Binary representation of next number
Given a binary input that represents binary representation of positive number n, find 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
We store input as string so that large numbers can be handled. We traverse the string from 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 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 above idea.
C++
// C++ implementation to find the binary // representation of next greater integer #include <bits/stdc++.h> 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; } |
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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 |
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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 |
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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 |
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PHP
<?php // PHP implementation to find the binary // representation of next greater integer // function to find the required // binary representation function nextGreater($num) { $l = strlen($num); // 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') { $num[$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 ?> |
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Output:
Binary representation of next number = 10100
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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