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 and nums = 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
lhs := mid + 1
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))
[-4, -1, 2, 3, 8]