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Finding Missing Number from integer Array using BitSet in Java
• Difficulty Level : Easy
• Last Updated : 16 Nov, 2020

Given an integer array of numbers 1 to n, you are asked to find the missing number from the array.

Example:

```Input : n = 5, a[] = {1, 2, 4, 5}
Output: 3
Explanation: From the array of numbers 1 to 5, 3 is missing.

Input : n = 10, a[] = {1, 3, 4, 6, 8, 10}
Output: 2, 5, 7, 9
Explanation: From the array of numbers 1 to 10, 2, 5, 7 and 9 are missing.
```

This question can be easily solved, by calculating the sum of the n numbers, with the formula,

```sum = (n * (n + 1)) / 2
```

But, this method cannot be used in the case, when the array contains more than one missing number.

For that condition, the BitSet utility class in Java can be used to solve the problem.

Approach:

1. Find the number of missing elements from the given array, missCnt.
2. Create a BitSet class object with n as a parameter.
3. For each number in the given array, set its second last bit to true, using the BitSet.set() method.
4. Initialize an integer variable lastMissIndex, to store the index of the last missing element.
5. Using for loop from 0 to missCnt, find the first bit set false from lastMissIndex, using BitSet.nextClearBit() method.
6. Increment lastMissIndex to 1, and print it.

Below is the implementation of the above approach

## Java

 `// Java Program to find the missing elements``// from integer array using BitSet class`` ` `import` `java.io.*;``import` `java.util.*;`` ` `public` `class` `FindMissingNo {``    ``private` `static` `void` `findMissingNumbers(``int` `arr[], ``int` `n)``    ``{``        ``int` `missCnt = n - arr.length;``        ``// create Bitset object b``        ``BitSet b = ``new` `BitSet(n);``        ``for` `(``int` `i : arr) {``            ``b.set(i - ``1``);``        ``}``        ``int` `lastMissIndex = ``0``;``        ``for` `(``int` `i = ``0``; i < missCnt; ++i) {``            ``lastMissIndex = b.nextClearBit(lastMissIndex);``            ``// print missing number``            ``System.out.println(++lastMissIndex);``        ``}``    ``}``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``10``;``        ``// array of 10 numbers``        ``int``[] arr = ``new` `int``[] { ``1``, ``2``, ``4``, ``6``, ``8``, ``9` `};``        ``// call function``        ``findMissingNumbers(arr, n);``    ``}``}`
Output
```3
5
7
10
```