data_structures.arrays.merge_intervals
======================================

.. py:module:: data_structures.arrays.merge_intervals


Functions
---------

.. autoapisummary::

   data_structures.arrays.merge_intervals.merge_intervals


Module Contents
---------------

.. py:function:: merge_intervals(intervals: list[list[int]]) -> list[list[int]]

   Merge all overlapping intervals.

   Each interval is represented as a list of two integers [start, end].
   The function merges overlapping intervals and returns a list of
   non-overlapping intervals sorted by start time.

   Parameters:
   intervals (list[list[int]]): A list of intervals.

   Returns:
   list[list[int]]: A list of merged non-overlapping intervals.

   Edge Cases Handled:
   - Empty list: returns []
   - Single interval: returns the interval itself
   - Intervals already sorted or unsorted
   - Fully overlapping intervals
   - Invalid intervals (e.g., [[]] or intervals not having exactly
     2 integers) raise ValueError

   Examples:
   >>> merge_intervals([[1, 3], [2, 6], [8, 10], [15, 18]])
   [[1, 6], [8, 10], [15, 18]]
   >>> merge_intervals([[1, 4], [4, 5]])
   [[1, 5]]
   >>> merge_intervals([[6, 8], [1, 3], [2, 4]])
   [[1, 4], [6, 8]]
   >>> merge_intervals([])
   []
   >>> merge_intervals([[1, 4]])
   [[1, 4]]

   Time Complexity:
   O(n log n) - sorting the intervals, where n is the number of intervals.

   Space Complexity:
   O(n) - storing the merged intervals.