# Find duplicate in an array of integers given that the integers are in random order and 
# not necessarily each integer i is 0 <= i <= N where N = length of array

def duplicate(arr):
    tortoise = arr[0]
    hare = arr[0]

    while True:
        tortoise = arr[tortoise]
        hare = arr[arr[hare]]
        if tortoise == hare:
            break

    ptr1 = nums[0]
    ptr2 = tortoise
    while ptr1 != ptr2:
        ptr1 = nums[ptr1]
        ptr2 = nums[ptr2]

    return ptr1