[PHP] Principle and implementation code of heap sorting

The main content of this article is to use PHP to implement heap sorting, which has certain reference value. Interested friends can learn about it.

1. Heap (binary heap): It can be regarded as a complete binary tree. Except for the bottom layer, every level is full, which allows the heap to use arrays. To represent, each node corresponds to an element in the array

2. Given the subscript of a node, the subscript of the parent node and the child node can be calculated Standard; parent(i)=floor(i/2) left(i)=2i right=2i 1
3. Maximum heap and minimum heap, maximum heap: the root node is the maximum value, minimum heap: the root node is the minimum value

4. Heap sorting is to take out the maximum number at the top of the maximum heap, continue to adjust the remaining heap to the maximum heap, and take out the maximum number at the top of the heap again until the remaining Numbers have only one end

5. Maximum heap adjustment (maintain the maximum heap, the child node is always smaller than the parent node); create a maximum heap (adjust an array into an array of the maximum heap); Heap sort (create maximum heap, exchange, maintain maximum heap)

maxHeapify (array,index,heapSize) //最大堆调整
    iMax,iLeft,iRight
    while true
        iMax=index;iLeft=2*index+1;iRight=2*index+2
        如果根结点小于左右子树里结点值,就交换一下这两个值
        利用第三方变量,交换下两个值
buildMaxHeap(array) //创建最大堆,把一个数组调整成最大堆的数组
    iParent=floor((size-1)/2)
    for i=iParent;i>=0;i--
        maxHeapify (array,i,size)
sort(arr)
    buildMaxHeap(array, heapSize);//创建最大堆
    for (int i = heapSize - 1; i > 0; i--) {
        swap(array, 0, i); //交换第一个和最后一个
         maxHeapify(array, 0, i);//维护最大堆,size小了一个

//交换元素
function swap(&$arr,$a,$b){
        $temp=$arr[$a];
        $arr[$a]=$arr[$b];
        $arr[$b]=$temp;
}
//排序的入口函数
function heapSort(&$arr){
        $heapSize=count($arr);
        buildMaxHeap($arr, $heapSize);//创建最大堆
        for ($i = $heapSize - 1; $i > 0; $i--) {
                swap($arr,0,$i); //交换第一个和最后一个
                maxHeapify($arr, 0, $i);//维护最大堆,size小了一个
        }   
}
//创建最大堆的函数
function buildMaxHeap(&$arr, $heapSize){
        $iParent=floor(($heapSize-1)/2);//根据最后一个元素的索引值计算该结点根结点的索引是哪个
        for($i=$iParent;$i>=0;$i--){//这个循环是循环的所有根结点
                maxHeapify($arr,$i,$heapSize);//维护最大堆
        }   
}
//维护最大堆
function maxHeapify(&$arr,$index,$heapSize){
        $iMax=0;$iLeft=0;$iRight=0;
        while(true){
                $iMax=$index;
                $iLeft=2*$iMax+1;
                $iRight=2*$iMax+2;
                if($iLeft<$heapSize && $arr[$iLeft]>$arr[$iMax]){
                        $iMax=$iLeft;
                }   
                if($iRight<$heapSize && $arr[$iRight]>$arr[$iMax]){
                        $iMax=$iRight;
                }   
                if($iMax!=$index){
                        swap($arr,$index,$iMax);
                        $index=$iMax;
                }else{
                        break;
                }   
        }   
}
$arr=array(2,1,3,5,9,6);
heapSort($arr);
var_dump($arr);

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