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day 60
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day 60
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#include <iostream>
#include <vector>
// store single digits with lowest digits first
// e.g. 1024 is stored as { 4,2,0,1 }
// only non-negative numbers supported
struct BigNum : public std::vector<unsigned int>
{
// string conversion works only properly when MaxDigit is a power of 10
static const unsigned int MaxDigit = 1000000000;
// store a non-negative number
BigNum(unsigned long long x = 0)
{
do
{
push_back(x % MaxDigit);
x /= MaxDigit;
} while (x > 0);
}
// add two big numbers
BigNum operator+(const BigNum& other) const
{
auto result = *this;
// add in-place, make sure it's big enough
if (result.size() < other.size())
result.resize(other.size(), 0);
unsigned int carry = 0;
for (size_t i = 0; i < result.size(); i++)
{
carry += result[i];
if (i < other.size())
carry += other[i];
else
if (carry == 0)
return result;
if (carry < MaxDigit)
{
// no overflow
result[i] = carry;
carry = 0;
}
else
{
// yes, we have an overflow
result[i] = carry - MaxDigit;
carry = 1;
}
}
if (carry > 0)
result.push_back(carry);
return result;
}
// multiply a big number by an integer
BigNum operator*(unsigned int factor) const
{
unsigned long long carry = 0;
auto result = *this;
for (auto& i : result)
{
carry += i * (unsigned long long)factor;
i = carry % MaxDigit;
carry /= MaxDigit;
}
// store remaining carry in new digits
while (carry > 0)
{
result.push_back(carry % MaxDigit);
carry /= MaxDigit;
}
return result;
}
};
int main()
{
unsigned int lastIndex;
std::cin >> lastIndex;
// to save memory we dont keep all numerators, only the latest three
BigNum numerators[3] = { 0, // dummy, will be overwritten immediately
1, // always 1
2 }; // the first number of the continuous fraction ("before the semicolon")
for (unsigned int index = 2; index <= lastIndex; index++)
{
// e = [2; 1,2,1, 1,4,1, ... 1,2k,1, ...]
unsigned int fractionNumber = 1;
if (index % 3 == 0)
fractionNumber = (index / 3) * 2;
// keep only the latest two numerators
numerators[0] = std::move(numerators[1]);
numerators[1] = std::move(numerators[2]);
// and generate the next one
if (fractionNumber == 1)
numerators[2] = numerators[0] + numerators[1];
else
numerators[2] = numerators[0] + numerators[1] * fractionNumber;
}
// add all digits of the last numerator
unsigned int sum = 0;
for (auto x : numerators[2])
// when MaxDigit != 10 then we have to split into single digits
while (x > 0)
{
sum += x % 10;
x /= 10;
}
std::cout << sum << std::endl;
return 0;
}