Create smallestRange.py (TheAlgorithms#11179)

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* Update and rename smallestRange.py to smallestrange.py

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 3 people

greedy_methods/smallest_range.py

@@ -0,0 +1,71 @@
+"""
+smallest_range function takes a list of sorted integer lists and finds the smallest
+range that includes at least one number from each list, using a min heap for efficiency.
+"""
+
+from heapq import heappop, heappush
+from sys import maxsize
+
+
+def smallest_range(nums: list[list[int]]) -> list[int]:
+    """
+    Find the smallest range from each list in nums.
+
+    Uses min heap for efficiency. The range includes at least one number from each list.
+
+    Args:
+        nums: List of k sorted integer lists.
+
+    Returns:
+        list: Smallest range as a two-element list.
+
+    Examples:
+    >>> smallest_range([[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]])
+    [20, 24]
+    >>> smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
+    [1, 1]
+    >>> smallest_range(((1, 2, 3), (1, 2, 3), (1, 2, 3)))
+    [1, 1]
+    >>> smallest_range(((-3, -2, -1), (0, 0, 0), (1, 2, 3)))
+    [-1, 1]
+    >>> smallest_range([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    [3, 7]
+    >>> smallest_range([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+    [0, 0]
+    >>> smallest_range([[], [], []])
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    """
+
+    min_heap: list[tuple[int, int, int]] = []
+    current_max = -maxsize - 1
+
+    for i, items in enumerate(nums):
+        heappush(min_heap, (items[0], i, 0))
+        current_max = max(current_max, items[0])
+
+    # Initialize smallest_range with large integer values
+    smallest_range = [-maxsize - 1, maxsize]
+
+    while min_heap:
+        current_min, list_index, element_index = heappop(min_heap)
+
+        if current_max - current_min < smallest_range[1] - smallest_range[0]:
+            smallest_range = [current_min, current_max]
+
+        if element_index == len(nums[list_index]) - 1:
+            break
+
+        next_element = nums[list_index][element_index + 1]
+        heappush(min_heap, (next_element, list_index, element_index + 1))
+        current_max = max(current_max, next_element)
+
+    return smallest_range
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    print(f"{smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])}")  # Output: [1, 1]