Master the steps to use fast and slow pointers for cycle detection and mid-point identification.

Central CIP Path

Fast and Slow Pointers

# Statement

Given an array of positive numbers, `nums`, such that the values lie in the range $[1, n]$, inclusive, and that there are $n+1$ numbers in the array, find and return the duplicate number present in `nums`. There is only one repeated number in `nums`, but it may appear more than once in the array.

> **Note:** You cannot modify the given array `nums`. You have to solve the problem using only constant extra space.

**Constraints:**

* $1 \leq n \leq 10^3$
* `nums.length` $= n + 1$
* $1 \leq$ `nums[i]` $\leq n$
* All the integers in `nums` are unique except for one integer that will appear more than once.

# Solution


Let's solve the Find the Duplicate Number problem using the the Fast and Slow pattern.

Solution: Find the Duplicate Number

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Solution

Solution: Find the Duplicate Number

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Solution