blocks|key|1440293|text|当使用基于数组的堆实现时，从最低到最高排序的数组是最小堆。父节点值小于或等于其子节点(2i+%2B1和2i+%2B+2，使用基于零的数组)的min堆属性适用于所有有子节点的节点。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1440294|最大堆的最小值位于其中一个叶节点中，但您不知道哪个节点。因为根据定义，最小节点不能有任何子节点，所以它必须是叶。但是，堆属性没有指定叶节点如何相互比较，只与它们的父节点进行比较。|1440295|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

An array sorted from lowest to highest is a min-heap when using the array-based heap implementation. The min-heap property that the parent node value is less than or equal to it's child nodes (2i + 1 and 2i + 2, using zero-based arrays) holds for all nodes that have children.
The minimum value of a max heap is in one of the leaf nodes, but you don't know which. Since the minimum node cannot, by definition, have any child nodes, it must be a leaf. The heap property, however, does not specify how leaf nodes compare with each other, only with their parent.

blocks|key|244311|text|排序数组是最小堆吗？|type|blockquote|depth|inlineStyleRanges|entityRanges|data|244312|是的，如果您正在使用典型的数组存储堆约定。|unstyled|244313|最大堆的最小值在哪里？|244314|在其中一片叶子上。确切地说是没有定义的。|244315|entityMap^0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|K|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|L|8|@]|9|@]|A|$]]|$1|E|3|F|5|6|7|M|8|@]|9|@]|A|$]]|$1|G|3|H|5|D|7|N|8|@]|9|@]|A|$]]|$1|I|3|-4|5|D|7|O|8|@]|9|@]|A|$]]]|J|$]]

<blockquote>
 Is a sorted array a min-heap?
</blockquote>

Yes, if you're using the typical array-stored heap convention.

<blockquote>
 Where is the minimum value of a max-heap?
</blockquote>

At one of the leaves. Which exactly is undefined.

blocks|key|1440386|text|您可以将二进制堆作为索引数组来实现，与2*i%2B1和2*i%2B2相比(我从0开始)。在min堆中ai+<+a2*i%2B1和ai+<+a2*i%2B2|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1440387|所以|1440388|1.排序数组是一个最小堆。|1440389|2.它没有具体的指数。我们只知道这只是一片叶子|1440390|我建议你读一下这个堆|offset|length|1440391|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Binary_heap^0|0|0|0|0|9|1|0|0^^$0|@$1|2|3|4|5|6|7|T|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|U|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|V|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|W|8|@]|9|@]|A|$]]|$1|H|3|I|5|6|7|X|8|@]|9|@$J|Y|K|Z|1|10]]|A|$]]|$1|L|3|-4|5|6|7|11|8|@]|9|@]|A|$]]]|M|$N|$5|O|P|Q|A|$R|S]]]]

You can implement binary heap as a array for index i compare with 2*i+1 and 2*i+2 (i starts from 0). in min heap a[i] &lt; a[2*i+1] and a[i] &lt; a[2*i+2]

so 

1 . A sorted array is a min heap.

2 . It hasn't specific index. All we know that it is just a leaf

I suggest you read this <a href="http://en.wikipedia.org/wiki/Binary_heap" rel="nofollow">http://en.wikipedia.org/wiki/Binary_heap</a>

blocks|key|244354|text|最大堆的最小值在哪里？|type|unstyled|depth|inlineStyleRanges|entityRanges|data|244355|Ans:+Max堆可以用简单的数组表示，索引从1开始到n。第一个元素是最大堆的根。堆属性:索引i处的节点在2i处有左子节点，在2i%2B1处有右子节点(如果2i和2i%2B1小于堆大小，即数组长度)。|244356|最大堆的叶节点从索引i%2B1到n。这里i=n/2；n是数组长度。其中一个叶节点具有最小值。|244357|因此，我们可以从ai%2B1的值找到最大堆的最小值。求最小值的时间复杂度是(n-i)的阶数.|244358|entityMap^0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|J|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|K|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|L|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|M|8|@]|9|@]|A|$]]|$1|H|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|I|$]]

where is the minimum value of a max heap?

Ans: Max heap can be represented using simple array with index start from 1 to n. 1st element is the root of the max heap.
Heap property: The node at index i has left child at 2i and right child at 2i+1 (if 2i and 2i+1 are less than heap size i.e. array length).

Leaf nodes of the max heap are found from index i+1 to n. Here i=n/2; n is array length. And one of the leaf nodes has the minimum value. 
So we can find the minimum value of max heap from the values of a[i+1] to a[n]. Time complexity to find minimum value is order-of(n-i).

blocks|key|244387|text|type|blockquote|depth|inlineStyleRanges|entityRanges|data|244388|排序数组是最小堆吗？|unordered-list-item|244389|如果排序升序--是的，一般来说，它是一个min堆，更准确地说--是二进制堆的一个数组，有以下规则：|unstyled|244390|索引i的节点的子节点可以在索引2i+%2B1和2i+%2B2处找到。|244391|索引i的节点的父节点可以在索引层((i-1)/2)找到。|244392|同时，它不能反向工作--基于数组的二进制堆不会存储排序列表。|244393|244394|最大堆的最小值在哪里？|244395|它没有定义，当您将密钥存储在一个min堆中时，这也不是您想要快速回答的问题。如果您希望能够在O(1)时间内查看堆的最小和最大值，可以使用像MinMaxPriorityQueue这样的类。|offset|length|244396|entityMap|0|LINK|mutability|MUTABLE|url|http://docs.guava-libraries.googlecode.com/git/javadoc/com/google/common/collect/MinMaxPriorityQueue.html^0|0|0|0|0|0|0|0|0|1X|J|0|0^^$0|@$1|2|3|-4|4|5|6|11|7|@]|8|@]|9|$]]|$1|A|3|B|4|C|6|12|7|@]|8|@]|9|$]]|$1|D|3|E|4|F|6|13|7|@]|8|@]|9|$]]|$1|G|3|H|4|C|6|14|7|@]|8|@]|9|$]]|$1|I|3|J|4|C|6|15|7|@]|8|@]|9|$]]|$1|K|3|L|4|F|6|16|7|@]|8|@]|9|$]]|$1|M|3|-4|4|5|6|17|7|@]|8|@]|9|$]]|$1|N|3|O|4|C|6|18|7|@]|8|@]|9|$]]|$1|P|3|Q|4|F|6|19|7|@]|8|@$R|1A|S|1B|1|1C]]|9|$]]|$1|T|3|-4|4|F|6|1D|7|@]|8|@]|9|$]]]|U|$V|$4|W|X|Y|9|$Z|10]]]]

<blockquote>
 <ul>
 <li>a sorted array is a min heap?</li>
 </ul>
</blockquote>

If it is ordered ascending - yes, generally speaking it is a min heap, more precisely - an array implementation of a binary heap with the following rules:

<ul>
<li>Children of the node with index i can be found at indexes 2i + 1 and 2i + 2</li>
<li>The parent of the node with index i can be found at index floor((i - 1)/2)</li>
</ul>

At the same time, it doesn't work in reverse - an array-based binary heap will not store a sorted list.

<blockquote>
 <ul>
 <li>where is the minimum value of a max heap?</li>
 </ul>
</blockquote>

It is not defined, and it is not the question that you want to answer quickly when you store your keys in a min heap. If you want to be able to peek both min and max of the heap in O(1) time, you can use classes like <a href="http://docs.guava-libraries.googlecode.com/git/javadoc/com/google/common/collect/MinMaxPriorityQueue.html" rel="nofollow">MinMaxPriorityQueue</a> in Java.

blocks|key|1794695|text|排序数组是最小堆吗？|type|blockquote|depth|inlineStyleRanges|entityRanges|data|1794696|排序数组不是最小堆就是最大堆，反之亦然。|unstyled|1794697|最小堆或最大堆不一定是排序数组.|1794698|最大堆的最小值是多少？|1794699|根据定义，max+-堆(或优先级队列)在O(1)时间内从集合中提供最大值。如果有人需要从最大堆中检索最小值，那么首先使用堆本身解决这个问题是不对的。这就像期望一个堆栈提供FIFO访问，或者期望队列提供LIFO访问。|1794700|但是jfyi，min值将在一棵树的叶子上形成成堆。可能在任何子树上。所以你需要另一个算法，它需要超过O(1)的时间来定位它。|1794701|作为附带说明：|1794702|具有n个元素的堆可能有1到(n%2B1)/2叶子。|1794703|如果由堆形成的树的高度是h，那么堆将有高达2%5E(h-1)的叶子。|1794704|entityMap^0|0|0|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|V|8|@]|9|@]|A|$]]|$1|E|3|F|5|D|7|W|8|@]|9|@]|A|$]]|$1|G|3|H|5|6|7|X|8|@]|9|@]|A|$]]|$1|I|3|J|5|D|7|Y|8|@]|9|@]|A|$]]|$1|K|3|L|5|D|7|Z|8|@]|9|@]|A|$]]|$1|M|3|N|5|D|7|10|8|@]|9|@]|A|$]]|$1|O|3|P|5|D|7|11|8|@]|9|@]|A|$]]|$1|Q|3|R|5|D|7|12|8|@]|9|@]|A|$]]|$1|S|3|-4|5|D|7|13|8|@]|9|@]|A|$]]]|T|$]]

<blockquote>
 Is a sorted array a min-heap? 
</blockquote>

sorted array is either min-heap or max-heap but vice versa is not true 
min-heap or max-heap are not necessarily sorted arrays. 

<blockquote>
 What is the minimum value of a max-heap? 
</blockquote>

max-heap (or priority queue) by definition provides max value from a collection in O(1) time. if anyone is required to retrieve min value from a max-heap then using heap itself in the first place for this problem is not right. it's like expecting a stack provide FIFO access or expecting queue to provide LIFO access.

But jfyi , min value will be at one of the leaves of the tree formed by heap. it could be on any subtree. so you need another algorithm which will take more than O(1) time to locate it. 
 
As a side note: 
A heap with n elements may have [ 1 to (n+1)/2] leaves. 
If height of the tree formed by heap is h then heap will have upto 2^(h-1) leaves

blocks|key|244485|text|数组可以按升序排序，也可以按降序排序。“排序数组是最小堆”的语句部分正确。该语句的正确版本是“按升序排序的数组可视为最小堆”，其互补语句是“按降序排列的数组可视为最大堆”。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|244486|“按升序排序的数组可视为最小堆”|244487|但请记住，“并非所有的最小堆都可以采用按升序排列的数组的形式”。|244488|关于最大堆的最小值，我们只知道它存在于叶中，我们可以在O(n)中搜索它。|244489|entityMap^0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|J|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|K|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|L|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|M|8|@]|9|@]|A|$]]|$1|H|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|I|$]]

Arrays either can be sorted in ascending order or in descending order.
The statement "A sorted array is min-heap" is partially correct. The correct version of this statement is "An array sorted in ascending order is can be treated as min- heap" and its complementry statement is "An array sorted in descending order can be treated as max heap".

"An array sorted in ascending order is can be treated as min- heap" 

But remember that "Not all min-heaps can take the form of array sorted in ascending order".

And about minimum value of max heap we only know that this is present in the leafs and we can search that in O(n)

blocks|key|244541|text|事实总是如此：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|244542|按升序排列的每个排序列表(按的顺序排列)都是一个min堆。|offset|length|style|BOLD|244543|试试看，这个规则也不例外！|244544|entityMap^0|0|C|2|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|M|8|@$D|N|E|O|F|G]]|9|@]|A|$]]|$1|H|3|I|5|6|7|P|8|@]|9|@]|A|$]]|$1|J|3|-4|5|6|7|Q|8|@]|9|@]|A|$]]]|K|$]]

Always True Fact is :
Every sorted list in ascending order is a minheap.
Try and test it, there is no exception about this rule!

I have studied min-heaps and max-heaps, and I have a couple of questions:

<ol>
<li>Is a sorted array a min-heap?</li>
<li>What is the minimum value of a max-heap?</li>
</ol>

Is a sorted array a min-heap? What's the minimum value of a max-heap?

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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我研究过最小堆和最大堆，我有几个问题：排序数组是最小堆吗？最大堆的最小值是多少？

问排序数组是最小堆吗？最大堆的最小值是多少？
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回答 8

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