## Pages

### Narcissistic numbers

You could find a thorough description of narcissistic number, also known as Armstrong number, perfect digital invariant, plus perfect number, on Wolfram Mathworld. In a few words, a narcissistic number is an n-digit numbers that equals the sum of all its digits at the nth power.

We want to write a function that checks if a given number respects this definition.

It is easy to see as any positive one-digit number is narcissistic, and the Wolfram page I linked above provides a list of other narcissistic numbers. I used them to write these test cases (in C++ for GoogleTest):
```bool isNarcissistic(const std::string& input);

TEST(Narcissus, Simple)
{
ASSERT_TRUE(isNarcissistic("2"));
ASSERT_FALSE(isNarcissistic("42"));
}

TEST(Narcissus, Three)
{
ASSERT_TRUE(isNarcissistic("153"));
ASSERT_TRUE(isNarcissistic("370"));
ASSERT_TRUE(isNarcissistic("371"));
ASSERT_TRUE(isNarcissistic("407"));
ASSERT_FALSE(isNarcissistic("497"));
}

TEST(Narcissus, Eight)
{
ASSERT_TRUE(isNarcissistic("24678050"));
ASSERT_TRUE(isNarcissistic("24678051"));
ASSERT_TRUE(isNarcissistic("88593477"));
ASSERT_FALSE(isNarcissistic("88583475"));
}
```

Here is a possible implementation for such function:
```bool isNarcissistic(const std::string& input)
{
assert(!input.empty()); // 1
if(input.size() == 1) // 2
return input[0] != '0';

int powered = 0; // 3
for(unsigned i = 0; i < input.size(); ++i)
powered += std::pow((input[i] - '0'), input.size());

return powered == std::atoi(input.c_str()); // 4
}
```
1. This should never happen. It should be user code responsibility ensure that the passed input parameter is not empty. Production code should also ensure that the input strings contains only decimal digits.
2. All one-digit numbers are accepted, with the noteworthy exception of zero.
3. Each digit in the number are elevated to the expected power (third, if there are three digits in the number) and the result is summed up.
4. Compare the original value with the calculated one, and return true if they are the same.