Create smallestRange.py

greedy_methods/smallestRange.py

@@ -0,0 +1,68 @@
+"""
+https://medium.com/@saiashish3760/leetcode-q632-smallest-range-covering-elements-from-k-lists-q507-496c21157914
+"""
+
+import doctest
+import heapq
+
+
+def smallest_range(nums):
+    """
+    Finds the smallest range that includes at least one number 
+    from each of the k lists.
+
+    The function uses a min heap to efficiently find the smallest range.
+    Each time, it pops the smallest element from the 
+    heap and adds the next element from the same list to 
+    maintain the invariant of having one element from each list in the heap.
+
+    Args:
+        nums (list of list of int): A list of k lists of sorted integers 
+        in non-decreasing order.
+
+    Returns:
+        list: A list containing two integers representing the smallest range.
+
+    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]
+    """
+
+    # Create a min heap to store the first element from each list
+    min_heap = []
+    current_max = float("-inf")
+
+    # Initialize the heap with the first element from each list
+    for i, list_ in enumerate(nums):
+        heapq.heappush(min_heap, (list_[0], i, 0))
+        current_max = max(current_max, list_[0])
+
+    # Initialize the smallest range as the largest possible
+    smallest_range = [float("-inf"), float("inf")]
+
+    while min_heap:
+        current_min, list_index, element_index = heapq.heappop(min_heap)
+
+        # Update the smallest range if the current range is smaller
+        if current_max - current_min < smallest_range[1] - smallest_range[0]:
+            smallest_range = [current_min, current_max]
+
+        # Break if rreaching the end of one of the lists
+        if element_index == len(nums[list_index]) - 1:
+            break
+
+        # Add the next element from the same list to the heap
+        next_element = nums[list_index][element_index + 1]
+        heapq.heappush(min_heap, (next_element, list_index, element_index + 1))
+        current_max = max(current_max, next_element)
+
+    return smallest_range
+
+
+if __name__ == "__main__":
+    doctest.testmod()
+    example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
+    output1 = smallest_range(example1)
+    print("Smallest Range:", output1)  # Smallest Range: [20, 24]