What are the most efficient ways to sum the digits of a number?

Summating Digits of a Number: Exploring Efficient Approaches

When aiming to ascertain the total sum of digits in a numerical input, various methodologies can be employed. While initial instinct may lead to utilizing a string-based approach, converting the number to a string and then applying mathematical operations on each individual digit, this method can be sub-optimal.

A more efficient technique lies in manipulating the number as an integer. This can be achieved through a while loop that iterates through the digits of the number, repeatedly extracting the last digit (using the modulo operator) and adding it to a running total while excluding that digit (through integer division). This method, known as the modulo-and-divide approach, is exemplified in the following code snippet:

def sum_digits(n):
    s = 0
    while n:
        s += n % 10
        n //= 10
    return s

For further optimization, one can employ the divmod() function, which simultaneously performs the modulo and integer division operations:

def sum_digits2(n):
    s = 0
    while n:
        n, remainder = divmod(n, 10)
        s += remainder
    return s

Furthermore, a single assignment statement can be utilized to improve execution speed by combining the summation and division operations:

def sum_digits3(n):
   r = 0
   while n:
       r, n = r + n % 10, n // 10
   return r

Benchmarking these approaches reveals that the modulo-and-divide method outperforms the string manipulation techniques, while the single assignment version emerges as the swiftest option:

%timeit sum_digits(n)
1000000 loops, best of 3: 574 ns per loop

%timeit sum_digits2(n)
1000000 loops, best of 3: 716 ns per loop

%timeit sum_digits3(n)
1000000 loops, best of 3: 479 ns per loop

%timeit sum(map(int, str(n)))
100000 loops, best of 3: 1.42 us per loop

%timeit sum([int(digit) for digit in str(n)])
100000 loops, best of 3: 1.52 us per loop

%timeit sum(int(digit) for digit in str(n))
100000 loops, best of 3: 2.04 us per loop

Therefore, when seeking to efficiently sum the digits of a number, it is advisable to opt for the modulo-and-divide technique or even the single assignment variant for maximum performance.

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