of its digits, as well as the sum of the squares of its digits is a prime number. How many
numbers between A and B are lucky?
Input: The first line contains the number of test cases T. Each of the next T lines contains two integers, A and B.
Output: Output T lines, one for each case containing the required answer for the corresponding case.
Constraints:
1 <= T <= 10000
1 <= A <= B <= 10^18
Sample Input:
2
1 20
120 130
Sample Output:
4
1
Explanation: For the first case, the lucky numbers are 11, 12, 14, 16. For the second case, the only lucky number is 120.
The problem is quite simple if we use brute force, however the running time is so critical that my program failed most test cases. My current idea is to use dynamic programming by storing the previous sum in a temporary array, so for example:
sum_digits(10) = 1 -> sum_digits(11) = sum_digits(10) + 1
The same idea is applied for sum square but with counter equals to odd numbers. Unfortunately, it still failed 9 of 10 test cases which makes me think there must be a better way to solve it. Any idea would be greatly appreciated.
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>
#include <cmath>
#include <cassert>
#include <bitset>
using namespace std;
bool prime_table[1540] = {
0, 0, 1, 1, 0, 1, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0
};
unsigned num_digits(long long i) {
return i > 0 ? (long) log10 ((double) i) + 1 : 1;
}
void get_sum_and_sum_square_digits(long long n, int& sum, int& sum_square) {
sum = 0;
sum_square = 0;
int digit;
while (n) {
digit = n % 10;
sum += digit;
sum_square += digit * digit;
n /= 10;
}
}
void init_digits(long long n, long long previous_sum[], const int size = 18) {
int current_no_digits = num_digits(n);
int digit;
for (int i = 0; i < current_no_digits; ++i) {
digit = n % 10;
previous_sum[i] = digit;
n /= 10;
}
for (int i = current_no_digits; i <= size; ++i) {
previous_sum[i] = 0;
}
}
void display_previous(long long previous[]) {
for (int i = 0; i < 18; ++i) {
cout << previous[i] << ",";
}
}
int count_lucky_number(long long A, long long B) {
long long n = A;
long long end = B;
int sum = 0;
int sum_square = 0;
int lucky_counter = 0;
get_sum_and_sum_square_digits(n, sum, sum_square);
long long sum_counter = sum;
long long sum_square_counter = sum_square;
if (prime_table[sum_counter] && prime_table[sum_square_counter]) {
lucky_counter++;
}
long long previous_sum[19] = {1};
init_digits(n, previous_sum);
while (n < end) {
n++;
if (n % 100000000000000000 == 0) {
previous_sum[17]++;
sum_counter = previous_sum[17] + previous_sum[18];
sum_square_counter = previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18];
previous_sum[16] = 0;
previous_sum[15] = 0;
previous_sum[14] = 0;
previous_sum[13] = 0;
previous_sum[12] = 0;
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10000000000000000 == 0) {
previous_sum[16]++;
sum_counter = previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[15] = 0;
previous_sum[14] = 0;
previous_sum[13] = 0;
previous_sum[12] = 0;
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 1000000000000000 == 0) {
previous_sum[15]++;
sum_counter = previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[14] = 0;
previous_sum[13] = 0;
previous_sum[12] = 0;
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 100000000000000 == 0) {
previous_sum[14]++;
sum_counter = previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[13] = 0;
previous_sum[12] = 0;
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10000000000000 == 0) {
previous_sum[13]++;
sum_counter = previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[12] = 0;
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 1000000000000 == 0) {
previous_sum[12]++;
sum_counter = previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[11] = 0;
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 100000000000 == 0) {
previous_sum[11]++;
sum_counter =
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[10] = 0;
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10000000000 == 0) {
previous_sum[10]++;
sum_counter =
previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[9] = 0;
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 1000000000 == 0) {
previous_sum[9]++;
sum_counter =
previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[8] = 0;
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 100000000 == 0) {
previous_sum[8]++;
sum_counter =
previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[7] = 0;
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10000000 == 0) {
previous_sum[7]++;
sum_counter =
previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[6] = 0;
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 1000000 == 0) {
previous_sum[6]++;
sum_counter =
previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[5] = 0;
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 100000 == 0) {
previous_sum[5]++;
sum_counter = previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[5] * previous_sum[5] +
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[4] = 0;
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10000 == 0) {
previous_sum[4]++;
sum_counter =
previous_sum[4] + previous_sum[5] +
previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[4] * previous_sum[4] +
previous_sum[5] * previous_sum[5] +
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[3] = 0;
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 1000 == 0) {
previous_sum[3]++;
sum_counter =
previous_sum[3] + previous_sum[4] + previous_sum[5] +
previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[3] * previous_sum[3] +
previous_sum[4] * previous_sum[4] +
previous_sum[5] * previous_sum[5] +
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[2] = 0;
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 100 == 0) {
previous_sum[2]++;
sum_counter =
previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] +
previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[2] * previous_sum[2] +
previous_sum[3] * previous_sum[3] +
previous_sum[4] * previous_sum[4] +
previous_sum[5] * previous_sum[5] +
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[1] = 0;
previous_sum[0] = 0;
}
else if (n % 10 == 0) {
previous_sum[1]++;
sum_counter =
previous_sum[1] + previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] +
previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] +
previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] +
previous_sum[16] + previous_sum[17] + previous_sum[18];
sum_square_counter =
previous_sum[1] * previous_sum[1] +
previous_sum[2] * previous_sum[2] +
previous_sum[3] * previous_sum[3] +
previous_sum[4] * previous_sum[4] +
previous_sum[5] * previous_sum[5] +
previous_sum[6] * previous_sum[6] +
previous_sum[7] * previous_sum[7] +
previous_sum[8] * previous_sum[8] +
previous_sum[9] * previous_sum[9] +
previous_sum[10] * previous_sum[10] +
previous_sum[11] * previous_sum[11] +
previous_sum[12] * previous_sum[12] +
previous_sum[13] * previous_sum[13] +
previous_sum[14] * previous_sum[14] +
previous_sum[15] * previous_sum[15] +
previous_sum[16] * previous_sum[16] +
previous_sum[17] * previous_sum[17] +
previous_sum[18] * previous_sum[18];
previous_sum[0] = 0;
}
else {
sum_counter++;
sum_square_counter += ((n - 1) % 10) * 2 + 1;
}
// get_sum_and_sum_square_digits(n, sum, sum_square);
// assert(sum == sum_counter && sum_square == sum_square_counter);
if (prime_table[sum_counter] && prime_table[sum_square_counter]) {
lucky_counter++;
}
}
return lucky_counter;
}
void inout_lucky_numbers() {
int n;
cin >> n;
long long a;
long long b;
while (n--) {
cin >> a >> b;
cout << count_lucky_number(a, b) << endl;
}
}
int main() {
inout_lucky_numbers();
return 0;
}
