#42 Medium Time O(n) Space O(1) Animated

Find the Duplicate Number

Find a duplicate number in an array of n+1 integers.

LeetCode ↗

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1 Predict
2 Trace
3 Explain
4 Implement

Pattern Pointer rewiring with saved next state

Before changing a link, save the only pointer that would otherwise be lost.

Approach: Floyd's Algorithm

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Core Insight

Before changing a link, save the only pointer that would otherwise be lost.

Common Pitfall

Always store next before redirecting current.next.

Description

Find a duplicate number in an array of n+1 integers.

Constraints

Time Complexity: O(n)
Space Complexity: O(1)

Solution — Floyd's Algorithm

TimeO(n) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Initialize the pointers.
Save the next node.
Rewire the current node.
Advance both pointers until the list is consumed.

def findDuplicate(nums):
    slow, fast = 0, 0
    while True:
        slow = nums[slow]
        fast = nums[nums[fast]]
        if slow == fast:
            break
            
    slow2 = 0
    while True:
        slow = nums[slow]
        slow2 = nums[slow2]
        if slow == slow2:
            return slow

Linked List Cycle

LRU Cache

Find the Duplicate Number

Steps

Description

Constraints

Tags

Solution — Floyd's Algorithm