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# Positive integers up to N that are not present in given Array

• Difficulty Level : Hard
• Last Updated : 20 Sep, 2021

Given an array a[] and an integer N, the task is to find all natural numbers from the range [1, N] that are nor present in the given array.

Examples:

Input: N = 5, a[] = {1, 2, 4, 5}
Output: 3
Explanation: 3 is the only integer from the range [1, 5] that is not present in the array.

Input: N = 10, a[] = {1, 3, 4, 6, 8, 10}
Output: 2 5 7 9

Naive Approach: The simplest approach to solve this problem is to traverse the range [1, N] and for each number from range, traverse the array and check if it is present in the array or not.
Time Complexity: O(N * len), where len denotes the length of the array.
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized using HashSet. Traverse the given array and insert all array elements into the HashSet. Then, traverse the range [1, N] and for each element, check if it is present in the HashSet or not using contains() method, to compute search in O(1) complexity.
Time Complexity: O(N)
Auxiliary Space: O(N)

Alternate Approach: The given problem can be solved using BitSet in C++. Follow the steps below to solve the problem:

1. Initialize a BitSet variable, bset with N as length.
2. For each array element, set its bit to false, using bset.set(arr[i]-1, 0), where it sets the bit at position arr[i] – 1 to 0.
3. Now, iterate from bset._Find_first() to bset.size() – 1 using a variable, say i.
4. Print i + 1 and set bset._Find_next().

Below is the implementation of the above approach.

## C++

 `// CPP program for the above approach` `#include ``using` `namespace` `std;` `// Function to find positive integers``// from 1 to N that are not present in the array``void` `findMissingNumbers(``int` `arr[], ``int` `len)``{``    ``const` `int` `M = 15;` `    ``// Declare bitset``    ``bitset bset;` `    ``// Iterate from 0 to M - 1``    ``for` `(``int` `i = 0; i < M; i++) {``        ``bset.set(i);``    ``}` `    ``// Iterate from 0 to len - 1``    ``for` `(``int` `i = 0; i < len; i++) {``        ``bset.set(arr[i] - 1, 0);``    ``}` `    ``// Iterate from bset._Find_first()``    ``// to bset.size() - 1``    ``for` `(``int` `i = bset._Find_first();``         ``i < bset.size();``         ``i = bset._Find_next(i)) {` `        ``if` `(i + 1 > len)``            ``break``;` `        ``cout << i + 1 << endl;``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 4, 6, 8, 9 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``findMissingNumbers(arr, n);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;``import` `java.util.*;``class` `GFG``{` `    ``// Function to find positive integers``    ``// from 1 to N that are not present in the array``    ``static` `void` `findMissingNumbers(``int``[] arr, ``int` `len)``    ``{``        ``int` `M = ``15``;` `        ``// Declare bitset``        ``BitSet bset = ``new` `BitSet(M);` `        ``// Iterate from 0 to M - 1``        ``for` `(``int` `i = ``0``; i < M; i++)``        ``{``            ``bset.set(i);``        ``}` `        ``// Iterate from 0 to len - 1``        ``for` `(``int` `i = ``0``; i < len; i++)``        ``{``            ``bset.set(arr[i] - ``1``, ``false``);``        ``}` `        ``// Iterate from bset._Find_first()``        ``// to bset.size() - 1``        ``for` `(``int` `i = bset.nextSetBit(``0``); i >= ``0``;``             ``i = bset.nextSetBit(i + ``1``))``        ``{``            ``if` `(i + ``1` `> len)``                ``break``;``            ``System.out.println(i + ``1``);``        ``}``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = ``new` `int``[] { ``1``, ``2``, ``4``, ``6``, ``8``, ``9` `};``        ``int` `n = arr.length;``        ``findMissingNumbers(arr, n);``    ``}``}` `// This code is contributed by Dharanendra L V`

## Python3

 `# Python 3 program for the above approach` `#  Function to find positive integers``# from 1 to N that are not present in the array``def` `findMissingNumbers(arr, n):` `    ``M ``=` `15` `    ``# Declare bitset``    ``bset ``=` `[``0``]``*``M` `    ``# Iterate from 0 to M - 1``    ``for` `i ``in` `range``(M):``        ``bset[i] ``=` `i` `    ``# Iterate from 0 to n - 1``    ``for` `i ``in` `range``(n):``        ``bset[arr[i] ``-` `1``] ``=` `0` `    ``bset ``=` `[i ``for` `i ``in` `bset ``if` `i !``=` `0``]` `    ``# Iterate from bset._Find_first()``    ``# to bset.size() - 1` `    ``for` `i ``in` `range``(``len``(bset)):` `        ``if` `(bset[i] ``+` `1` `> n):``            ``break` `        ``print``(bset[i] ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[``1``, ``2``, ``4``, ``6``, ``8``, ``9``]``    ``n ``=` `len``(arr)` `    ``findMissingNumbers(arr, n)` `    ``# This code is contributed by ukasp.`

Output:
```3
5```

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

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