1. This solution is much faster on re-invocation than the one without the persistent num_ones variable. Unless of course it is performed on a much larger (than num_ones) array of 32-bit integer.
2. It is essential to have the statement
The reason for this is that the floor() function has a problem with precision. If can fail with 32-bit integer that are close to 2^32.
For instance, consider this Matlab code and system response:
Test if a Number is a Palindrome without using any String Operations
Is the Point in a Circle?
Convert from Base 10 to base 5
Graceful Double Wheel Graph
Maximum Intra-Vector Swaps
RISK Calculator - Large Armies, High Accuracy, Fast
Create Circular Perfect Square Sequence
Battleship - Seaman Level
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