Python sum of N consecutive digits of a large numb

问题:

I need to get the largest sum of n consecutive digits in a range of a large number.

For example, the range could be 5^150000, within this range I want to find out the largest sum of 50,000 consecutive digits.

The approach I have taken of using two loops seems to never terminate. I will appreciate any input.

The code:

count = 0
tempsum = 0
summ = 0                 # variables init
oldlist = ''
newlist = ''
num = str(3**2209) # for example

for digit in num: # go over all the digits in the number
    while count < 12 and len(num) >= 12 : # check in 12-digits blocks while possible
        oldlist += num[count] # update old list with new digit
        tempsum += int(num[count]) # add current digit to sum
        count += 1

    if tempsum > summ: # check if new sum is larger than old one
        summ = tempsum # update sum
        newlist = oldlist # update the sequence list
    oldlist = ''
    count = 0
    tempsum = 0
    num = num[1:] # slice the 'first' digit of the number

print(newlist, summ) # print sequence and desired sum

回答1:

You don't need two loops.

First, let's put all the digits in a list:

>>> a = list(map(int, str(5**150000)))

Then calculate the sum of the first 50000 digits:

>>> maximum = current = sum(a[:50000])
>>> current
225318

Now, let's loop through the list, removing the lowest digit from the sum and adding the next one 50000 digits ahead during each iteration:

>>> for i in range(0, len(a)-50000):
...     current = current - a[i] + a[i+50000]

Check if that new sum is larger than the previous one, and if so, make it the new "interim maximum":

...     if current > maximum: maximum = current
...

Once the loop exits, maximum contains the maximum value:

>>> maximum
225621

Let's put it all into a function, so no copying mistakes occur:

def maxdigitsum(number, digits):
    l = list(map(int, str(number)))
    maximum = current = sum(l[:digits])
    for i in range(0, len(l)-digits):
        current = current - l[i] + l[i+digits]
        if current > maximum: maximum = current
    return maximum

回答2:

#!/usr/bin/python
def maxSumOfNConsecutiveDigits(number,numberConsecutiveDigits):
    digits = [int(i) for i in str(number)]
    consecutiveSum = sum(digits[:numberConsecutiveDigits])
    largestSum = consecutiveSum
    for i in xrange(numberConsecutiveDigits,len(digits)):
        consecutiveSum += (digits[i]- digits[i - numberConsecutiveDigits])
        largestSum = max(largestSum, consecutiveSum)
    return largestSum
print maxSumOfNConsecutiveDigits(5**150000,50000)