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# Binary representation of next number

Given a binary input that represents binary representation of positive number n, find a binary representation of n+1.
The binary input may be and may not fit even in unsigned long long int.

Examples:

```Input : 10011
Output : 10100
Here n = (19)10 = (10011)2
next greater integer = (20)10 = (10100)2

Input : 111011101001111111
Output : 111011101010000000 ```

### Approach 1:

We store input as a string so that large numbers can be handled. We traverse the string from the rightmost character and convert all 1s to 0s until we find a 0. Finally, convert the found 0 to 1. If we do not find a 0, we append a 1 to the overall string.

```string nextGreater(num)
l = num.length

// Find first 0 from right side. While
// searching, convert 1s to 0s
for i = l-1 to 0
if num[i] == '0'
num[i] = '1'
break
else
num[i] = '0'

// If there was no 0
if i < 0
num = '1' + num
return num        ```

Below is the implementation of the above idea.

## C++

 `// C++ implementation to find the binary` `// representation of next greater integer` `#include ` `using` `namespace` `std;`   `// function to find the required` `// binary representation` `string nextGreater(string num)` `{` `    ``int` `l = num.size();`   `    ``// examine bits from the right` `    ``for` `(``int` `i=l-1; i>=0; i--)` `    ``{` `        ``// if '0' is encountered, convert` `        ``// it to '1' and then break` `        ``if` `(num.at(i) == ``'0'``)` `        ``{` `            ``num.at(i) = ``'1'``;` `            ``break``;` `        ``}`   `        ``// else convert '1' to '0'` `        ``else` `            ``num.at(i) = ``'0'``;`     `    ``// if the binary representation` `    ``// contains only the set bits` `    ``if` `(i < 0)` `        ``num = ``"1"` `+ num;` `    ``}` `    ``// final binary representation` `    ``// of the required integer` `    ``return` `num;` `}`   `// Driver program to test above` `int` `main()` `{` `    ``string num = ``"10011"``;` `    ``cout << ``"Binary representation of next number = "` `         ``<< nextGreater(num);` `    ``return` `0;` `}`

## Java

 `// Java implementation to find the binary` `// representation of next greater integer`   `class` `GFG {`   `// function to find the required` `// binary representation` `    ``static` `String nextGreater(String num) {`   `        ``int` `l = num.length();` `        ``int` `i;` `        ``// examine bits from the right` `        ``for` `(i = l - ``1``; i >= ``0``; i--) {` `            ``// if '0' is encountered, convert` `            ``// it to '1' and then break` `            ``if` `(num.charAt(i) == ``'0'``) {` `                ``num = num.substring(``0``, i) + ``'1'` `+ num.substring(i+``1``);` `                ``break``;` `            ``} ``// else convert '1' to '0'` `            ``else` `{` `                ``num = num.substring(``0``, i) + ``'0'` `+ num.substring(i + ``1``);` `            ``}` `            ``// num[i] = '0';` `        ``}`   `        ``// if the binary representation` `        ``// contains only the set bits` `        ``if` `(i < ``0``) {` `            ``num = ``"1"` `+ num;` `        ``}`   `        ``// final binary representation` `        ``// of the required integer` `        ``return` `num;` `    ``}`   `// Driver program to test above` `    ``public` `static` `void` `main(String[] args) {` `        ``String num = ``"10011"``;` `        ``System.out.println(``"Binary representation of next number = "` `                ``+ nextGreater(num));` `    ``}` `}` `//this code contributed by Rajput-Ji`

## Python3

 `# Python3 implementation to find the binary` `# representation of next greater integer`   `# function to find the required` `# binary representation` `def` `nextGreater(num1):`   `    ``l ``=` `len``(num1);` `    ``num ``=` `list``(num1);`   `    ``# examine bits from the right` `    ``i ``=` `l``-``1``;` `    ``while``(i >``=` `0``):` `        ``# if '0' is encountered, convert` `        ``# it to '1' and then break` `        ``if` `(num[i] ``=``=` `'0'``):` `            ``num[i] ``=` `'1'``;` `            ``break``;`   `        ``# else convert '1' to '0'` `        ``else``:` `            ``num[i] ``=` `'0'``;` `        ``i``-``=``1``;`   `    ``# if the binary representation` `    ``# contains only the set bits` `    ``num1 ``=` `''.join(num);` `    ``if` `(i < ``0``):` `        ``num1 ``=` `'1'` `+` `num1;`   `    ``# final binary representation` `    ``# of the required integer` `    ``return` `num1;`   `# Driver Code` `num ``=` `"10011"``;` `print``(``"Binary representation of next number = "``,nextGreater(num));`   `# This code is contributed by mits`

## C#

 `    `  `// C# implementation to find the binary` `// representation of next greater integer` ` ``using` `System;` `public` `class` `GFG {` ` `  `// function to find the required` `// binary representation` `    ``static` `String nextGreater(String num) {` ` `  `        ``int` `l = num.Length;` `        ``int` `i;` `        ``// examine bits from the right` `        ``for` `(i = l - 1; i >= 0; i--) {` `            ``// if '0' is encountered, convert` `            ``// it to '1' and then break` `            ``if` `(num[i] == ``'0'``) {` `                ``num = num.Substring(0, i) + ``'1'` `+ num.Substring(i+1);` `                ``break``;` `            ``} ``// else convert '1' to '0'` `            ``else` `{` `                ``num = num.Substring(0, i) + ``'0'` `+ num.Substring(i + 1);` `            ``}` `            ``// num[i] = '0';` `        ``}` ` `  `        ``// if the binary representation` `        ``// contains only the set bits` `        ``if` `(i < 0) {` `            ``num = ``"1"` `+ num;` `        ``}` ` `  `        ``// final binary representation` `        ``// of the required integer` `        ``return` `num;` `    ``}` ` `  `// Driver program to test above` `    ``public` `static` `void` `Main() {` `        ``String num = ``"10011"``;` `        ``Console.WriteLine(``"Binary representation of next number = "` `                ``+ nextGreater(num));` `    ``}` `}` `//this code contributed by Rajput-Ji`

## PHP

 `= 0; ``\$i``--)` `    ``{` `        ``// if '0' is encountered, convert` `        ``// it to '1' and then break` `        ``if` `(``\$num``[``\$i``] == ``'0'``)` `        ``{` `            ``\$num``[``\$i``] = ``'1'``;` `            ``break``;` `        ``}`   `        ``// else convert '1' to '0'` `        ``else` `            ``\$num``[``\$i``] = ``'0'``;` `    ``}`   `    ``// if the binary representation` `    ``// contains only the set bits` `    ``if` `(``\$i` `< 0)` `        ``\$num` `= ``"1"` `. ``\$num``;`   `    ``// final binary representation` `    ``// of the required integer` `    ``return` `\$num``;` `}`   `// Driver Code` `\$num` `= ``"10011"``;` `echo` `"Binary representation of next number = "` `.` `                              ``nextGreater(``\$num``);`   `// This code is contributed by ita_c` `?>`

## Javascript

 ``

Output

`Binary representation of next number = 10100`

Time Complexity: O(n) where n is the number of bits in the input.
Auxiliary Space: O(n), since the string gets copied when we pass it to a function.

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

### Approach 2:

#### Step by step implementation:

1. The nextGreater function takes a binary string num as input.
2. The binary string is converted to an integer using the bitset class. The to_ulong method of the bitset class returns the integer representation of the binary string.
3. The integer is incremented by 1.
4. The incremented integer is converted back to a binary string using the bitset class. The to_string method of the bitset class returns the binary string representation of the integer.
5. The resulting binary string may have leading zeros, so these are removed using the erase and find_first_not_of methods of the string class.
6. The resulting binary string is returned.

## C++

 `#include ` `#include ` `using` `namespace` `std;`   `string nextGreater(string num) {` `    ``// Convert binary string to integer` `    ``bitset<32> b(num);` `    ``int` `n = b.to_ulong();` `    `  `    ``// Increment integer by 1` `    ``n++;` `    `  `    ``// Convert integer back to binary string` `    ``string result = bitset<32>(n).to_string();` `    `  `    ``// Remove leading zeros` `    ``result.erase(0, result.find_first_not_of(``'0'``));` `    `  `    ``return` `result;` `}`   `int` `main() {` `    ``string num = ``"10011"``;` `    ``cout << ``"Binary representation of next number = "` `<< nextGreater(num);` `    ``return` `0;` `}`

Output

`Binary representation of next number = 10100`

Time Complexity: O(n)
Auxiliary Space: O(1)

Explanation:

The time complexity of this approach is O(n), where n is the length of the input binary string. This is because each operation (conversion to integer, incrementing, conversion to binary string, and removing leading zeros) takes O(n) time.

The auxiliary space complexity of this approach is O(1), because only a constant amount of extra space is used (for variables such as b, n, and result).

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