Given a number maximize it by swapping bits at its extreme positions i.e. at the first and last position, second and second last position, and so on.
Examples:
Input : 4 (0000...0100) Output : 536870912 (0010...0000) In the above example swapped 3rd and 3rd last bit to maximize the given unsigned number. Input : 12 (00000...1100) Output : 805306368 (0011000...0000) In the above example 3rd and 3rd last bit and 4th and 4th last bit are swapped to maximize the given unsigned number.
Naive Approach:
1. Convert the number into its bit representation and store its bit representation in an array.
2. Traverse the array from both ends, if the less significant bit of the bit representation is greater than the more significant bit i.e. if the less significant bit is 1 and the more significant bit is 0 then swap them else take no action.
3. Convert the obtained binary representation back to the number.
Efficient Approach:
1. Create a copy of the original number because the original number would be modified, iteratively obtaining the bits at the extreme positions.
2. If less significant bit is 1 and the more significant bit is 0 then swap the bits in the bit from only, and continue the process until less significant bit’s position is less than more significant bit’s position.
3. Display the maximized number.
// C++ program to find maximum number by // swapping extreme bits. #include <bits/stdc++.h> using namespace std;
#define ull unsigned long long int ull findMax(ull num) { ull num_copy = num;
/* Traverse bits from both extremes */
int j = sizeof (unsigned long long int ) * 8 - 1;
int i = 0;
while (i < j) {
// Obtaining i-th and j-th bits
int m = (num_copy >> i) & 1;
int n = (num_copy >> j) & 1;
/* Swapping the bits if lesser significant
is greater than higher significant
bit and accordingly modifying the number */
if (m > n) {
int x = (1 << i | 1 << j);
num = num ^ x;
}
i++;
j--;
}
return num;
} // Driver code int main()
{ ull num = 4;
cout << findMax(num);
return 0;
} |
// Java program to find maximum number by // swapping extreme bits. class GFG {
static int findMax( int num) {
byte size_of_int = 4 ;
int num_copy = num;
/* Traverse bits from both extremes */
int j = size_of_int * 8 - 1 ;
int i = 0 ;
while (i < j) {
// Obtaining i-th and j-th bits
int m = (num_copy >> i) & 1 ;
int n = (num_copy >> j) & 1 ;
/* Swapping the bits if lesser significant
is greater than higher significant
bit and accordingly modifying the number */
if (m > n) {
int x = ( 1 << i | 1 << j);
num = num ^ x;
}
i++;
j--;
}
return num;
}
// Driver code
static public void main(String[] args) {
int num = 4 ;
System.out.println(findMax(num));
}
} // This code is contributed by 29AjayKumar |
# Python 3 program to find maximum number # by swapping extreme bits. def findMax( num):
num_copy = num
# Traverse bits from both extremes
j = 4 * 8 - 1 ;
i = 0
while (i < j) :
# Obtaining i-th and j-th bits
m = (num_copy >> i) & 1
n = (num_copy >> j) & 1
# Swapping the bits if lesser significant
# is greater than higher significant
# bit and accordingly modifying the number
if (m > n) :
x = ( 1 << i | 1 << j)
num = num ^ x
i + = 1
j - = 1
return num
# Driver code if __name__ = = "__main__" :
num = 4
print (findMax(num))
# This code is contributed by ita_c |
// C# program to find maximum number by // swapping extreme bits. using System;
public class GFG {
static int findMax( int num) {
byte size_of_int = 4;
int num_copy = num;
/* Traverse bits from both extremes */
int j = size_of_int * 8 - 1;
int i = 0;
while (i < j) {
// Obtaining i-th and j-th bits
int m = (num_copy >> i) & 1;
int n = (num_copy >> j) & 1;
/* Swapping the bits if lesser significant
is greater than higher significant
bit and accordingly modifying the number */
if (m > n) {
int x = (1 << i | 1 << j);
num = num ^ x;
}
i++;
j--;
}
return num;
}
// Driver code static public void Main() {
int num = 4;
Console.Write(findMax(num));
}
} // This code is contributed by 29AjayKumar |
<script> // JavaScript program to find maximum number by // swapping extreme bits. function findMax(num)
{ let num_copy = num;
/* Traverse bits from both extremes */
let j = 4 * 8 - 1;
let i = 0;
while (i < j) {
// Obtaining i-th and j-th bits
let m = (num_copy >> i) & 1;
let n = (num_copy >> j) & 1;
/* Swapping the bits if lesser significant
is greater than higher significant
bit and accordingly modifying the number */
if (m > n) {
let x = (1 << i | 1 << j);
num = num ^ x;
}
i++;
j--;
}
return num;
} // Driver code let num = 4;
document.write(findMax(num));
// This code is contributed by Manoj. </script> |
536870912
Time Complexity: O(1)
Auxiliary Space: O(1)