# Php Program to Find the smallest missing number

• Last Updated : 17 Dec, 2021

Given a sorted array of n distinct integers where each integer is in the range from 0 to m-1 and m > n. Find the smallest number that is missing from the array.

Examples

```Input: {0, 1, 2, 6, 9}, n = 5, m = 10
Output: 3

Input: {4, 5, 10, 11}, n = 4, m = 12
Output: 0

Input: {0, 1, 2, 3}, n = 4, m = 5
Output: 4

Input: {0, 1, 2, 3, 4, 5, 6, 7, 10}, n = 9, m = 11
Output: 8```

Thanks to Ravichandra for suggesting following two methods.

Method 1 (Use Binary Search)
For i = 0 to m-1, do binary search for i in the array. If i is not present in the array then return i.
Time Complexity: O(m log n)

Method 2 (Linear Search
If arr[0] is not 0, return 0. Otherwise traverse the input array starting from index 0, and for each pair of elements a[i] and a[i+1], find the difference between them. if the difference is greater than 1 then a[i]+1 is the missing number.
Time Complexity: O(n)

Method 3 (Use Modified Binary Search)
Thanks to yasein and Jams for suggesting this method.
In the standard Binary Search process, the element to be searched is compared with the middle element and on the basis of comparison result, we decide whether to search is over or to go to left half or right half.
In this method, we modify the standard Binary Search algorithm to compare the middle element with its index and make decision on the basis of this comparison.

• If the first element is not same as its index then return first index
• Else get the middle index say mid
• If arr[mid] greater than mid then the required element lies in left half.
• Else the required element lies in right half.

## PHP

 ` ``\$end``)``        ``return` `\$end` `+ 1;`` ` `    ``if` `(``\$start` `!= ``\$array``[``\$start``])``        ``return` `\$start``;`` ` `    ``\$mid` `= (``\$start` `+ ``\$end``) / 2;`` ` `    ``// Left half has all ``    ``// elements from 0 to mid``    ``if` `(``\$array``[``\$mid``] == ``\$mid``)``        ``return` `findFirstMissing(``\$array``, ``                                ``\$mid` `+ 1, ``                                ``\$end``);`` ` `    ``return` `findFirstMissing(``\$array``, ``                            ``\$start``, ``                            ``\$mid``);``}`` ` `    ``// Driver Code``    ``\$arr` `= ``array` `(0, 1, 2, 3, 4, 5, 6, 7, 10);``    ``\$n` `= ``count``(``\$arr``);``    ``echo` `"Smallest missing element is "` `,``          ``findFirstMissing(``\$arr``, 2, ``\$n` `- 1);``         ` `// This code Contributed by Ajit.``?>`

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