added merge interval problem on the array data structure (#14009)

* added merge interval problem on the array ds

* removed typing which is  deprecated

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Refactor type hints in merge_intervals function

Updated type hints from List to built-in list for compatibility.

* Enhance merge_intervals function documentation

Added edge cases handling and updated complexity notes.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Refactor docstring and type hints in merge_intervals

Updated type hints and docstring formatting in merge_intervals function.

* Refactor merge_intervals function docstring

Updated docstring formatting and improved error message clarity.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update data_structures/arrays/merge_intervals.py

Co-authored-by: priya-sundaram-dev <oc-409d01@agentmail.to>

* updating DIRECTORY.md

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: priya-sundaram-dev <oc-409d01@agentmail.to>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 4 people

DIRECTORY.md

@@ -269,6 +269,7 @@
     * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py)
     * [Kth Largest Element](data_structures/arrays/kth_largest_element.py)
     * [Median Two Array](data_structures/arrays/median_two_array.py)
+    * [Merge Intervals](data_structures/arrays/merge_intervals.py)
     * [Merge Sorted](data_structures/arrays/merge_sorted.py)
     * [Monotonic Array](data_structures/arrays/monotonic_array.py)
     * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py)

data_structures/arrays/merge_intervals.py

@@ -0,0 +1,64 @@
+def 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.
+    """
+
+    if not intervals:
+        return []
+
+    for interval in intervals:
+        msg = f"Each interval must have exactly 2 integers, got {interval}"
+        if len(interval) != 2:
+            raise ValueError(msg)
+
+    # Sort intervals based on the start time
+    # Sort a copy so the caller's list (and its inner lists) are never mutated
+    sorted_intervals = sorted(intervals, key=lambda interval: interval[0])
+
+    merged: list[list[int]] = [sorted_intervals[0][:]]
+
+    for current in sorted_intervals[1:]:
+        last = merged[-1]
+
+        # If current interval overlaps with the last merged interval
+        if current[0] <= last[1]:
+            last[1] = max(last[1], current[1])
+        else:
+            merged.append(current[:])
+    return merged