Euler – Coder.si

Bouncy numbers

Problem 112

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.

Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.

We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.

Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.

Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.

Find the least number for which the proportion of bouncy numbers is exactly 99%.

def is_bouncy_string(n):
    inc = False
    dec = False
    s = str(n)
    for i in range(len(s) - 1):
        if s[i + 1] > s[i]:
            inc = True
        elif s[i + 1] < s[i]:
            dec = True
        if inc and dec:
            return True
    return False

def is_bouncy(n):
    inc = False
    dec = False

    last = n % 10
    n /= 10

    while n > 0:
        tmp = n % 10
        n /= 10
        if tmp < last:
            inc = True
        elif tmp > last:
            dec = True
        
        last = tmp
        if inc and dec:
            return True
    
    return False

def run():
    target = 100

    i = 1
    non_bouncy = 1
    while non_bouncy * target != i:
        i += 1
        if not is_bouncy(i):
            non_bouncy += 1

    return i