algorithm-explained.md

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Prompt

An interval is represented as a pair of numbers. We will only consider intervals of the form [begin, end) where the interval is inclusive of the left point and exclusive of the right. Write a python class to represent these intervals and write a python function that checks if these intervals overlap. Try to use as few compares as possible.

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ASSISTANT: Here is a possible implementation of a Python class to represent intervals and a function to check if they overlap:

class Interval:

    def __init__(self, begin, end):

        self.begin = begin

        self.end = end

    

    def overlaps(self, other):

        return self.begin < other.end and self.end > other.begin

The Interval class has two attributes, begin and end, representing the left and right endpoints of the interval, respectively. The overlaps method takes another Interval object as an argument and returns True if the two intervals overlap, and False otherwise.

This implementation checks for overlap using only two comparisons: one to check if the left endpoint of one interval is less than the right endpoint of the other interval, and another to check if the right endpoint of one interval is greater than the left endpoint of the other interval. These conditions are sufficient to determine whether there is any overlap between the two intervals.

To test this implementation, we can create two intervals and check if they overlap:

# create two intervals [1, 5) and [4, 8)

interval1 = Interval(1, 5)

interval2 = Interval(4, 8)



# check if they overlap

print(interval1.overlaps(interval2)) # True

In this example, the two intervals overlap at the point [4, 5), so the overlaps method correctly returns True.