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Find the Duplicate Number in Python Using Floyd's Cycle Detection

Detects the duplicate integer in an array of n+1 numbers (values 1 to n) in O(n) time and O(1) space using Floyd's cycle detection algorithm applied to a linked-list model.

floyd-cycle duplicate-number two-pointers

Python

def find_duplicate(nums):
    slow = nums[0]
    fast = nums[0]
    
    # Phase 1: Find intersection point of the cycle
    while True:
        slow = nums[slow]
        fast = nums[nums[fast]]
        if slow == fast:
            break
    
    # Phase 2: Find the start of the cycle (the duplicate)
    slow = nums[0…

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