Solve interval merging and histogram area

The coding round included two algorithm problems:

1. Merge overlapping intervals: Given a list of closed intervals [[start1, end1], [start2, end2], ...], merge all overlapping intervals and return a new list of non-overlapping intervals sorted by start time.

2. Maximum rectangle in a histogram: Given an array of non-negative integers where each value represents the height of a histogram bar of width 1, return the maximum rectangular area that can be formed using one or more consecutive bars.