Explanation of Floyd Cycle Detection Algo (TheAlgorithms#122)

* update

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

Co-authored-by: David Leal <[email protected]>

* Update en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

* minor changes

Co-authored-by: Vitor Oliveira <[email protected]>
Co-authored-by: David Leal <[email protected]>

Author: 3 people

en/Search Algorithms/Floyd Cycle Detection Algorithm to Find Duplicate Number.md

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+# Floyd Cycle Detection Algorithm to find duplicate number in an array
+
+## Problem Statement
+
+Given an array of integers containing `n + 1` integers, where each integer is in the range `[1, n]` inclusive. If there is only one duplicate number in the input array, this algorithm returns the duplicate number without modifying the original array, otherwise, it returns -1.
+
+## Approach
+
+- Use the function `f(x) = arr[x]` to construct the sequence: 
+`arr[0]`, `arr[arr[0]]`, `arr[arr[arr[0]]]`, `arr[arr[arr[arr[0]]]]`, etc....
+- Each new element in the sequence is an element in `arr[]` at the index of the previous element.
+- Starting from `x = arr[0]`, it will produce a linked list with a cycle.
+- The cycle appears because `arr[]` contains duplicate elements(at least one). The duplicate value is an entrance to the cycle. 
+
+## Time Complexity
+
+O(n)
+
+## Space Complexity
+
+O(1) 
+
+## Example
+
+```
+arr = [3, 4, 8, 5, 9, 1, 2, 6, 7, 4]  
+
+return value = 4
+```
+
+## Code Implementation Links
+
+- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/floyd_cycle_detection_algo.cpp)
+- [C](https://github.com/TheAlgorithms/C/blob/master/searching/floyd_cycle_detection_algorithm.c)
+
+#### Video Explanation
+
+[YouTube video explaining the Floyd Cycle Detection algorithm](https://www.youtube.com/watch?v=B6smdk7pZ14)