Merge transactions in bank sheets in the order of their occurrence such that their sum remains positive

Given an array arr[][] consisting of N lists representing N transactions, the task is to merge the given lists of transactions in the order of their occurrences, such that at any point of time, the sum of already performed transactions is non-negative. If found to negative, then print "-1". Otherwise, print the merged list of transactions.

Examples:

Input: arr[][] = {{100 ? 400 ? -1000 ? -500}, {-300 ? 2000 ? -500}}
Output: 100 ? 400 ? -300 ? 2000 ? -500 ? -1000 ? -500
Explanation: The sum at every instant of the above list of transactions is given by {100, 500, 200, 2200, 1700, 700, 200}, which has no negative values.

Input: arr[][] = [[100 ? 400]]
Output: 100 400

Approach: The given problem can be visualized as a variation of merge K-sorted linked lists with criteria that the sum of the merged list of transactions at any instant should be non-negative. 
Follow the steps below to solve the problem:

• Initialize a new node, say P, that denotes the head of the constructed Linked List.
• Initialize a priority queue, say PQ, of size N to implement a Max Heap.
• Insert the first N transactions as nodes into PQ.
• Iterate until PQ is non-empty and perform the following steps:
  • Pop the top node of the priority queue and insert that node at the end of the list, having head P.
  • If the next node of the popped node exists, then insert the next node of the popped node in PQ.
• After completing the above steps, print the linked list formed having head P.

Below is the implementation of the above approach:-

100 400 -300 2000 -500 -1000 -500

Time Complexity: O(N * log K)
Auxiliary Space: O(K)