6.5-9 merge k sorted lists into one sorted list with O(n lg k)

Give an O(n lg k)-time algorithm to merge k sorted lists into one sorted list,

where n is the total number of elements in all the input lists. (Hint: Use a minheap

for k-way merging.)

Solution

1. For each sorted list, maintain a 0 initilized array of k elements each representing the index of the current element to be dealt.

2. Build a k-element max heap, the elements are from the cur head of the k sorted list.

3. Each time, get the max from the heap, (lg k) and insert a new element from which the max of the heap is from before the delete.(lg k ) These two steps can be combined to consume only a single lg k, instead of a double lg k -> Record the max, replace the max with the new element, and then let it sink downward.

If all elements from a certain array has dealt, use minux INT_MAX as 

4. Put the max at the final array of element N.

5. repeat 3 and 4, until the number of dealt elements is N.

From: http://blog.youkuaiyun.com/cheetach119/article/details/9353035