Find Removed Term from Arithmetic Sequence in Python

Suppose we have an array called nums holding n-1 arithmetic sequence terms. One element except the first or last element of nums was removed before. We have to find the removed number.

So, if the input is like nums = [5, 7, 11, 13], then the output will be 9 because, the items are following the formula 2i+5, so for i = 2 it will be 2*2 + 5 = 9 which is missing.

To solve this, we will follow these steps −

• if size of nums is same as 2, then

  • return floor of (sum of all elements present in nums)/2

• if nums[0] is same as nums[1], then/p>

  • return nums[0]

• lower := nums[0]

• upper := last element of nums

• interval := floor of (upper - lower) / size of nums

• pointer := floor of size of nums / 2

• left := 0

• right := size of nums - 1

• while left is not same as right, do

  • if nums[pointer] is not same as nums[0] + interval * pointer, then

    • if nums[pointer - 1] is same as nums[0] + interval *(pointer - 1) , then

      • return nums[0] + interval * pointer

    • otherwise,

      • right := pointer

      • pointer :=floor of(left + right) / 2

  • otherwise,

    • if right - left is same as 1, then

      • pointer := right

    • otherwise,

      • left := pointer

      • pointer := floor of(left + right) / 2

Example

Let us see the following implementation to get better understanding

def solve(nums):
   if len(nums) == 2:
      return sum(nums) // 2

   if nums[0] == nums[1]:
      return nums[0]

   lower = nums[0]
   upper = nums[-1]
   interval = (upper - lower) // len(nums)

   pointer = len(nums) // 2

   left = 0
   right = len(nums) - 1

   while left != right:
      if nums[pointer] != nums[0] + interval * pointer:
         if nums[pointer - 1] == nums[0] + interval * (pointer -1):
            return nums[0] + interval * pointer
         else:
            right = pointer
            pointer = (left + right) // 2
      else:
         if right - left == 1:
            pointer = right
         else:
            left = pointer
            pointer = (left + right) // 2

nums = [5, 7, 11, 13]
print(solve(nums))

Input

[5, 7, 11, 13]

Output

9