Podcast Summary
Merging k sorted linked lists: Use a priority queue to efficiently merge k sorted linked lists into one sorted linked list by always picking the node with the smallest value and attaching it to the answer, while adjusting pointers accordingly.
To merge k sorted linked lists into one sorted linked list, the key is to always pick the node with the smallest value and attach it to the answer while adjusting pointers accordingly. However, directly implementing this approach with an array of k-sorted list heads would result in poor time complexity. A more efficient solution involves adding each list's head to a priority queue and repeatedly extracting the minimum value from it to build the final sorted linked list. This approach ensures a constant time complexity for extracting the minimum value from the priority queue.
Merging k sorted linked lists: An efficient algorithm to merge k sorted linked lists uses a priority queue, achieving a time complexity of O(n log k) and a space complexity of O(n)
The discussed algorithm merges k sorted linked lists into one sorted linked list using a priority queue. The time complexity is O(n log k), where n is the total number of nodes in all lists and k is the number of sorted-link lists. The priority queue allows for efficient addition and removal of elements, enabling the algorithm to maintain the minimum node from each list at each step. The space complexity is O(n + k), which can be simplified to O(n) as k is typically much smaller than n. The algorithm starts by creating a dummy node as a temporary head and a priority queue to store the minimum nodes from each list. It then adds all non-null heads to the priority queue and enters a main loop where it updates the current node by removing the minimum node from the priority queue, updates the next and previous pointers, and pushes the next node of the current list back to the priority queue. This process continues until all nodes have been processed, resulting in a single sorted linked list.