Suppose we have some lists, these are sorted. We have to merge these lists into one list. To solve this, we will use the heap data structure. So if the lists are [1,4,5], [1,3,4], [2,6], then the final list will be [1,1,2,3,4,4,5,6].
To solve this, we will follow these steps −
make one heap
for each linked list l in lists −
if is in not 0, then insert I into a heap
res := null and res_next := null
Do one infinite loop −
temp := min of heap
if heap has no element, then return res
if res is 0, then
res := temp, res_next := temp
temp := next element of temp
if temp is not zero, then insert temp into heap
next of res := null
otherwise −
next of res_next := temp, temp := next of temp, res_next := next of res_next
if temp is not null, then insert temp into heap
next of res_next := null
Example
Let us see the following implementation to get a better understanding −
class ListNode: def __init__(self, data, next = None): self.val = data self.next = next def make_list(elements): head = ListNode(elements[0]) for element in elements[1:]: ptr = head while ptr.next: ptr = ptr.next ptr.next = ListNode(element) return head def print_list(head): ptr = head print('[', end = "") while ptr: print(ptr.val, end = ", ") ptr = ptr.next print(']') class Heap: def __init__(self): self.arr = [] def print_heap(self): res = " " for i in self.arr: res += str(i.val) + " " print(res) def getVal(self,i): return self.arr[i].val def parent(self,i): return (i-1)//2 def left(self,i): return (2*i + 1) def right(self,i): return (2*i + 2) def insert(self,value): self.arr.append(value) n = len(self.arr)-1 i = n while i != 0 and self.arr[i].val<self.arr[self.parent(i)].val: self.arr[i],self.arr[self.parent(i)] = self.arr[self.parent(i)],self.arr[i] i = self.parent(i) def heapify(self,i): left = self.left(i) right = self.right(i) smallest = i n= len(self.arr) if left<n and self.getVal(left)<self.getVal(smallest): smallest = left if right <n and self.getVal(right)<self.getVal(smallest): smallest = right if smallest!=i: self.arr[i],self.arr[smallest] = self.arr[smallest],self.arr[i] self.heapify(smallest) def extractMin(self): n = len(self.arr) if n==0: return '#' if n== 1: temp =self.arr[0] self.arr.pop() return temp root = self.arr[0] self.arr[0] = self.arr[-1] self.arr.pop() self.heapify(0) return root class Solution(object): def mergeKLists(self, lists): heap = Heap() for i in lists: if i: heap.insert(i) res = None res_next = None while True: temp = heap.extractMin() if temp == "#": return res if not res: res = temp res_next = temp temp = temp.next if temp: heap.insert(temp) res.next = None else: res_next.next = temp temp = temp.next res_next=res_next.next if temp: heap.insert(temp) res_next.next = None ob = Solution() lists = [[1,4,5],[1,3,4],[2,6]] lls = [] for ll in lists: l = make_list(ll) lls.append(l) print_list(ob.mergeKLists(lls))
Input
[[1,4,5],[1,3,4],[2,6]]
Output
[1, 1, 2, 3, 4, 4, 5, 6, ]