Question
What is the method to calculate the mean of two integers (or longs) without causing overflow, ensuring that the result truncates towards zero?
int mean(int a, int b) {
return (a & b) + ((a ^ b) >> 1);
}
Answer
Calculating the mean of two integer values can be straightforward, but special care must be taken to prevent overflow, especially when dealing with large values. Here, we will explore a safe method to compute the mean of two integers (or longs) that ensures the result truncates towards zero without risking overflow.
int mean(int a, int b) {
return (a & b) + ((a ^ b) >> 1);
}
Causes
- Calculating the mean using the formula (a + b) / 2 can lead to overflow if a and b are large integers.
- Integer overflow occurs when the result of an arithmetic operation exceeds the maximum limit of the data type.
Solutions
- Utilize bitwise operations to compute the mean without directly adding the two numbers.
- The formula used is (a & b) + ((a ^ b) >> 1), which effectively averages the two integers while preventing overflow.
Common Mistakes
Mistake: Using the formula (a + b) / 2 without checking for overflow.
Solution: Always use the bitwise approach to prevent overflow.
Mistake: Assuming that integer division will round properly when it may truncate instead.
Solution: When doing integer division, explicitly handle cases to ensure truncation behavior is as expected.
Helpers
- mean of two integers
- calculate mean without overflow
- integer mean calculation
- overflow-safe mean calculation
- truncated mean of integers
