Given an integer N, the task is to find the Nth natural number with exactly two bits set.
Examples:
Input: N = 4
Output: 9
Explanation:
Numbers with exactly two bits set: 3, 5, 6, 9, 10, 12, …
4th number in this is 9Input: N = 15
Output: 48
Naive Approach:
- Run a loop through all natural numbers, and for each number, check if it has two bits set or not by counting set bits in a number.
- Print the Nth number having two set bits.
Efficient Approach:
- Find the leftmost set bit by finding the partition to which N belongs (Partition ‘i’ has ‘i’ numbers in it).
- To find the other set bit, we’ll have to first find the distance of N from the last number of the previous partition. Based on their difference, we set the corresponding bit.
Note: To set ith bit (i = 0, 1, 2…) in a number K:
k = k | (1<<(i))
Below is the implementation of the above approach:
C++
// C++ Code to find the Nth number
// with exactly two bits set
#include <bits/stdc++.h>
using
namespace
std;
// Function to find the Nth number
// with exactly two bits set
void
findNthNum(
long
long
int
N)
{
long
long
int
bit_L = 1, last_num = 0;
// Keep incrementing until
// we reach the partition of 'N'
// stored in bit_L
while
(bit_L * (bit_L + 1) / 2 < N) {
last_num = last_num + bit_L;
bit_L++;
}
// set the rightmost bit
// based on bit_R
int
bit_R = N - last_num - 1;
cout << (1 << bit_L) + (1 << bit_R)
<< endl;
}
// Driver code
int
main()
{
long
long
int
N = 13;
findNthNum(N);
return
0;
}
chevron_rightfilter_noneJava
// Java Code to find the Nth number
// with exactly two bits set
class
GFG{
// Function to find the Nth number
// with exactly two bits set
static
void
findNthNum(
int
N)
{
int
bit_L =
1
, last_num =
0
;
// Keep incrementing until
// we reach the partition of 'N'
// stored in bit_L
while
(bit_L * (bit_L +
1
) /
2
< N) {
last_num = last_num + bit_L;
bit_L++;
}
// set the rightmost bit
// based on bit_R
int
bit_R = N - last_num -
1
;
System.out.print((
1
<< bit_L) + (
1
<< bit_R)
+
"\n"
);
}
// Driver code
public
static
void
main(String[] args)
{
int
N =
13
;
findNthNum(N);
}
}
// This code is contributed by Princi Singh
chevron_rightfilter_nonePython3
# Python Code to find the Nth number
# with exactly two bits set
# Function to find the Nth number
# with exactly two bits set
def
findNthNum(N):
bit_L
=
1
;
last_num
=
0
;
# Keep incrementing until
# we reach the partition of 'N'
# stored in bit_L
while
(bit_L
*
(bit_L
+
1
)
/
2
< N):
last_num
=
last_num
+
bit_L;
bit_L
+
=
1
;
# set the rightmost bit
# based on bit_R
bit_R
=
N
-
last_num
-
1
;
print
((
1
<< bit_L)
+
(
1
<< bit_R));
# Driver code
if
__name__
=
=
'__main__'
:
N
=
13
;
findNthNum(N);
# This code contributed by PrinciRaj1992
chevron_rightfilter_noneC#
// C# Code to find the Nth number
// with exactly two bits set
using
System;
class
GFG{
// Function to find the Nth number
// with exactly two bits set
static
void
findNthNum(
int
N)
{
int
bit_L = 1, last_num = 0;
// Keep incrementing until
// we reach the partition of 'N'
// stored in bit_L
while
(bit_L * (bit_L + 1) / 2 < N) {
last_num = last_num + bit_L;
bit_L++;
}
// set the rightmost bit
// based on bit_R
int
bit_R = N - last_num - 1;
Console.Write((1 << bit_L) + (1 << bit_R)
+
"\n"
);
}
// Driver code
public
static
void
Main(String[] args)
{
int
N = 13;
findNthNum(N);
}
}
// This code is contributed by Princi Singh
chevron_rightfilter_noneOutput:36
Time Complexity : O(Partition of Number)
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