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# Find a Fixed Point (Value equal to index) in a given array

• Difficulty Level : Easy
• Last Updated : 09 Apr, 2021

Given an array of n distinct integers sorted in ascending order, write a function that returns a Fixed Point in the array, if there is any Fixed Point present in array, else returns -1. Fixed Point in an array is an index i such that arr[i] is equal to i. Note that integers in array can be negative.
Examples:

```  Input: arr[] = {-10, -5, 0, 3, 7}
Output: 3  // arr == 3

Input: arr[] = {0, 2, 5, 8, 17}
Output: 0  // arr == 0

Input: arr[] = {-10, -5, 3, 4, 7, 9}
Output: -1  // No Fixed Point```

Method 1 (Linear Search)
Linearly search for an index i such that arr[i] == i. Return the first such index found. Thanks to pm for suggesting this solution.

## C++

 `// C++ program to check fixed point``// in an array using linear search``#include ``using` `namespace` `std;` `int` `linearSearch(``int` `arr[], ``int` `n)``{``    ``int` `i;``    ``for``(i = 0; i < n; i++)``    ``{``        ``if``(arr[i] == i)``            ``return` `i;``    ``}` `    ``/* If no fixed point present then return -1 */``    ``return` `-1;``}` `/* Driver code */``int` `main()``{``    ``int` `arr[] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);``    ``cout << ``"Fixed Point is "` `<< linearSearch(arr, n);``    ``return` `0;``}` `// This is code is contributed by rathbhupendra`

## C

 `// C program to check fixed point``// in an array using linear search``#include` `int` `linearSearch(``int` `arr[], ``int` `n)``{``    ``int` `i;``    ``for``(i = 0; i < n; i++)``    ``{``        ``if``(arr[i] == i)``            ``return` `i;``    ``}` `    ``/* If no fixed point present then return -1 */``    ``return` `-1;``}` `/* Driver program to check above functions */``int` `main()``{``    ``int` `arr[] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);``    ``printf``(``"Fixed Point is %d"``, linearSearch(arr, n));``    ``getchar``();``    ``return` `0;``}`

## Java

 `// Java program to check fixed point``// in an array using linear search`` ` `class` `Main``{``    ``static` `int` `linearSearch(``int` `arr[], ``int` `n)``    ``{``        ``int` `i;``        ``for``(i = ``0``; i < n; i++)``        ``{``            ``if``(arr[i] == i)``                ``return` `i;``        ``}``      ` `        ``/* If no fixed point present``           ``then return -1 */``        ``return` `-``1``;``    ``}``    ``//main function``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `arr[] = {-``10``, -``1``, ``0``, ``3``, ``10``, ``11``, ``30``, ``50``, ``100``};``        ``int` `n = arr.length;``        ``System.out.println(``"Fixed Point is "``                     ``+ linearSearch(arr, n));``    ``}``}`

## Python

 `# Python program to check fixed point``# in an array using linear search``def` `linearSearch(arr, n):``    ``for` `i ``in` `range``(n):``        ``if` `arr[i] ``is` `i:``            ``return` `i``    ``# If no fixed point present then return -1``    ``return` `-``1` `# Driver program to check above functions``arr ``=` `[``-``10``, ``-``1``, ``0``, ``3``, ``10``, ``11``, ``30``, ``50``, ``100``]``n ``=` `len``(arr)``print``(``"Fixed Point is "` `+` `str``(linearSearch(arr,n)))` `# This code is contributed by Pratik Chhajer`

## C#

 `// C# program to check fixed point``// in an array using linear search``using` `System;` `class` `GFG``{``    ``static` `int` `linearSearch(``int` `[]arr, ``int` `n)``    ``{``        ``int` `i;``        ``for``(i = 0; i < n; i++)``        ``{``            ``if``(arr[i] == i)``                ``return` `i;``        ``}``        ` `        ``/* If no fixed point present``        ``then return -1 */``        ``return` `-1;``    ``}``    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[]arr = {-10, -1, 0, 3, 10, 11, 30, 50, 100};``        ``int` `n = arr.Length;``        ``Console.Write(``"Fixed Point is "``+ linearSearch(arr, n));``    ``}``}` `// This code is contributed by Sam007`

## PHP

 ``

## Javascript

 ``

Output:

`Fixed Point is 3`

Time Complexity: O(n)
Method 2 (Binary Search)
First check whether middle element is Fixed Point or not. If it is, then return it; otherwise check whether index of middle element is greater than value at the index. If index is greater, then Fixed Point(s) lies on the right side of the middle point (obviously only if there is a Fixed Point). Else the Fixed Point(s) lies on left side.

## C++

 `// C++ program to check fixed point``// in an array using binary search``#include ``using` `namespace` `std;` `int` `binarySearch(``int` `arr[], ``int` `low, ``int` `high)``{``    ``if``(high >= low)``    ``{``        ``int` `mid = (low + high)/2; ``/*low + (high - low)/2;*/``        ``if``(mid == arr[mid])``            ``return` `mid;``        ``if``(mid > arr[mid])``            ``return` `binarySearch(arr, (mid + 1), high);``        ``else``            ``return` `binarySearch(arr, low, (mid -1));``    ``}` `    ``/* Return -1 if there is no Fixed Point */``    ``return` `-1;``}` `/* Driver code */``int` `main()``{``    ``int` `arr = {-10, -1, 0, 3, 10, 11, 30, 50, 100};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);``    ``cout<<``"Fixed Point is "``<< binarySearch(arr, 0, n-1);``    ``return` `0;``}` `// This code is contributed by rathbhupendra`

## C

 `// C program to check fixed point``// in an array using binary search``#include` `int` `binarySearch(``int` `arr[], ``int` `low, ``int` `high)``{``    ``if``(high >= low)``    ``{``        ``int` `mid = (low + high)/2;  ``/*low + (high - low)/2;*/``        ``if``(mid == arr[mid])``            ``return` `mid;``        ``if``(mid > arr[mid])``            ``return` `binarySearch(arr, (mid + 1), high);``        ``else``            ``return` `binarySearch(arr, low, (mid -1));``    ``}` `    ``/* Return -1 if there is no Fixed Point */``    ``return` `-1;``}` `/* Driver program to check above functions */``int` `main()``{``    ``int` `arr = {-10, -1, 0, 3, 10, 11, 30, 50, 100};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);``    ``printf``(``"Fixed Point is %d"``, binarySearch(arr, 0, n-1));``    ``getchar``();``    ``return` `0;``}`

## Java

 `// Java program to check fixed point``// in an array using binary search` `class` `Main``{``    ``static` `int` `binarySearch(``int` `arr[], ``int` `low, ``int` `high)``    ``{``        ``if``(high >= low)``        ``{  ``            ``/* low + (high - low)/2; */``            ``int` `mid = (low + high)/``2``; ``            ``if``(mid == arr[mid])``                ``return` `mid;``            ``if``(mid > arr[mid])``                ``return` `binarySearch(arr, (mid + ``1``), high);``            ``else``                ``return` `binarySearch(arr, low, (mid -``1``));``        ``}``      ` `        ``/* Return -1 if there is``           ``no Fixed Point */``        ``return` `-``1``;``    ``}``      ` `    ``//main function``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `arr[] = {-``10``, -``1``, ``0``, ``3` `, ``10``, ``11``, ``30``, ``50``, ``100``};``        ``int` `n = arr.length;``        ``System.out.println(``"Fixed Point is "``                   ``+ binarySearch(arr,``0``, n-``1``));       ``    ``}``}`

## Python

 `# Python program to check fixed point``# in an array using binary search``def` `binarySearch(arr, low, high):``    ``if` `high >``=` `low:``        ``mid ``=` `(low ``+` `high)``/``/``2``    ` `    ``if` `mid ``is` `arr[mid]:``        ``return` `mid``    ` `    ``if` `mid > arr[mid]:``        ``return` `binarySearch(arr, (mid ``+` `1``), high)``    ``else``:``        ``return` `binarySearch(arr, low, (mid ``-``1``))``    ` `    ``# Return -1 if there is no Fixed Point``    ``return` `-``1`  `# Driver program to check above functions */``arr ``=` `[``-``10``, ``-``1``, ``0``, ``3``, ``10``, ``11``, ``30``, ``50``, ``100``]``n ``=` `len``(arr)``print``(``"Fixed Point is "` `+` `str``(binarySearch(arr, ``0``, n``-``1``)))`  `# This code is contributed by Pratik Chhajer`

## C#

 `// C# program to check fixed point``// in an array using binary search``using` `System;` `class` `GFG``{``    ``static` `int` `binarySearch(``int` `[]arr, ``int` `low, ``int` `high)``    ``{``        ``if``(high >= low)``        ``{``            ``// low + (high - low)/2;``            ``int` `mid = (low + high)/2;``            ` `            ``if``(mid == arr[mid])``                ``return` `mid;``            ``if``(mid > arr[mid])``                ``return` `binarySearch(arr, (mid + 1), high);``            ``else``                ``return` `binarySearch(arr, low, (mid -1));``        ``}``        ` `        ``/* Return -1 if there is``        ``no Fixed Point */``        ``return` `-1;``    ``}``        ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[]arr = {-10, -1, 0, 3 , 10, 11, 30, 50, 100};``        ``int` `n = arr.Length;``        ``Console.Write(``"Fixed Point is "``+ binarySearch(arr,0, n-1));    ``    ``}``}``// This code is contributed by Sam007`

## PHP

 `= ``\$low``)``    ``{``        ` `         ``/*low + (high - low)/2;*/``        ``\$mid` `= (int)((``\$low` `+ ``\$high``) / 2);``        ``if``(``\$mid` `== ``\$arr``[``\$mid``])``            ``return` `\$mid``;``        ``if``(``\$mid` `> ``\$arr``[``\$mid``])``            ``return` `binarySearch(``\$arr``, (``\$mid` `+ 1), ``\$high``);``        ``else``            ``return` `binarySearch(``\$arr``, ``\$low``, (``\$mid` `- 1));``    ``}` `    ``/* Return -1 if there is``       ``no Fixed Po*/``    ``return` `-1;``}` `    ``// Driver Code``    ``\$arr` `= ``array``(-10, -1, 0, 3, 10,``                  ``11, 30, 50, 100);``    ``\$n` `= ``count``(``\$arr``);``    ``echo` `"Fixed Point is: "``        ``. binarySearch(``\$arr``, 0, ``\$n` `- 1);``        ` `// This code is contributed by Anuj_67``?>`

## Javascript

 ``

Output:

`Fixed Point is 3`

Time Complexity: O(Logn)

Find a Fixed Point (Value equal to index) in a given array | Duplicates Allowed