Bouncy numbers : Problem 112 : Project Euler : Python Code

Bouncy numbers : Problem 112 : Project Euler

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%.

Python Code

def bouncyNumbers():
    def increasing(numb):
        iflag = True
        strNumb = str(numb)
        for i in range(len(strNumb)-1):
            if int(strNumb[i]) > int(strNumb[i+1]):
                iflag = False
                break
        return iflag
    def decreasing(numb):
        dflag = True
        strNumb = str(numb)
        for i in range(len(strNumb)-1):
            if int(strNumb[i]) < int(strNumb[i+1]):
                dflag = False
                break
        return dflag
    bouncyCount = 0
    percentagebCount = 0.0
    n = 99
    while int(percentagebCount) != 99:   
        n = n + 1
        if increasing(n) == False and decreasing(n) == False:
            bouncyCount = bouncyCount + 1
        percentagebCount = (bouncyCount*100.0)/n
        print percentagebCount,n
    print "least number for which the proportion of bouncy numbers is exactly 99% is :",n   
bouncyNumbers()