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Merge k sorted lists into a sorted list in O(n lg k), HINT: use a min-heap, *CORMEN Introduction to Algorithms exercise
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| from math import floor | |
| class Heap: | |
| def __init__(self): | |
| self.nodes = list() | |
| self.heap_size = -1 | |
| def __left(self, i): | |
| return i * 2 + 1 | |
| def __right(self, i): | |
| return i * 2 + 2 | |
| def __parent(self, i): | |
| return int(floor(i/2)) | |
| def insert(self, element): | |
| element = element[:] # original lists shouldn't be edited. | |
| self.nodes.append(element) | |
| self.heap_size += 1 | |
| i = self.heap_size | |
| while i > 0 and self.nodes[self.__parent(i)][0] > self.nodes[i][0]: | |
| self.nodes[i], self.nodes[self.__parent(i)] = self.nodes[self.__parent(i)], self.nodes[i] | |
| i = self.__parent(i) | |
| def heapify(self, i): | |
| min_i = i | |
| if self.heap_size >= self.__left(i): | |
| if self.nodes[i][0] > self.nodes[self.__left(i)][0]: | |
| min_i = self.__left(i) | |
| if self.heap_size >= self.__right(i): | |
| if self.nodes[min_i][0] > self.nodes[self.__right(i)][0]: | |
| min_i = self.__right(i) | |
| if min_i != i: | |
| self.nodes[i], self.nodes[min_i] = self.nodes[min_i], self.nodes[i] | |
| self.heapify(min_i) | |
| def extract(self): | |
| if self.heap_size >= 0: | |
| x = self.nodes[0][0] | |
| del self.nodes[0][0] | |
| if not len(self.nodes[0]): | |
| self.nodes[self.heap_size - 1], self.nodes[0] = self.nodes[0], self.nodes[self.heap_size - 1] | |
| del self.nodes[self.heap_size - 1] | |
| self.heap_size -= 1 | |
| if self.heap_size >= 0: | |
| self.heapify(0) | |
| return x | |
| def extract_all(self): | |
| data = list() | |
| while self.heap_size >= 0: | |
| data.append(self.extract()) | |
| return data | |
| heap = Heap() | |
| heap.insert([2, 4, 5, 8, 13, 22]) | |
| heap.insert([1, 3, 6, 10, 11, 13]) | |
| heap.insert([4, 5, 7, 8, 9, 40]) | |
| heap.insert([5, 6, 10, 12, 20, 22]) | |
| print heap.extract_all() |
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