AVL树----java

AVL树是高度平衡的二叉查找树

1.单旋转LL旋转

理解记忆：1.在不平衡的节点的左孩子的左孩子插入导致的不平衡，所以叫LL

private AVLTreeNode<T> leftLeftRotation(AVLTreeNode<T> k2) {AVLTreeNode<T> k1;k1 = k2.left;k2.left = k1.right;k1.right = k2;k2.height = max( height(k2.left), height(k2.right)) + 1;k1.height = max( height(k1.left), k2.height) + 1;return k1;
}

2.单旋转RR

理解记忆：1.不平衡节点的右孩子的有孩子插入导致的不平衡，所以叫RR

private AVLTreeNode<T> rightRightRotation(AVLTreeNode<T> k1) {AVLTreeNode<T> k2;k2 = k1.right;k1.right = k2.left;k2.left = k1;k1.height = max( height(k1.left), height(k1.right)) + 1;k2.height = max( height(k2.right), k1.height) + 1;return k2;
}

3.双旋转LR

理解记忆：1.不平衡节点的左孩子的有孩子导致的不平衡，所以叫LR

2.须要先对k1  RR,再对根K3  LL

private AVLTreeNode<T> leftRightRotation(AVLTreeNode<T> k3) {k3.left = rightRightRotation(k3.left);return leftLeftRotation(k3);
}

4.双旋转RL

理解记忆：1.不平衡节点的右孩子的左孩子导致的不平衡，所以叫RL

2.须要先对k3 LL,在对k1 RR

private AVLTreeNode<T> rightLeftRotation(AVLTreeNode<T> k1) {k1.right = leftLeftRotation(k1.right);return rightRightRotation(k1);
}

5.AVL的样例

遍历，查找等和二叉查找树一样就不在列出，主要是 插入 和  删除

public class AVLTree<T extends Comparable<T>> {private AVLTreeNode<T> mRoot;    // 根结点// AVL树的节点(内部类)class AVLTreeNode<T extends Comparable<T>> {T key;                // keyword(键值)int height;         // 高度AVLTreeNode<T> left;    // 左孩子AVLTreeNode<T> right;    // 右孩子public AVLTreeNode(T key, AVLTreeNode<T> left, AVLTreeNode<T> right) {this.key = key;this.left = left;this.right = right;this.height = 0;}}// 构造函数public AVLTree() {mRoot = null;}/** 获取树的高度*/private int height(AVLTreeNode<T> tree) {if (tree != null)return tree.height;return 0;}public int height() {return height(mRoot);}/** 比較两个值的大小*/private int max(int a, int b) {return a>b ? a : b;}/** 前序遍历"AVL树"*/private void preOrder(AVLTreeNode<T> tree) {if(tree != null) {System.out.print(tree.key+" ");preOrder(tree.left);preOrder(tree.right);}}public void preOrder() {preOrder(mRoot);}/** 中序遍历"AVL树"*/private void inOrder(AVLTreeNode<T> tree) {if(tree != null){inOrder(tree.left);System.out.print(tree.key+" ");inOrder(tree.right);}}public void inOrder() {inOrder(mRoot);}/** 后序遍历"AVL树"*/private void postOrder(AVLTreeNode<T> tree) {if(tree != null) {postOrder(tree.left);postOrder(tree.right);System.out.print(tree.key+" ");}}public void postOrder() {postOrder(mRoot);}/** (递归实现)查找"AVL树x"中键值为key的节点*/private AVLTreeNode<T> search(AVLTreeNode<T> x, T key) {if (x==null)return x;int cmp = key.compareTo(x.key);if (cmp < 0)return search(x.left, key);else if (cmp > 0)return search(x.right, key);elsereturn x;}public AVLTreeNode<T> search(T key) {return search(mRoot, key);}/** (非递归实现)查找"AVL树x"中键值为key的节点*/private AVLTreeNode<T> iterativeSearch(AVLTreeNode<T> x, T key) {while (x!=null) {int cmp = key.compareTo(x.key);if (cmp < 0)x = x.left;else if (cmp > 0)x = x.right;elsereturn x;}return x;}public AVLTreeNode<T> iterativeSearch(T key) {return iterativeSearch(mRoot, key);}/* * 查找最小结点：返回tree为根结点的AVL树的最小结点。*/private AVLTreeNode<T> minimum(AVLTreeNode<T> tree) {if (tree == null)return null;while(tree.left != null)tree = tree.left;return tree;}public T minimum() {AVLTreeNode<T> p = minimum(mRoot);if (p != null)return p.key;return null;}/* * 查找最大结点：返回tree为根结点的AVL树的最大结点。*/private AVLTreeNode<T> maximum(AVLTreeNode<T> tree) {if (tree == null)return null;while(tree.right != null)tree = tree.right;return tree;}public T maximum() {AVLTreeNode<T> p = maximum(mRoot);if (p != null)return p.key;return null;}/** LL：左左相应的情况(左单旋转)。** 返回值：旋转后的根节点*/private AVLTreeNode<T> leftLeftRotation(AVLTreeNode<T> k2) {AVLTreeNode<T> k1;k1 = k2.left;k2.left = k1.right;k1.right = k2;k2.height = max( height(k2.left), height(k2.right)) + 1;k1.height = max( height(k1.left), k2.height) + 1;return k1;}/** RR：右右相应的情况(右单旋转)。** 返回值：旋转后的根节点*/private AVLTreeNode<T> rightRightRotation(AVLTreeNode<T> k1) {AVLTreeNode<T> k2;k2 = k1.right;k1.right = k2.left;k2.left = k1;k1.height = max( height(k1.left), height(k1.right)) + 1;k2.height = max( height(k2.right), k1.height) + 1;return k2;}/** LR：左右相应的情况(左双旋转)。** 返回值：旋转后的根节点*/private AVLTreeNode<T> leftRightRotation(AVLTreeNode<T> k3) {k3.left = rightRightRotation(k3.left);return leftLeftRotation(k3);}/** RL：右左相应的情况(右双旋转)。** 返回值：旋转后的根节点*/private AVLTreeNode<T> rightLeftRotation(AVLTreeNode<T> k1) {k1.right = leftLeftRotation(k1.right);return rightRightRotation(k1);}/* * 将结点插入到AVL树中，并返回根节点** 參数说明：*     tree AVL树的根结点*     key 插入的结点的键值* 返回值：*     根节点*/private AVLTreeNode<T> insert(AVLTreeNode<T> tree, T key) {if (tree == null) {// 新建节点tree = new AVLTreeNode<T>(key, null, null);if (tree==null) {System.out.println("ERROR: create avltree node failed!");return null;}} else {int cmp = key.compareTo(tree.key);if (cmp < 0) {    // 应该将key插入到"tree的左子树"的情况tree.left = insert(tree.left, key);// 插入节点后，若AVL树失去平衡，则进行相应的调节。if (height(tree.left) - height(tree.right) == 2) {if (key.compareTo(tree.left.key) < 0)tree = leftLeftRotation(tree);elsetree = leftRightRotation(tree);}} else if (cmp > 0) {    // 应该将key插入到"tree的右子树"的情况tree.right = insert(tree.right, key);// 插入节点后，若AVL树失去平衡，则进行相应的调节。if (height(tree.right) - height(tree.left) == 2) {if (key.compareTo(tree.right.key) > 0)tree = rightRightRotation(tree);elsetree = rightLeftRotation(tree);}} else {    // cmp==0System.out.println("加入�失败：不同意加入�同样的节点！");}}tree.height = max( height(tree.left), height(tree.right)) + 1;return tree;}public void insert(T key) {mRoot = insert(mRoot, key);}/* * 删除结点(z)，返回根节点** 參数说明：*     tree AVL树的根结点*     z 待删除的结点* 返回值：*     根节点*/private AVLTreeNode<T> remove(AVLTreeNode<T> tree, AVLTreeNode<T> z) {// 根为空 或者 没有要删除的节点，直接返回null。if (tree==null || z==null)return null;int cmp = z.key.compareTo(tree.key);if (cmp < 0) {        // 待删除的节点在"tree的左子树"中tree.left = remove(tree.left, z);// 删除节点后，若AVL树失去平衡，则进行相应的调节。if (height(tree.right) - height(tree.left) == 2) {AVLTreeNode<T> r =  tree.right;if (height(r.left) > height(r.right))tree = rightLeftRotation(tree);elsetree = rightRightRotation(tree);}} else if (cmp > 0) {    // 待删除的节点在"tree的右子树"中tree.right = remove(tree.right, z);// 删除节点后，若AVL树失去平衡，则进行相应的调节。if (height(tree.left) - height(tree.right) == 2) {AVLTreeNode<T> l =  tree.left;if (height(l.right) > height(l.left))tree = leftRightRotation(tree);elsetree = leftLeftRotation(tree);}} else {    // tree是相应要删除的节点。// tree的左右孩子都非空if ((tree.left!=null) && (tree.right!=null)) {if (height(tree.left) > height(tree.right)) {// 假设tree的左子树比右子树高；// 则(01)找出tree的左子树中的最大节点//   (02)将该最大节点的值赋值给tree。//   (03)删除该最大节点。// 这相似于用"tree的左子树中最大节点"做"tree"的替身；// 採用这样的方式的优点是：删除"tree的左子树中最大节点"之后，AVL树仍然是平衡的。AVLTreeNode<T> max = maximum(tree.left);tree.key = max.key;tree.left = remove(tree.left, max);} else {// 假设tree的左子树不比右子树高(即它们相等，或右子树比左子树高1)// 则(01)找出tree的右子树中的最小节点//   (02)将该最小节点的值赋值给tree。//   (03)删除该最小节点。// 这相似于用"tree的右子树中最小节点"做"tree"的替身；// 採用这样的方式的优点是：删除"tree的右子树中最小节点"之后，AVL树仍然是平衡的。AVLTreeNode<T> min = maximum(tree.right);tree.key = min.key;tree.right = remove(tree.right, min);}} else {AVLTreeNode<T> tmp = tree;tree = (tree.left!=null) ? tree.left : tree.right;tmp = null;}}return tree;}public void remove(T key) {AVLTreeNode<T> z; if ((z = search(mRoot, key)) != null)mRoot = remove(mRoot, z);}/* * 销毁AVL树*/private void destroy(AVLTreeNode<T> tree) {if (tree==null)return ;if (tree.left != null)destroy(tree.left);if (tree.right != null)destroy(tree.right);tree = null;}public void destroy() {destroy(mRoot);}/** 打印"二叉查找树"** key        -- 节点的键值 * direction  --  0，表示该节点是根节点;*               -1，表示该节点是它的父结点的左孩子;*                1，表示该节点是它的父结点的右孩子。*/private void print(AVLTreeNode<T> tree, T key, int direction) {if(tree != null) {if(direction==0)    // tree是根节点System.out.printf("%2d is root\n", tree.key, key);else                // tree是分支节点System.out.printf("%2d is %2d's %6s child\n", tree.key, key, direction==1?"right" : "left");print(tree.left, tree.key, -1);print(tree.right,tree.key,  1);}}public void print() {if (mRoot != null)print(mRoot, mRoot.key, 0);}
}

文章大量參考：http://www.cnblogs.com/skywang12345/p/3577479.html