HeapSort 堆排序 基于伪代码实现

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GIF 动态图 

 

 

伪代码

/* From Wikipedia, the free encyclopedia */

1.父子节点特征

iParent = floor((i-1) / 2);
iLeftChild = 2*i + 1;
iRightChild = 2*i + 2;

2.算法伪代码

/* 保持原汁原味就不翻译了 =。= */

procedure heapsort(a, count) is
    input: an unordered array a of length count
 
    (Build the heap in array a so that largest value is at the root)
    heapify(a, count)

    (The following loop maintains the invariants that a[0:end] is a heap and every element
     beyond end is greater than everything before it (so a[end:count] is in sorted order))
    end ← count - 1
    while end > 0 do
        (a[0] is the root and largest value. The swap moves it in front of the sorted elements.)
        swap(a[end], a[0])
        (the heap size is reduced by one)
        end ← end - 1
        (the swap ruined the heap property, so restore it)
        siftDown(a, 0, end)

(Put elements of 'a' in heap order, in-place)
procedure heapify(a, count) is
    (start is assigned the index in 'a' of the last parent node)
    (the last element in a 0-based array is at index count-1; find the parent of that element)
    start ← floor ((count - 2) / 2)
    
    while start ≥ 0 do
        (sift down the node at index 'start' to the proper place such that all nodes below
         the start index are in heap order)
        siftDown(a, start, count - 1)
        (go to the next parent node)
        start ← start - 1
    (after sifting down the root all nodes/elements are in heap order)

(Repair the heap whose root element is at index 'start', assuming the heaps rooted at its children are valid)
procedure siftDown(a, start, end) is
    root ← start

    while root * 2 + 1 ≤ end do    (While the root has at least one child)
        child ← root * 2 + 1       (Left child)
        swap ← root                (Keeps track of child to swap with)

        if a[swap] < a[child]
            swap ← child
        (If there is a right child and that child is greater)
        if child+1 ≤ end and a[swap] < a[child+1]
            swap ← child + 1
        if swap = root
            (The root holds the largest element. Since we assume the heaps rooted at the
             children are valid, this means that we are done.)
            return
        else
            swap(a[root], a[swap])
            root ← swap            (repeat to continue sifting down the child now)

Java实现

 

    public void heapsort(int[] a, int count) {
        if (count < 2)
            return;
        heapify(a, count);
        int end = count - 1;
        while (end > 0) {
            swap(a, 0, end);
            end--;
            siftdown(a, 0, end);
        }
    }
    public void heapify(int[] a, int count) {
        int start = (count - 2) / 2;
        while (start >= 0) {
            siftdown(a, start, count - 1);
            start--;
        }
    }
    public void siftdown(int[] a, int start, int end) {
        int root = start;

        while (root * 2 + 1 <= end) {
            int child = root * 2 + 1;
            int swap = root;

            if (a[swap] < a[child]) {
                swap = child;
            }
            if (child + 1 <= end && a[swap] < a[child + 1]) {
                swap = child + 1;
            }
            if (root == swap) {
                return;
            } else {
                swap(a, root, swap);
            }
            root = swap;
        }
    }
    public void swap(int[] a, int i, int j) {
        int t = a[i];
        a[i] = a[j];
        a[j] = t;
    }