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