堆排序实例(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
 }
}

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