loop through the list to get Maximum sum for a given range in python

Question

I am a novice in python. I have a code where I loop through a list to capture maximum sum of numbers for given range k. It is working fine but I want it to make it shorter/optimal. 'k' may vary

numb = [100,33,22,200,333,1000,22]
m=0
k=2
sum1=0
temp=[]
for j in range(len(numb)-(k-1)):
   for i in range(m,k):
     temp.append(numb[i])
   if sum1 < sum(temp):
     sum1 = sum(temp)
   temp=[]
   m+=1
   k+=1
print(sum1)

Ans: 1533 when k = 3 Ans: 1333 when k = 2

Answer 1

You can start by adding up the first k numbers. That is your starting sum and your current max. Then run a sliding window along the list, adding the next number and removing the one that goes out of the window.

def sum_k(x, k):
    m = s = sum(x[:k])
    for i, a in enumerate(x[k:]):
        b = x[i]  # number to remove
        s += a - b
        m = max(m, s)
    return m


numb = [100, 33, 22, 200, 333, 1000, 22]
print(sum_k(numb, 2), sum_k(numb, 3))

This runs in linear time, which is optimal since you need to at least look at every element in your input.

The index, i , in the loop runs from zero to nk-1 , so although we enumerate over x[k:] the indices we pick are from x[0:] , so when we pick b we are picking the number that goes out of the window. Meanwhile, a is the new number that comes in.

Answer 2

This is the simplified code you want which takes O(n) of time complexity . This approach is based on Sliding Window Algorithm .

maxSum is the function which takes 2 arguments (array of numbers and k) and returns maximum for any value of k.

def maxSum(arr, k):
    # Edge case
    if len(arr) <= k:
        return sum(arr)

    sums = sum(arr[:k]) # sum the first 3 val in arr.
    start = 0 # tell us the first element index whose value is in sums variable
    maximum = sums
    for val in arr[k:]:
        sums = (sums - arr[start]) + val
        # here we first subtracted the start value and then added current value. 
        # Eg. From [1,2,3,4] sums have 1+2+3, but now sums have ( 1+2+3(previous) - 1(start) ) + 4(current)
        # Now check for maximum.
        if sums > maximum:
            maximum = sums
        # now increase start by 1 to make pointer to value '2' and so on.
        start += 1
    
    # return maximum
    return maximum

arr = [100,33,22,200,333,1000,22]
k = 2
print("For k=2: ", maxSum(arr, k))
k = 3
print("For k=3: ", maxSum(arr, k))

Output:

For k=2:  1333
For k=2:  1533