Find the Duplicate Number (Leetcode: 287)

# Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate
# number must exist. Assume that there is only one duplicate number, find the duplicate one.

# You must not modify the array (assume the array is read only).
# You must use only constant, O(1) extra space.
# Your runtime complexity should be less than O(n2).
# There is only one duplicate number in the array, but it could be repeated more than once.

class Solution:
    def findDuplicate(self, nums: List[int]) -> int:
        sp = nums[nums[0]]
        fp = nums[nums[nums[0]]]

        while sp != fp:
            sp = nums[sp]
            fp = nums[nums[fp]]

        fp = nums[0]

        while sp != fp:
            sp = nums[sp]
            fp = nums[fp]

        return fp