Count of numbers in range [L, R] with LSB as 0 in their Binary representation
Last Updated :
16 Jul, 2021
Given two integers L and R. The task is to find the count of all numbers in the range [L, R] whose Least Significant Bit in binary representation is 0.
Examples:
Input: L = 10, R = 20
Output: 6
Input: L = 7, R = 11
Output: 2
Naive approach: The simplest approach is to solve this problem is to check for every number in the range [L, R], if Least Significant Bit in binary representation is 0.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int countNumbers( int l, int r)
{
int count = 0;
for ( int i = l; i <= r; i++) {
if ((i & 1) == 0) {
count++;
}
}
return count;
}
int main()
{
int l = 10, r = 20;
cout << countNumbers(l, r);
return 0;
}
|
Java
import java.io.*;
class GFG{
static int countNumbers( int l, int r)
{
int count = 0 ;
for ( int i = l; i <= r; i++)
{
if ((i & 1 ) == 0 )
count += 1 ;
}
return count;
}
public static void main(String[] args)
{
int l = 10 , r = 20 ;
System.out.println(countNumbers(l, r));
}
}
|
Python3
def countNumbers(l, r):
count = 0
for i in range (l, r + 1 ):
if ((i & 1 ) = = 0 ):
count + = 1
return count
l = 10
r = 20
print (countNumbers(l, r))
|
C#
using System;
class GFG {
static int countNumbers( int l, int r)
{
int count = 0;
for ( int i = l; i <= r; i++) {
if ((i & 1) == 0)
count += 1;
}
return count;
}
public static void Main()
{
int l = 10, r = 20;
Console.WriteLine(countNumbers(l, r));
}
}
|
Javascript
<script>
function countNumbers(l, r)
{
let count = 0;
for (let i = l; i <= r; i++) {
if ((i & 1) == 0) {
count++;
}
}
return count;
}
let l = 10, r = 20;
document.write(countNumbers(l, r));
</script>
|
Time Complexity: O(r – l)
Auxiliary Space: O(1)
Efficient approach: This problem can be solved by using properties of bits. Only even numbers have rightmost bit as 0. The count can be found using this formula ((R / 2) – (L – 1) / 2) in O(1) time.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int countNumbers( int l, int r)
{
return ((r / 2) - (l - 1) / 2);
}
int main()
{
int l = 10, r = 20;
cout << countNumbers(l, r);
return 0;
}
|
Java
import java.io.*;
class GFG{
static int countNumbers( int l, int r)
{
return ((r / 2 ) - (l - 1 ) / 2 );
}
public static void main(String[] args)
{
int l = 10 ;
int r = 20 ;
System.out.println(countNumbers(l, r));
}
}
|
Python3
def countNumbers(l, r):
return ((r / / 2 ) - (l - 1 ) / / 2 )
l = 10
r = 20
print (countNumbers(l, r))
|
C#
using System;
using System.Collections.Generic;
class GFG{
static int countNumbers( int l, int r)
{
return ((r / 2) - (l - 1) / 2);
}
public static void Main()
{
int l = 10, r = 20;
Console.Write(countNumbers(l, r));
}
}
|
Javascript
<script>
function countNumbers(l, r)
{
return (parseInt(r / 2) -
parseInt((l - 1) / 2));
}
let l = 10, r = 20;
document.write(countNumbers(l, r));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
Share your thoughts in the comments
Please Login to comment...