This updated information has been further expanded upon on my new website. You can find the updated details here: https://k5kc.com/cs/algorithms/find-the-nearest-numbers-that-have-same-number-of-1s-for-an-integer/.
Problem
Given an integer, print the next smallest and next largest number that have the same number of 1 bits in their binary representation.Example
Next higher number for 3 is 5. i.e. (00000011 => 00000101)
Likewise next lower number of 5 is 3.
Solution
Method 1 - Adding or subtracting 1 until we have same number of 1sFor the next largest, keep adding 1 to the number until find the number that has same number of 1 bits. For the next smallest, keep decreasing 1.
public static int findNextSmallest(int number) { int result = number - 1; while (Integer.bitCount(result) != Integer.bitCount(number)) result--; return result; } public static int findNextLargest(int number) { int result = number + 1; while (Integer.bitCount(result) != Integer.bitCount(number)) result++; return result; }
Definitely gonna work but terribly boring. We know this is not what the interviewer expects, he wants some bit manipulation.
Method 2- Change the bits
For getting the next higher number
- Traverse from right to left i.e. LSB to MSB. 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. - 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 - Make the number as small as possible by rearranging all the 1s to be as far right as possible:
Example: xxxxx101100 becomes xxxxx100011
We can do something like this.
int getNextSmaller(int num) { return ~getNextLarger(~num); }i.e. follow the above algorithm for number's complement.
Java code
public static boolean GetBit(int n, int index) { return ((n & (1 << index)) > 0); } public static int SetBit(int n, int index, boolean b) { if (b) { return n | (1 << index); } else { int mask = ~(1 << index); return n & mask; } } public static int GetNext_NP(int n) { if (n <= 0) return -1; int index = 0; int countOnes = 0; // Find first one. while (!GetBit(n, index)) index++; // Turn on next zero. while (GetBit(n, index)) { index++; countOnes++; } n = SetBit(n, index, true); // Turn off previous one index--; n = SetBit(n, index, false); countOnes--; // Set zeros for (int i = index - 1; i >= countOnes; i--) { n = SetBit(n, i, false); } // Set ones for (int i = countOnes - 1; i >= 0; i--) { n = SetBit(n, i, true); } return n; } public static int GetPrevious_NP(int n) { if (n <= 0) return -1; // Error int index = 0; int countZeros = 0; // Find first zero. while (GetBit(n, index)) index++; // Turn off next 1. while (!GetBit(n, index)) { index++; countZeros++; } n = SetBit(n, index, false); // Turn on previous zero index--; n = SetBit(n, index, true); countZeros--; // Set ones for (int i = index - 1; i >= countZeros; i--) { n = SetBit(n, i, true); } // Set zeros for (int i = countZeros - 1; i >= 0; i--) { n = SetBit(n, i, false); } return n; }
References
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