Syntax error Program to find smallest index for which array element is also same as index in Python

Program to find smallest index for which array element is also same as index in Python

Suppose we have a list of elements called nums where all items are unique, and they are sorted in ascending order, we have to find the minimum i such that nums[i] = i. If we cannot find any solution, then return -1. We have to solve this problem in O(log(n)) time.

So, if the input is like nums = [-4, -1, 2, 3, 8], then the output will be 2, because both nums[2] = 2 and nums[3] = 3 but 2 is smaller.

To solve this, we will follow these steps −

  • ret := -1, lhs := 0, rhs := size of nums - 1

  • while lhs <= rhs, do

    • mid := floor of (lhs + rhs) / 2

    • if nums[mid] is same as mid, then

      • ret := mid

    • if nums[mid] >= mid, then

      • rhs := mid - 1

    • otherwise,

      • lhs := mid + 1

  • return ret

Example

Let us see the following implementation to get better understanding

def solve(nums):
   ret = -1
   lhs = 0
   rhs = len(nums) - 1
   while lhs <= rhs:
      mid = (lhs + rhs) // 2
      if nums[mid] == mid:
         ret = mid
      if nums[mid] >= mid:
         rhs = mid - 1
      else:
         lhs = mid + 1
   return ret

nums = [-4, -1, 2, 3, 8]
print(solve(nums))

Input

[-4, -1, 2, 3, 8]

Output

2
Updated on: 2021-10-11T07:20:25+05:30

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