[Project Euler] Problem 56

Problem Description

A googol (10¹⁰⁰) is a massive number: one followed by one-hundred zeros; 100¹⁰⁰ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, a^b, where a, b < 100, what is the maximum digital sum?

 

Python

Of course python, here is the code:

def Power(a, b) :
    result = 1
    for i in xrange(b):
        result = result * a    
    return result

def GetSum(num) :
    strNum = str(num)
    result = 0;
    for index in xrange(len(strNum)) :
        result = result + int(strNum[index])
    return result

def Problem_56() :
    maxNum = 0
    maxA =0;
    maxB =0;
    for a in xrange(1, 100):
        for b in xrange(1, 100) :
            temp = GetSum(Power(a, b))
            # print "a=%d, b=%d temp=%d" % (a, b, temp)
            if(temp > maxNum) :
                maxNum = temp
                maxA = a
                maxB = b
    print "%d^%d = %d" % (maxA, maxB, maxNum)

Problem_56()

Thi problem is easy, brute force is needed.