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用Python实现数据结构之优先级队列

5b51 2022/1/14 8:24:16 python 字数 47396 阅读 610 来源 www.jb51.cc/python

优先级队列 如果我们给每个元素都分配一个数字来标记其优先级,不妨设较小的数字具有较高的优先级,这样我们就可以在一个集合中访问优先级最高的元素并对其进行查找和删除操作了。这样,我们就引入了优先级队列 这

概述

<div class="markdown-here-wrapper" data-md-url="https://i.cnblogs.com/EditPosts.aspx?postid=10346607"&gt;
<h1 id="-" style="margin: 20px 0px 10px; padding: 0px; font-weight: bold; color: black; font-size: 24px; border-bottom: 2px solid #aaaaaa;">优先级队列
<blockquote style="margin: 1.2em 0px; border-left: 4px solid #dddddd; padding: 0px 1em; color: #777777; quotes: none;">
<p style="margin: 0px 0px 1.2em !important; font-size: 16px; line-height: 1.75em; padding-right: 0.5em; padding-left: 0.5em;">如果我们给每个元素都分配一个数字来标记其优先级,不妨设较小的数字具有较高的优先级,这样我们就可以在一个集合中访问优先级最高的元素并对其进行查找和删除操作了。这样,我们就引入了优先级队列 这种数据结构@H_404_1@

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一个元组来表示元素和它的优先级,将所有的元组都放到列表中存储,接下来当想要找到其中优先级最小的元组时会有以下两种方式@H_404_1@

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一个结论:@H_404_1@

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=2^h-1+1且n<=2^h-1+2^h@H_404_1@

=log(n+1)-1@H_404_1@

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包括向堆中添加一个元素和堆向上冒泡@H_404_1@

添加元素时要为了满足 完全二叉树的特性,需要将其放到树最下层的最右节点的最右位置,如果最下层已经满了,则放到再下一层的最左位置。@H_404_1@

一个很有趣的算法,为了使添加元素后的树满足堆排序,需要做一定的调整,调整方法为将添加的元素的优先级与其父节点相比较,如果小于父节点,则该元素与父节点交换,然后再与新的父节点比较,知道父节点小于了自己的优先级或者自己成为了根节点。如图:@H_404_1@

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删除之后,就变成了两颗分离的树,为了保持二叉树的完整性,我们要进行如下操作@H_404_1@

删除这最下层最右端的节点,然后再进行堆的向下排序@H_404_1@

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404_1@@H_404_1@

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函数为f(p)@H_404_1@

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一个元素就是二叉树的最下层的最右端的元素@H_404_1@

代码:@H_404_1@

 :
    

<span class="hljs-class"><span class="hljs-keyword" style="font-weight: bold;">class <span class="hljs-title" style="font-weight: bold; color: #0048ab;">HeapPriorityQueue<span class="hljs-params">():

<span class="hljs-string" style="color: #0048ab;"&gt;"""
使用堆与列表实现的优先级队列
"""</span>

<span class="hljs-class"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;class</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;Item</span><span class="hljs-params"&gt;()</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    队列中的项类
    """</span>

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self,key,value)</span>:</span>
        self.key = key
        self.value = value

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__it__</span><span class="hljs-params"&gt;(self,other)</span>:</span>
        <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.key < other.key

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;is_empty</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self) == <span class="hljs-number"&gt;0</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;parent</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    返回父节点的索引
    """</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (j - <span class="hljs-number"&gt;1</span>) // <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回左孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;1</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回右孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""通过判断索引是否出了列表来判断是否存在"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.left(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.right(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;swap</span><span class="hljs-params"&gt;(self,i,j)</span>:</span>
    self.data[i],self.data[j] = self.data[j],self.data[i]

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;upheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向上堆排序"""</span>
    parent = self.parent(j)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> j > <span class="hljs-number"&gt;0</span> <span class="hljs-keyword" style="font-weight: bold;"&gt;and</span> self.data[j] < self.data[parent]:
        self.swap(j,parent)
        self.upheap(parent)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;downheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向下堆排序"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_left(j):
        left = self.left(j)
        small = left
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_right(j):
            right = self.right(j)
            <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[right] < self.data[left]:
                small = right
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[small] < self.data[j]:
            self.swap(small,j)
            self.downheap(small)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self)</span>:</span>
    self.data = []

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__len__</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;add</span><span class="hljs-params"&gt;(self,value)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""<a href="https://www.jb51.cc/tag/tianjia/" target="_blank" class="keywords">添加</a><a href="https://www.jb51.cc/tag/yige/" target="_blank" class="keywords">一个</a>元素,并进行向上堆排序"""</span>
    self.data.append(self.Item(key,value))
    self.upheap(len(self.data) - <span class="hljs-number"&gt;1</span>)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    item = self.data[<span class="hljs-number"&gt;0</span>]
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;remove_min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    self.swap(<span class="hljs-number"&gt;0</span>,len(self.data) - <span class="hljs-number"&gt;1</span>)
    item = self.data.pop()
    self.downheap(<span class="hljs-number"&gt;0</span>)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)

<span class="hljs-string" style="color: #0048ab;"&gt;"""
使用堆与列表实现的优先级队列
"""</span>

<span class="hljs-class"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;class</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;Item</span><span class="hljs-params"&gt;()</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    队列中的项类
    """</span>

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self,key,value)</span>:</span>
        self.key = key
        self.value = value

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__it__</span><span class="hljs-params"&gt;(self,other)</span>:</span>
        <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.key < other.key

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;is_empty</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self) == <span class="hljs-number"&gt;0</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;parent</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    返回父节点的索引
    """</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (j - <span class="hljs-number"&gt;1</span>) // <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回左孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;1</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回右孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""通过判断索引是否出了列表来判断是否存在"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.left(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.right(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;swap</span><span class="hljs-params"&gt;(self,i,j)</span>:</span>
    self.data[i],self.data[j] = self.data[j],self.data[i]

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;upheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向上堆排序"""</span>
    parent = self.parent(j)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> j > <span class="hljs-number"&gt;0</span> <span class="hljs-keyword" style="font-weight: bold;"&gt;and</span> self.data[j] < self.data[parent]:
        self.swap(j,parent)
        self.upheap(parent)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;downheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向下堆排序"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_left(j):
        left = self.left(j)
        small = left
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_right(j):
            right = self.right(j)
            <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[right] < self.data[left]:
                small = right
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[small] < self.data[j]:
            self.swap(small,j)
            self.downheap(small)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self)</span>:</span>
    self.data = []

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__len__</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;add</span><span class="hljs-params"&gt;(self,value)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""<a href="https://www.jb51.cc/tag/tianjia/" target="_blank" class="keywords">添加</a><a href="https://www.jb51.cc/tag/yige/" target="_blank" class="keywords">一个</a>元素,并进行向上堆排序"""</span>
    self.data.append(self.Item(key,value))
    self.upheap(len(self.data) - <span class="hljs-number"&gt;1</span>)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    item = self.data[<span class="hljs-number"&gt;0</span>]
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;remove_min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    self.swap(<span class="hljs-number"&gt;0</span>,len(self.data) - <span class="hljs-number"&gt;1</span>)
    item = self.data.pop()
    self.downheap(<span class="hljs-number"&gt;0</span>)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)

<span class="hljs-class"><span class="hljs-keyword" style="font-weight: bold;">class <span class="hljs-title" style="font-weight: bold; color: #0048ab;">HeapPriorityQueue<span class="hljs-params">():

<span class="hljs-class"><span class="hljs-keyword" style="font-weight: bold;">class <span class="hljs-title" style="font-weight: bold; color: #0048ab;">HeapPriorityQueue<span class="hljs-params">():

<span class="hljs-string" style="color: #0048ab;"&gt;"""
使用堆与列表实现的优先级队列
"""</span>

<span class="hljs-class"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;class</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;Item</span><span class="hljs-params"&gt;()</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    队列中的项类
    """</span>

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self,key,value)</span>:</span>
        self.key = key
        self.value = value

    <span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__it__</span><span class="hljs-params"&gt;(self,other)</span>:</span>
        <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.key < other.key

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;is_empty</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self) == <span class="hljs-number"&gt;0</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;parent</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""
    返回父节点的索引
    """</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (j - <span class="hljs-number"&gt;1</span>) // <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回左孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;1</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""返回右孩子索引"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> <span class="hljs-number"&gt;2</span> * j + <span class="hljs-number"&gt;2</span>

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_left</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""通过判断索引是否出了列表来判断是否存在"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.left(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;has_right</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> self.right(j) < len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;swap</span><span class="hljs-params"&gt;(self,i,j)</span>:</span>
    self.data[i],self.data[j] = self.data[j],self.data[i]

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;upheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向上堆排序"""</span>
    parent = self.parent(j)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> j > <span class="hljs-number"&gt;0</span> <span class="hljs-keyword" style="font-weight: bold;"&gt;and</span> self.data[j] < self.data[parent]:
        self.swap(j,parent)
        self.upheap(parent)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;downheap</span><span class="hljs-params"&gt;(self,j)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""向下堆排序"""</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_left(j):
        left = self.left(j)
        small = left
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.has_right(j):
            right = self.right(j)
            <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[right] < self.data[left]:
                small = right
        <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.data[small] < self.data[j]:
            self.swap(small,j)
            self.downheap(small)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;<a href="https://www.jb51.cc/tag/init/" target="_blank" class="keywords">__init__</a></span><span class="hljs-params"&gt;(self)</span>:</span>
    self.data = []

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;__len__</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> len(self.data)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;add</span><span class="hljs-params"&gt;(self,value)</span>:</span>
    <span class="hljs-string" style="color: #0048ab;"&gt;"""<a href="https://www.jb51.cc/tag/tianjia/" target="_blank" class="keywords">添加</a><a href="https://www.jb51.cc/tag/yige/" target="_blank" class="keywords">一个</a>元素,并进行向上堆排序"""</span>
    self.data.append(self.Item(key,value))
    self.upheap(len(self.data) - <span class="hljs-number"&gt;1</span>)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    item = self.data[<span class="hljs-number"&gt;0</span>]
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)

<span class="hljs-function"&gt;<span class="hljs-keyword" style="font-weight: bold;"&gt;def</span> <span class="hljs-title" style="font-weight: bold; color: #0048ab;"&gt;remove_min</span><span class="hljs-params"&gt;(self)</span>:</span>
    <span class="hljs-keyword" style="font-weight: bold;"&gt;if</span> self.is_empty():
        <span class="hljs-keyword" style="font-weight: bold;"&gt;raise</span> Empty(<span class="hljs-string" style="color: #0048ab;"&gt;'Priority queue is empty'</span>)
    self.swap(<span class="hljs-number"&gt;0</span>,len(self.data) - <span class="hljs-number"&gt;1</span>)
    item = self.data.pop()
    self.downheap(<span class="hljs-number"&gt;0</span>)
    <span class="hljs-keyword" style="font-weight: bold;"&gt;return</span> (item.key,item.value)


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