Great learning for me:
https://www.hackerrank.com/rest/contests/master/challenges/lucky-numbers/hackers/turuthok/download_solution

Basically it is memorized search application. And we follow a discrete strategy: split it into digits and go digit by digit.

Here is my C++ version of the code above, with comments for easier understanding.

#include <iostream>
#include <limits>
#include <vector>
using namespace std; typedef long long LL; const int D = ; // max digit count
const int MD = ; // max single digit
const LL MAX = std::numeric_limits<LL>::max(); vector<vector<vector<LL>>> dp(D, vector<vector<LL>>(D*MD + , vector<LL>(D*MD*MD + , -)));
vector<int> hi(D);
vector<bool> isPrime(D*MD*MD + , true); LL go(int inx, int sd, int ssd, bool limited)
{
if (inx == D) return isPrime[sd] && isPrime[ssd] ? : ; // Memorized Search
LL &ret = dp[inx][sd][ssd];
if (!limited && ret >= ) return ret; // We only cache unlimited count int upper = limited ? hi[inx] : ;
// DP: count of current digit = sum of all counts of all previous digits
LL r = ;
for (int i = ; i <= upper; i++)
{
r += go(inx + , sd + i, ssd + i * i, limited && i == upper);
}
if (!limited) ret = r; // We only cache unlimited count
return r;
} LL go(LL n)
{
if (n <= ) return ; // split digits
for (int i = D - ; i >= ; i--)
{
hi[i] = n % ;
n /= ;
} return go(, , , true);
} int main()
{
// sieving
isPrime[] = isPrime[] = false;
for (int i = ; i <= D*MD*MD; i++)
if (isPrime[i])
for (int j = i * ; j <= D*MD*MD; j += i) isPrime[j] = false; // go
int t; cin >> t;
while (t--)
{
LL a, b; cin >> a >> b;
cout << (go(b) - go(a - )) << endl;
} return ;
}

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