Partition Array Into Three Parts With Equal Sum in Python

Suppose we have an array A of integers, our output will be true if and only if we can partition the array into three non-empty parts whose sum is equal.

Formally, we can partition the array if we can find the indexes i+1 < j with (A[0] + A[1] + ... + A[i] is same as A[i+1] + A[i+2] + ... + A[j-1] and A[j] + A[j-1] + ... + A[A.length - 1])

So if the input is [0,2,1,-6,6,-7,9,1,2,0,1], then the output will be true. Three arrays will be [0,2,1], [-6,6,-7,9,1] and [2,0,1]

To solve this, we will follow these steps −

• temp := sum of all elements, and required_sum := temp / 3
• set sum_left to store cumulative sum from left to right
• set sum_right to store cumulative sum from right to left
• index1 := 0 and index2 := length of the array – 1
• while index1 < index2:
  • while index1 < index2 and sum_left[index1] != required_sum
    • index1 := index1 + 1
  • while index2 > index1 and sum_right[index2] != required_sum
    • index2 := index2 – 1
  • if index1 < index2 and index1 != index2, then return true, otherwise false

Example

Let us see the following implementation to get better understanding −

 Live Demo

class Solution(object):
   def canThreePartsEqualSum(self, A):
      temp = sum(A)
      if (temp%3 != 0):
         return 0
      sum_left=[0 for i in range(len(A))]
      sum_left[0] = A[0]
      sum_right=[0 for i in range(len(A))]
      sum_right[-1] = A[-1]
      for i in range(1,len(A)):
         sum_left[i] = A[i]+sum_left[i-1]
      for i in range(len(A)-2,-1,-1):
         sum_right[i] = A[i]+sum_right[i+1]
      #print(sum_left,sum_right)
      required_sum = temp/3
      index1 = 0
      index2 = len(A)-1
      while index1 < index2:
      while index1 <index2 and sum_left[index1]!=required_sum:
         index1+=1
      while index2>index1 and sum_right[index2]!=required_sum:
         index2-=1
      return index1<index2 and index1 != index2
ob1 = Solution()
print(ob1.canThreePartsEqualSum([0,2,2,-6,6,-7,9,2,2,0,2]))

Input

[0,2,1,-6,6,-7,9,1,2,0,1]

Output

true