Added merge_k_sorted_list algo in linked_list

data_structures/linked_list/merge_k_sorted_list.py

@@ -0,0 +1,114 @@
+"""This algorithm merges k sorted linked lists into a single sorted linked list.
+
+Each input linked list is assumed to be sorted in non-decreasing order. The algorithm uses a min-heap (priority queue) to efficiently determine the next smallest node among all the heads of the lists.
+
+At every step:
+
+The smallest element among the current nodes of all lists is extracted from the heap.
+
+That node is appended to the result list.
+
+The next node from the same list (if any) is then pushed into the heap.
+
+This process repeats until all nodes from all lists have been processed.
+The final result is a single sorted linked list containing all elements from the input lists.
+
+Solve on:
+https://leetcode.com/problems/merge-k-sorted-lists/
+"""
+
+from __future__ import annotations
+from collections.abc import Iterable, Iterator
+from dataclasses import dataclass
+import heapq
+
+
+test_data_odd = (3, 9, -11, 0, 7, 5, 1, -1)
+test_data_even = (4, 6, 2, 0, 8, 10, 3, -2)
+test_data_mixed = (1, 4, 7), (2, 5, 8), (3, 6, 9)
+
+
+@dataclass
+class Node:
+    data: int
+    next_node: Node | None
+
+
+class SortedLinkedList:
+    def __init__(self, ints: Iterable[int]) -> None:
+        self.head: Node | None = None
+        for i in sorted(ints, reverse=True):
+            self.head = Node(i, self.head)
+
+    def __iter__(self) -> Iterator[int]:
+        node = self.head
+        while node:
+            yield node.data
+            node = node.next_node
+
+    def __len__(self) -> int:
+        return sum(1 for _ in self)
+
+    def __str__(self) -> str:
+        return " -> ".join([str(node) for node in self])
+
+
+def merge_two_lists(
+    sll_one: SortedLinkedList, sll_two: SortedLinkedList
+) -> SortedLinkedList:
+    """Merge two sorted linked lists."""
+    return SortedLinkedList(list(sll_one) + list(sll_two))
+
+
+def merge_k_sorted_lists(lists: list[SortedLinkedList]) -> SortedLinkedList:
+    """
+    Merge k sorted linked lists into one sorted linked list.
+
+    >>> SSL = SortedLinkedList
+    >>> lists = [SSL([1, 4, 7]), SSL([2, 5, 8]), SSL([3, 6, 9])]
+    >>> merged = merge_k_sorted_lists(lists)
+    >>> str(merged)
+    '1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9'
+    >>> len(merged)
+    9
+    """
+    # Create a min-heap (stores tuples of value, index, node)
+    heap: list[tuple[int, int, Node]] = []
+    for i, sll in enumerate(lists):
+        if sll.head:
+            heapq.heappush(heap, (sll.head.data, i, sll.head))
+
+    dummy = Node(0, None)
+    current = dummy
+
+    while heap:
+        value, idx, node = heapq.heappop(heap)
+        current.next_node = Node(value, None)
+        current = current.next_node
+
+        if node.next_node:
+            heapq.heappush(heap, (node.next_node.data, idx, node.next_node))
+
+    # Convert to SortedLinkedList for consistency
+    result = SortedLinkedList([])
+    result.head = dummy.next_node
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    SSL = SortedLinkedList
+
+    # Example usage
+    list1 = SSL(test_data_odd)
+    list2 = SSL(test_data_even)
+    list3 = SSL([-15, -10, -5, 0, 5])
+    merged_k = merge_k_sorted_lists([list1, list2, list3])
+
+    print("Merged K Sorted Lists:")
+    print(merged_k)
+
+"""
+"""