heapsort | 易学教程

how to build heap tree?

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问题 I understand the algorithm of building heap tree (max or min) but i don't understand the code of it: First: How does this loop build a max heap?, why we started the i with n/2-1 ? // Build heap (rearrange array) for (int i = n / 2 - 1; i >= 0; i--) heapify(arr, n, i); and this is the Heapify function: Secondly: how did we assume that largest is "i" ? Third: why we heapify again in the last line? // To heapify a subtree rooted with node i which is // an index in arr[]. n is size of heap void

Heapsort 和 priority queue

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一、二叉堆含义及属性: 堆（heap)亦被称为：优先队列（priority queue），是计算机科学中一类特殊的数据结构的统称。堆通常是一个可以被看做一棵完全二叉树的数组对象。在队列中，调度程序反复提取队列中第一个作业并运行，因而实际情况中某些时间较短的任务将等待很长时间才能结束，或者某些不短小，但具有重要性的作业，同样应当具有优先权。堆即为解决此类问题设计的一种数据结构。同垃圾收集存储的堆含义不同。表示堆的数组A有两个属性: A.length : 代表A数组的元素个数; A.heapsize : 代表A数组中属于堆元素个数。有时候(排序时)，数组A的部分元素不属于堆。刚开始建堆的是偶，A.heapsize = A.length，排序时，每次从堆顶取出最大值，A.heapsize递减，直至排序完成. 下图是一个建好后的二叉堆: 从图中可知，已知某节点的索引值i，可以轻松获取其对应父节点，左,右子节点的索引值。有: Parent(i) return i/2; 或者 return i >> 1; Left(i) return i*2; 或者 return i << 1; Right(i) return i*2+1; 或者 return (i << 1) + 1; 二叉堆分两种: 最大堆，最小堆，均遵循堆属性。最大堆，每个节点i满足: A[Parent(i)] ≥ A[i]

Iterative in place sub-list Heap Sort python implementation

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问题 I've found different versions of heap sort for python, but I can't seem to find the one that matches my needs. Iterative Heap Sort is the closest I found, but I can't quite figure out how to change it to work with a sub-list (index start, index end) and remain in place. If I get it right then I'll post my answer here. If anyone has an implementation in even C or Java that will be great. 回答1: I managed to do what I want. This code works on objects and sorts by a specific attribute. def

Why use a flat list in heapsort?

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问题 In heapsort , the data is stored in something called a " heap ". Almost all the implementations I've seen use a flat list for the data structure. Can someone explain to me why this is? Why not use nested arrays or an instance of a binary Tree ? Isn't explicit better than implicit? Is it because of implementation difficulties like traversing the structure, or something else? 回答1: If you want to see how heapsort can be implemented in Python then look no further than the standard library module

Heapsort Algorithm using min-heap

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问题 When I implement heapsort using a min-heap it sorts the array from largest to smallest. Is this the desired output for a heapsort using min-heap ? It seems redundant to sort again to output smallest to largest after the sort is complete since the heap itself has a smallest to largest structure. CODE: #include <iostream> #include <vector> #include "random.h" #include "print.h" int parent(int i) { return (i - 1) / 2; } int left(int i) { if(i == 0) return 1; else return 2*i; } int right(int i) {

Heap sort Python implementation

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问题 def heap_sort(nos): global size size = len(nos) print "the size of the List is : %d " %size Build_heap(size,nos) for i in range(size-1,0,-1): nums[0],nums[i] = nums[i],nums[0] size = size-1 print "\n", nums heapify(nos,i,size) print "heap sort array:" ,nums def left_child(i): return 2*i+1 def right_child(i): return 2*i+2 def heapify(nums,i,size): l = left_child(i) r = right_child(i) if l <= size and r <= size: if r != size: if nums[l] >= nums[r]: max = nums[l] max_index = l elif nums[l] <=

BUILD-MAX-HEAP running time for array sorted in decreasing order

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问题 I know that the running time for BUILD-MAX-HEAP in heap sort is O(n) . But, if we have an array that already sorted in a decreasing order, why do we still have O(n) for the running time of BUILD-MAX-HEAP? Isn't it supposed to be something like O(1) ? It's already sorted from the maximum value to the minimum value, so we do not need MAX-HEAPIFY. Is my understanding correct? Could someone please explain it to me? 回答1: You are right. It can of course be O(1) . When you know for sure that your

BUILD-MAX-HEAP running time for array sorted in decreasing order

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Why does heapify swap the top of the heap with the element at the bottom of the heap?

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问题 In a max heap (assuming it's represented by an array), the top of the heap (ie. the largest value in the heap) swaps with the last element in the array (ie. one of the smallest values in the heap), the last element is removed, and then the new top-of-the-heap element swaps with other values to settle back into its proper place. Instead, why isn't the top element just removed and then other elements can "fill in" for the the heap? 回答1: One of the key properties of a heap is that the underlying

An intuitive understanding of heapsort?

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问题 At school we are currently learning sorting algorithms in Java and I got for my homework the Heap Sort. I did my reading, I tried to find out as much as I could, but it seems I just can't grasp the concept. I'm not asking you to write me a Java program, if you could just explain to me as simply as you can how the Heap Sort works. 回答1: Right, so basically you take a heap and pull out the first node in the heap - as the first node is guaranteed to be the largest / smallest depending on the