堆排序(Java数组实现)

堆排序：利用大根堆

数组全部入堆，再出堆从后向前插入回数组中，数组就从小到大有序了。

public class MaxHeap<T extends Comparable<? super T>> {
    private T[] data;
    private int size;
    private int capacity;

    public MaxHeap(int capacity) {
        this.data = (T[]) new Comparable[capacity + 1];
        size = 0;
        this.capacity = capacity;
    }

    public int size() {
        return this.size;
    }

    public boolean isEmpty() {
        return size == 0;
    }

    public int getCapacity() {
        return this.capacity;
    }

    /**
     * @return 查看最大根(只看不删, 与popMax对比)
     */
    public T seekMax() {
        return data[1];
    }

    public void swap(int i, int j) {
        if (i != j) {
            T temp = data[i];
            data[i] = data[j];
            data[j] = temp;
        }
    }

    public void insert(T item) {
        size++;
        data[size] = item;
        shiftUp(size);
    }

    /**
     * @return 弹出最大根(弹出意味着删除, 与seekMax对比)
     */
    public T popMax() {
        swap(1, size--);
        shiftDown(1);
        return data[size + 1];
    }

    /**
     * @param child 孩子节点下角标是child，父节点下角表是child/2
     */
    public void shiftUp(int child) {
        while (child > 1 && data[child].compareTo(data[child / 2]) > 0) {
            swap(child, child / 2);
            child = child / 2;
        }
    }

    /**
     * @param a data数组中某个元素的下角标
     * @param b data数组中某个元素的下角标
     * @return 哪个元素大就返回哪个的下角标
     */
    private int max(int a, int b) {
        if (data[a].compareTo(data[b]) < 0) {//如果data[b]大
            return b;//返回b
        } else {//如果data[a]大
            return a;//返回a
        }
    }

    /**
     * @param a data数组中某个元素的下角标
     * @param b data数组中某个元素的下角标
     * @param c data数组中某个元素的下角标
     * @return 哪个元素大就返回哪个的下角标
     */
    private int max(int a, int b, int c) {
        int biggest = max(a, b);
        biggest = max(biggest, c);
        return biggest;
    }


    /**
     * @param father 父节点下角标是father,左右两个孩子节点的下角表分别是：father*2 和 father*2+1
     */
    public void shiftDown(int father) {
        while (true) {
            int lchild = father * 2;//左孩子
            int rchild = father * 2 + 1;//右孩子
            int newFather = father;//newFather即将更新，父、左、右三个结点谁大，newFather就是谁的下角标

            if (lchild > size) {//如果该father结点既没有左孩子，也没有右孩子
                return;
            } else if (rchild > size) {//如果该father结点只有左孩子，没有右孩子
                newFather = max(father, lchild);
            } else {//如果该father结点既有左孩子，又有右孩子
                newFather = max(father, lchild, rchild);
            }

            if (newFather == father) {//说明father比两个子结点都要大，表名已经是大根堆，不用继续调整了
                return;
            } else {//否则，还需要继续调整堆，直到满足大根堆条件为止
                swap(father, newFather);//值进行交换
                father = newFather;//更新father的值，相当于继续调整shiftDown(newFather)
            }
        }
    }

    public static <T extends Comparable<? super T>> void sort(T[] arr) {
        int len = arr.length;
        //入堆
        MaxHeap<T> maxHeap = new MaxHeap<T>(len);
        for (int i = 0; i < len; i++) {
            maxHeap.insert(arr[i]);
        }
        //出堆
        for (int i = len - 1; i >= 0; i--) {
            arr[i] = maxHeap.popMax();
        }
    }

    public static void printArr(Object[] arr) {
        for (Object o : arr) {
            System.out.print(o);
            System.out.print("\t");
        }
        System.out.println();
    }

    public static void main(String args[]) {
        Integer[] arr = {3, 5, 1, 7, 2, 9, 8, 0, 4, 6};
        printArr(arr);//3   5   1   7   2   9   8   0   4   6
        sort(arr);
        printArr(arr);//0   1   2   3   4   5   6   7   8   9
    }
}

堆排序：对数组进行构造堆(最大堆)

public class MaxHeap<T extends Comparable<? super T>> {
    private T[] data;
    private int size;
    private int capacity;

    public MaxHeap(int capacity) {
        this.capacity = capacity;
        this.size = 0;
        this.data = (T[]) new Comparable[capacity + 1];
    }

    public MaxHeap(T[] arr) {//heapify,数组建堆
        capacity = arr.length;
        data = (T[]) new Comparable[capacity + 1];
        System.arraycopy(arr, 0, data, 1, arr.length);
        size = arr.length;
        for (int i = size / 2; i >= 1; i--) {
            shiftDown(i);
        }
    }

    public int size() {
        return this.size;
    }

    public int getCapacity() {
        return this.capacity;
    }

    public boolean isEmpty() {
        return size == 0;
    }

    public T seekMax() {
        return data[1];
    }

    public void swap(int i, int j) {
        if (i != j) {
            T temp = data[i];
            data[i] = data[j];
            data[j] = temp;
        }
    }

    public void insert(T item) {
        size++;
        data[size] = item;
        shiftUp(size);
    }

    public T popMax() {
        swap(1, size--);
        shiftDown(1);
        return data[size + 1];
    }

    public void shiftUp(int child) {
        while (child > 1 && data[child].compareTo(data[child / 2]) > 0) {
            swap(child, child / 2);
            child /= 2;
        }
    }

    /**
     * @param a data数组中某个元素的下角标
     * @param b data数组中某个元素的下角标
     * @return 哪个元素大就返回哪个的下角标
     */
    private int max(int a, int b) {
        if (data[a].compareTo(data[b]) < 0) {//如果data[b]大
            return b;//返回b
        } else {//如果data[a]大
            return a;//返回a
        }
    }

    /**
     * @param a data数组中某个元素的下角标
     * @param b data数组中某个元素的下角标
     * @param c data数组中某个元素的下角标
     * @return 哪个元素大就返回哪个的下角标
     */
    private int max(int a, int b, int c) {
        int biggest = max(a, b);
        biggest = max(biggest, c);
        return biggest;
    }

    public void shiftDown(int father) {
        while (true) {
            int lchild = father * 2;
            int rchild = father * 2 + 1;
            int newFather = father;//这里赋不赋值无所谓，如果把下面这个return改成break,那就必须赋值了

            if (lchild > size) {//如果没有左、右孩子
                return;
            } else if (rchild > size) {//如果没有右孩子
                newFather = max(father, lchild);
            } else {//如果有左、右孩子
                newFather = max(father, lchild, rchild);
            }

            if (newFather == father) {//如果原父结点就是三者最大，则不用继续整理堆了
                return;
            } else {//父节点不是最大，则把大的孩子交换上来，然后继续往下堆调整，直到满足大根堆为止
                swap(newFather, father);
                father = newFather;//相当于继续shiftDown(newFather)。假如newFather原来是father的左孩子，那就相当于shiftDown(2*father)
            }
        }
    }

    public static <T extends Comparable<? super T>> void sort(T[] arr) {
        int len = arr.length;
        MaxHeap<T> maxHeap = new MaxHeap<>(arr);
        for (int i = len - 1; i >= 0; i--) {
            arr[i] = maxHeap.popMax();
        }
    }

    public static void printArr(Object[] arr) {
        for (Object o : arr) {
            System.out.print(o);
            System.out.print("\t");
        }
        System.out.println();
    }

    public static void main(String args[]) {
        Integer[] arr = {3, 5, 1, 7, 2, 9, 8, 0, 4, 6};
        printArr(arr);//3   5   1   7   2   9   8   0   4   6
        sort(arr);
        printArr(arr);//0   1   2   3   4   5   6   7   8   9
    }
}