# This program finds the distribution of leading digits in a set
# of positive integers.  The program is useful for exploring the
# phenomenon known as Benford's Law.

# Reads integers from input file, computing a list of tallies
# for the occurrences of each leading digit (0 - 9).
def count_digits(file):
    tally = [0] * 10
    for next in file.read().split():
        next = int(next)
        tally[first_digit(next)] += 1
    return tally

# Reports percentages for each leading digit, excluding zeros.
def report_results(tally):
    if tally[0] > 0:
        print("excluding", tally[0], "zeros")
    
    # sum of all tallies, excluding 0
    total = sum(tally) - tally[0]
    
    # report percentage of each tally, excluding 0
    print("Digit\tCount\tPercent")
    for i in range(1, len(tally)):
        pct = tally[i] * 100 / total
        print(i, tally[i], round(pct, 2), sep="\t")
    print("Total", total, 100.0, sep="\t")

# Returns the first digit of the given integer.
def first_digit(n):
    result = abs(n)
    while result >= 10:
        result = result // 10
    return result

def main():
    print("Let's count those leading digits...")
    filename = input("input file name? ")
    print()
    with open(filename) as file:
        tally = count_digits(file)
        report_results(tally)

main()