Binary representation of previous number

Given a binary input that represents binary representation of positive number n, find binary representation of n-1. It may be assumed that input binary number is greater than 0.

The binary input may or may not fit even in unsigned long long int.

Examples:

```Input : 10110
Output : 10101
Here n  = (22)10 = (10110)2
Previous number = (21)10 = (10101)2

Input : 11000011111000000
Output : 11000011110111111
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We store input as string so that large numbers can be handled. We traverse the string from rightmost character and convert all 0’s to 1’s until we find a 1. Finally convert the found 1 to 0. The number so formed after this process is the required number. If input is “1”, then previous number will be “0”. If only the first character in the entire string is ‘1’, then we discard this character and change all the 0’s to 1’s.

```// C++ implementation to find the binary
// representation of previous number
#include <bits/stdc++.h>
using namespace std;

// function to find the required
// binary representation
string previousNumber(string num)
{
int n = num.size();

// if the number is '1'
if (num.compare("1") == 0)
return "0";

// examine bits from right to left
int i;
for (i = n - 1; i >= 0; i--) {

// if '1' is encountered, convert
// it to '0' and then break
if (num.at(i) == '1') {
num.at(i) = '0';
break;
}

// else convert '0' to '1'
else
num.at(i) = '1';
}

// if only the 1st bit in the
// binary representation was '1'
if (i == 0)
return num.substr(1, n - 1);

// final binary representation
// of the required number
return num;
}

// Driver program to test above
int main()
{
string num = "10110";
cout << "Binary representation of previous number = "
<< previousNumber(num);
return 0;
}
```

Output:

```Binary representation of previous number = 10101
```

Time Complexity : O(n) where n is number of bits in input.

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

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