# euler 37 truncatable primes

Mar 13, 2015

I realize using C++ is a bit like cheating since the initial motive of doing ProjectEuler was to explore a new language. But I reserve the right to “revise” that motive :P. Besides, I find it hard to overrule the part of myself that just wants to know the answer now, quickly.

``````static const int kMaxNumbers = 1000000;

void filterPrimes(vector<bool>* numbers) {
for (int candidate = 2; candidate < kMaxNumbers; ) {
int multiple = candidate * 2;
while (multiple < kMaxNumbers) {
numbers->at(multiple) = false;
multiple += candidate;
}
++candidate;
while (candidate < kMaxNumbers && !numbers->at(candidate)) {
++candidate;
}
if (candidate == kMaxNumbers) {
return;
}
}
}

int getNumber(const vector<int>& digits, int start, int end) {
int num = 0;
for (int i = end; i >= start; --i) {
num = num * 10 + digits[i];
}
return num;
}

bool isTruncatablePrime(int num, const vector<bool>& primes) {
if (num == 2 || num == 3 || num == 5 || num == 7) {
return false;
}
assert(primes.size() == kMaxNumbers);
vector<int> digits;
for (int t = num; t > 0; t /= 10) {
digits.push_back(t % 10);
}
for (int i = 0; i < digits.size(); ++i) {
int n1 = getNumber(digits, 0, i);
int n2 = getNumber(digits, i, digits.size() - 1);
if (!primes[n1] || !primes[n2]) {
return false;
}
}
return true;
}

int main() {
vector<bool> prime_candidates(kMaxNumbers, true);
prime_candidates[0] = false;
prime_candidates[1] = false;
filterPrimes(&prime_candidates);
int sum_truncatables = 0;
for (int i = 13; i < kMaxNumbers; ++i) {
if (prime_candidates[i]) {
if (isTruncatablePrime(i, prime_candidates)) {
std::cout << "Debug: found " << i << std::endl;
sum_truncatables += i;
}
}
}
std::cout << "The sum is: " << sum_truncatables << std::endl;
}
``````

which runs as

``````Debug: found 23
Debug: found 37
Debug: found 53
Debug: found 73
Debug: found 313
Debug: found 317
Debug: found 373
Debug: found 797
Debug: found 3137
Debug: found 3797
Debug: found 739397
The sum is: <redacted>
``````