Find Intersections Between Two Interval Lists

Problem Statement

You are given two lists of closed intervals, listA and listB, where each interval is represented as [start, end]. In both lists, intervals are disjoint and sorted in ascending order by their start times.

Your task is to compute the intersection of these two interval lists. An intersection exists if there is at least one point common to an interval from listA and an interval from listB. Since both lists contain closed intervals, the intersection of [a1, a2] and [b1, b2] is [max(a1, b1), min(a2, b2)], provided that max(a1, b1) <= min(a2, b2).

Implement the function find_intersections(listA, listB):

def find_intersections(listA, listB):
    # listA and listB are lists of lists, e.g., [[0, 2], [5, 10]]
    pass

Examples

Example 1: Input: listA = [[0, 2], [5, 10]], listB = [[1, 5], [8, 12]] Output: [[1, 2], [5, 5], [8, 10]] Explanation: The interval [1, 2] is the intersection of [0, 2] and [1, 5]. [5, 5] is the intersection of [5, 10] and [1, 5]. [8, 10] is the intersection of [5, 10] and [8, 12].

Example 2: Input: listA = [[1, 3], [5, 9]], listB = [] Output: []

Constraints

• 0 <= len(listA), len(listB) <= 10^5
• start <= end for all intervals.
• The lists are sorted and intervals within a single list are disjoint.

Edge Cases

• Empty lists should return an empty list.
• Intervals that touch at a single point (e.g., [1, 2] and [2, 3]) should result in an intersection of [2, 2].