Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 5 | Bit Manipulation
5.3 Given an integer, print the next smallest and next largest number that have the same
number of 1 bits in their binary representation.
SOLUTION
pg 58
The Brute Force Approach:
An easy approach is simply brute force: count the number of 1’s in n, and then increment
(or decrement) until you find a number with the same number of 1’s. Easy - but not terribly
interesting. Can we do something a bit more optimal? Yes!
Number Properties Approach for Next Number
Observations:
»»
If we “turn on” a 0, we need to “turn off” a 1
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If we turn on a 0 at bit i and turn off a 1 at bit j, the number changes by 2^i - 2^j.
»»
If we want to get a bigger number with the same number of 1s and 0s, i must be bigger
than j.
Solution:
1. Traverse from right to left. Once we’ve passed a 1, turn on the next 0. We’ve now increased
the number by 2^i. Yikes! Example: xxxxx011100 becomes xxxxx111100
2. Turn off the one that’s just to the right side of that. We’re now bigger by 2^i - 2^(i-1)
Example: xxxxx111100 becomes xxxxx101100
3. Make the number as small as possible by rearranging all the 1s to be as far right as possible:
Example: xxxxx101100 becomes xxxxx100011
To get the previous number, we do the reverse.
1. Traverse from right to left. Once we’ve passed a zero, turn off the next 1. Example:
xxxxx100011 becomes xxxxx000011.
2. Turn on the 0 that is directly to the right. Example: xxxxx000011 becomes
xxxxx010011.
3. Make the number as big as possible by shifting all the ones as far to the left as possible.
Example: xxxxx010011 becomes xxxxx011100 .
And now, for the code. Note the emphasis on pulling common code out into a reusable function.
Your interviewer will look for “clean code” like this.
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Cracking the Coding Interview | Concepts and Algorithms