Find Sum of All Odd Length Subarrays in Python

Suppose we have an array of positive values called nums, we have to find the sum of all possible odd-length subarrays. As we know a subarray is a contiguous subsequence of the array. We have to find the sum of all odd-length subarrays of nums.

So, if the input is like nums = [3,8,2,5,7], then the output will be The odd-length subarrays are −

nums[0] = 3
nums[1] = 8
nums[2] = 2
nums[3] = 5
nums[4] = 7
nums[0..2], so sum = 13
nums[1..3], so sum = 15
nums[2..4], so sum = 14
nums[0..4] = 25
So total sum is 3+8+2+5+7+13+15+14+25 = 92

To solve this, we will follow these steps −

• total:= 0

• idx:= 0

• l:= a list of all odd placed indices

• while idx < size of l, do

  • k:= l[idx]

  • for i in range 0 to size of nums, do

    • if i+k < size of nums + 1, then

      • total := total + sum of all elements in nums from index i to i+k-1

  • idx := idx + 1

• return total

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

def solve(nums):
   total=0
   idx=0
   l=[i for i in range(len(nums)+1) if i%2!=0]

   while(idx<len(l)):
      k=l[idx]
      for i in range(len(nums)):
         if i+k < len(nums)+1:
            total+=sum(nums[i:i+k])
      idx+=1
   return total

nums = [3,8,2,5,7]
print(solve(nums))

Input

[3,8,2,5,7]

Output

92