# Find missing element in a sorted array of consecutive numbers

Given an array arr[] of n distinct integers. Elements are placed sequentially in ascending order with one element missing. The task is to find the missing element.
Examples:

Input: arr[] = {1, 2, 4, 5, 6, 7, 8, 9}
Output: 3
Input: arr[] = {-4, -3, -1, 0, 1, 2}
Output: -2
Input: arr[] = {1, 2, 3, 4}
Output: -1
No element is missing.

Principles:

• Look for inconsistency: Ideally, the difference between any element and its index must be arr[0] for every element.
Example
A[] = {1, 2, 3, 4, 5} -> Consistent
B[] = {101, 102, 103, 104} -> Consistent
C[] = {1, 2, 4, 5, 6} -> Inconsistent as C[2] – 2 != C[0] i.e. 4 – 2 != 1

• Finding inconsistency helps to scan only half of the array each time in O(logN).

Algorithm

1. Find middle element and check if it’s consistent.
2. If middle element is consistent, then check if the difference between middle element and its next element is greater than 1 i.e. check if arr[mid + 1] – arr[mid] > 1
• If yes, then arr[mid] + 1 is the missing element.
• If not, then we have to scan the right half array from the middle element and jump to step-1.
3. If middle element is inconsistent, then check if the difference between middle element and its previous element is greater than 1 i.e. check if arr[mid] – arr[mid – 1] > 1
• If yes, then arr[mid] – 1 is the missing element.
• If not, then we have to scan the left half array from the middle element and jump to step-1.

Below is the implementation of the above approach:

## C++

 `// CPP implementation of the approach` `#include` `using` `namespace` `std;`   `// Function to return the missing element` `int` `findMissing(``int` `arr[], ``int` `n)` `{`   `    ``int` `l = 0, h = n - 1;` `    ``int` `mid;`   `    ``while` `(h > l) ` `    ``{`   `        ``mid = l + (h - l) / 2;`   `        ``// Check if middle element is consistent` `        ``if` `(arr[mid] - mid == arr[0]) ` `        ``{`   `            ``// No inconsistency till middle elements` `            ``// When missing element is just after` `            ``// the middle element` `            ``if` `(arr[mid + 1] - arr[mid] > 1)` `                ``return` `arr[mid] + 1;` `            ``else` `            ``{` `                ``// Move right` `                ``l = mid + 1;` `            ``}` `        ``}` `        ``else` `        ``{`   `            ``// Inconsistency found` `            ``// When missing element is just before` `            ``// the middle element` `            ``if` `(arr[mid] - arr[mid - 1] > 1)` `                ``return` `arr[mid] - 1;` `            ``else` `            ``{` `                ``// Move left` `                ``h = mid - 1;` `            ``}` `        ``}` `    ``}`   `    ``// No missing element found` `    ``return` `-1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { -9, -8, -7, -5, -4, -3, -2, -1, 0 };` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]);`   `    ``cout << (findMissing(arr, n));` `}` `    `  `// This code iscontributed by` `// Surendra_Gangwar`

## Java

 `// Java implementation of the approach` `class` `GFG {`   `    ``// Function to return the missing element` `    ``public` `static` `int` `findMissing(``int` `arr[], ``int` `n)` `    ``{`   `        ``int` `l = ``0``, h = n - ``1``;` `        ``int` `mid;`   `        ``while` `(h > l) {`   `            ``mid = l + (h - l) / ``2``;`   `            ``// Check if middle element is consistent` `            ``if` `(arr[mid] - mid == arr[``0``]) {`   `                ``// No inconsistency till middle elements` `                ``// When missing element is just after` `                ``// the middle element` `                ``if` `(arr[mid + ``1``] - arr[mid] > ``1``)` `                    ``return` `arr[mid] + ``1``;` `                ``else` `{`   `                    ``// Move right` `                    ``l = mid + ``1``;` `                ``}` `            ``}` `            ``else` `{`   `                ``// Inconsistency found` `                ``// When missing element is just before` `                ``// the middle element` `                ``if` `(arr[mid] - arr[mid - ``1``] > ``1``)` `                    ``return` `arr[mid] - ``1``;` `                ``else` `{`   `                    ``// Move left` `                    ``h = mid - ``1``;` `                ``}` `            ``}` `        ``}`   `        ``// No missing element found` `        ``return` `-``1``;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``int` `arr[] = { -``9``, -``8``, -``7``, -``5``, -``4``, -``3``, -``2``, -``1``, ``0` `};` `        ``int` `n = arr.length;`   `        ``System.out.print(findMissing(arr, n));` `    ``}` `}`

## Python3

 `# Python implementation of the approach`   `# Function to return the missing element` `def` `findMissing(arr, n):`   `    ``l, h ``=` `0``, n ``-` `1` `    ``mid ``=` `0`   `    ``while` `(h > l):`   `        ``mid ``=` `l ``+` `(h ``-` `l) ``/``/` `2`   `        ``# Check if middle element is consistent` `        ``if` `(arr[mid] ``-` `mid ``=``=` `arr[``0``]):`   `            ``# No inconsistency till middle elements` `            ``# When missing element is just after` `            ``# the middle element` `            ``if` `(arr[mid ``+` `1``] ``-` `arr[mid] > ``1``):` `                ``return` `arr[mid] ``+` `1` `            ``else``:`   `                ``# Move right` `                ``l ``=` `mid ``+` `1` `            `  `        ``else``:`   `            ``# Inconsistency found` `            ``# When missing element is just before` `            ``# the middle element` `            ``if` `(arr[mid] ``-` `arr[mid ``-` `1``] > ``1``):` `                ``return` `arr[mid] ``-` `1` `            ``else``:`   `                ``# Move left` `                ``h ``=` `mid ``-` `1` `            `  `    ``# No missing element found` `    ``return` `-``1`   `# Driver code` `arr ``=` `[``-``9``, ``-``8``, ``-``7``, ``-``5``, ``-``4``, ``-``3``, ``-``2``, ``-``1``, ``0` `]` `n ``=` `len``(arr)`   `print``(findMissing(arr, n))`   `# This code is contributed` `# by mohit kumar`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG` `{`   `    ``// Function to return the missing element` `    ``public` `static` `int` `findMissing(``int``[] arr, ``int` `n)` `    ``{`   `        ``int` `l = 0, h = n - 1;` `        ``int` `mid;`   `        ``while` `(h > l)` `        ``{`   `            ``mid = l + (h - l) / 2;`   `            ``// Check if middle element is consistent` `            ``if` `(arr[mid] - mid == arr[0]) ` `            ``{`   `                ``// No inconsistency till middle elements` `                ``// When missing element is just after` `                ``// the middle element` `                ``if` `(arr[mid + 1] - arr[mid] > 1)` `                    ``return` `arr[mid] + 1;` `                ``else` `                ``{`   `                    ``// Move right` `                    ``l = mid + 1;` `                ``}` `            ``}` `            ``else` `            ``{`   `                ``// Inconsistency found` `                ``// When missing element is just before` `                ``// the middle element` `                ``if` `(arr[mid] - arr[mid - 1] > 1)` `                    ``return` `arr[mid] - 1;` `                ``else` `                ``{`   `                    ``// Move left` `                    ``h = mid - 1;` `                ``}` `            ``}` `        ``}`   `        ``// No missing element found` `        ``return` `-1;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr = { -9, -8, -7, -5, -4, -3, -2, -1, 0 };` `        ``int` `n = arr.Length;`   `        ``Console.WriteLine(findMissing(arr, n));` `    ``}` `}`   `// This code is contributed by Code_Mech`

## PHP

 ` ``\$l``)` `    ``{ `   `        ``\$mid` `= ``floor``(``\$l` `+ (``\$h` `- ``\$l``) / 2); `   `        ``// Check if middle element is consistent ` `        ``if` `(``\$arr``[``\$mid``] - ``\$mid` `== ``\$arr``[0]) ` `        ``{ `   `            ``// No inconsistency till middle elements ` `            ``// When missing element is just after ` `            ``// the middle element ` `            ``if` `(``\$arr``[``\$mid` `+ 1] - ``\$arr``[``\$mid``] > 1) ` `                ``return` `\$arr``[``\$mid``] + 1; ` `            ``else` `            ``{ `   `                ``// Move right ` `                ``\$l` `= ``\$mid` `+ 1; ` `            ``} ` `        ``} ` `        ``else` `        ``{ `   `            ``// Inconsistency found ` `            ``// When missing element is just before ` `            ``// the middle element ` `            ``if` `(``\$arr``[``\$mid``] - ``\$arr``[``\$mid` `- 1] > 1) ` `                ``return` `\$arr``[``\$mid``] - 1; ` `            ``else` `            ``{ `   `                ``// Move left ` `                ``\$h` `= ``\$mid` `- 1; ` `            ``} ` `        ``} ` `    ``} `   `    ``// No missing element found ` `    ``return` `-1; ` `} `   `// Driver code ` `\$arr` `= ``array``( -9, -8, -7, -5, -` `               ``4, -3, -2, -1, 0 ); ` `\$n` `= ``count``(``\$arr``); `   `echo` `findMissing(``\$arr``, ``\$n``); `   `// This code is contributed by Ryuga` `?>`

## Javascript

 ``

Output:

`-6`

Time Complexity : O(log(N) )
Auxiliary Space: O(1)

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