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Find the largest number with n set and m unset bits in C++
In this problem, we are given two integer values, n and m. Our task is to find the largest number with n set and m unset bits in the binary representation of the number.
Let's take an example to understand the problem
Input : n = 3, m = 1 Output : 14
Explanation −
Largest number will have 3 set bits and then 1 unset bit. (1110)2 = 14
Solution Approach
A simple solution to the problem is by finding the number consisting of (n+m) set bits. From this number, toggle off the m bits from the end (LSB). To create a number with (n+m) set bits,
$$(1\ll(n+m))-1$$
Then toggle m bits and return the number.
Example
Program to illustrate the working of our solution
#include <iostream>
using namespace std;
int findlargestNumber(int n, int m){
int maxNum = (1 << (n + m)) - 1;
if (m == 0)
return maxNum;
int number = (1 << m) - 1;
return (maxNum ^ number);
}
int main(){
int n = 5,
m = 2;
cout<<"The largest number with "<<n<<" set bits and "<<m<<" unset bits is "<<findlargestNumber(n, m);
return 0;
}Output
The largest number with 5 set bits and 2 unset bits is 124
Updated on: 28-Jan-2022
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