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; } |
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
<?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 ?> |
Output:
Binary representation of next number = 10100
Time Complexity : O(n) where n is number of bits in input.
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