Program to find number of sub-arrays with odd sum using Python

Suppose we have an array arr. We have to find the number of sub-arrays with odd sum. If the answer is too large then return result modulo 10^9+7.

So, if the input is like arr = [8,3,7], then the output will be 3 because all sub arrays are [[8],[3],[7],[8,3],[3,7],[8,3,7]] Now their sum values are [8,3,7,11,10,18] so there are three odd sum values [3,7,11].

To solve this, we will follow these steps −

• freq := a list with two elements 1 and 0

• ans := 0

• prefix := 0

• for each x in arr, do

  • prefix := prefix + x

  • ans := ans + freq[1 XOR prefix AND 1]

  • freq[prefix AND 1] := freq[prefix AND 1] + 1

• return ans mod (10^9+7)

Let us see the following implementation to get better understanding −

Example

 Live Demo

def solve(arr):
   freq = [1, 0]
   ans = prefix = 0
   for x in arr:
      prefix += x
      ans += freq[1 ^ prefix&1]
      freq[prefix &s; 1] += 1
   return ans % (10**9+7)
arr = [8,3,7]
print(solve(arr))

Input

[8,3,7]

Output

3

Arnab Chakraborty

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Updated on: 29-May-2021

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