? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? AVL樹----java

AVL樹是高度平衡的二叉查找樹

1.單旋轉LL旋轉

理解記憶：1.在不平衡的節點的左孩子的左孩子插入導致的不平衡，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.單旋轉RR

理解記憶：1.不平衡節點的右孩子的有孩子插入導致的不平衡，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.雙旋轉LR

理解記憶：1.不平衡節點的左孩子的有孩子導致的不平衡，所以叫LR

? ? ? ? ? ? ? ? ? ? ?2.須要先對k1 ?RR,再對根K3 ?LL

private AVLTreeNode<T> leftRightRotation(AVLTreeNode<T> k3) {k3.left = rightRightRotation(k3.left);return leftLeftRotation(k3); } 4.雙旋轉RL

理解記憶：1.不平衡節點的右孩子的左孩子導致的不平衡，所以叫RL

? ? ? ? ? ? ? ? ? ? ?2.須要先對k3 LL,在對k1 RR

private AVLTreeNode<T> rightLeftRotation(AVLTreeNode<T> k1) {k1.right = leftLeftRotation(k1.right);return rightRightRotation(k1); }5.AVL的樣例

遍歷，查找等和二叉查找樹一樣就不在列出，主要是 插入 和 ?刪除

public class AVLTree<T extends Comparable<T>> {private AVLTreeNode<T> mRoot; // 根結點// AVL樹的節點(內部類)class AVLTreeNode<T extends Comparable<T>> {T key; // keyword(鍵值)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;}}// 構造函數public AVLTree() {mRoot = null;}/** 獲取樹的高度*/private int height(AVLTreeNode<T> tree) {if (tree != null)return tree.height;return 0;}public int height() {return height(mRoot);}/** 比較兩個值的大小*/private int max(int a, int b) {return a>b ? a : b;}/** 前序遍歷"AVL樹"*/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);}/** 中序遍歷"AVL樹"*/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);}/** 后序遍歷"AVL樹"*/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);}/** (遞歸實現)查找"AVL樹x"中鍵值為key的節點*/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);}/** (非遞歸實現)查找"AVL樹x"中鍵值為key的節點*/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);}/* * 查找最小結點：返回tree為根結點的AVL樹的最小結點。*/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;}/* * 查找最大結點：返回tree為根結點的AVL樹的最大結點。*/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：左左相應的情況(左單旋轉)。** 返回值：旋轉后的根節點*/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：右右相應的情況(右單旋轉)。** 返回值：旋轉后的根節點*/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：左右相應的情況(左雙旋轉)。** 返回值：旋轉后的根節點*/private AVLTreeNode<T> leftRightRotation(AVLTreeNode<T> k3) {k3.left = rightRightRotation(k3.left);return leftLeftRotation(k3);}/** RL：右左相應的情況(右雙旋轉)。** 返回值：旋轉后的根節點*/private AVLTreeNode<T> rightLeftRotation(AVLTreeNode<T> k1) {k1.right = leftLeftRotation(k1.right);return rightRightRotation(k1);}/* * 將結點插入到AVL樹中，并返回根節點** 參數說明：* tree AVL樹的根結點* key 插入的結點的鍵值* 返回值：* 根節點*/private AVLTreeNode<T> insert(AVLTreeNode<T> tree, T key) {if (tree == null) {// 新建節點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) { // 應該將key插入到"tree的左子樹"的情況tree.left = insert(tree.left, key);// 插入節點后，若AVL樹失去平衡，則進行相應的調節。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) { // 應該將key插入到"tree的右子樹"的情況tree.right = insert(tree.right, key);// 插入節點后，若AVL樹失去平衡，則進行相應的調節。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�失敗：不同意加入�同樣的節點！");}}tree.height = max( height(tree.left), height(tree.right)) + 1;return tree;}public void insert(T key) {mRoot = insert(mRoot, key);}/* * 刪除結點(z)，返回根節點** 參數說明：* tree AVL樹的根結點* z 待刪除的結點* 返回值：* 根節點*/private AVLTreeNode<T> remove(AVLTreeNode<T> tree, AVLTreeNode<T> z) {// 根為空 或者 沒有要刪除的節點，直接返回null。if (tree==null || z==null)return null;int cmp = z.key.compareTo(tree.key);if (cmp < 0) { // 待刪除的節點在"tree的左子樹"中tree.left = remove(tree.left, z);// 刪除節點后，若AVL樹失去平衡，則進行相應的調節。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) { // 待刪除的節點在"tree的右子樹"中tree.right = remove(tree.right, z);// 刪除節點后，若AVL樹失去平衡，則進行相應的調節。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是相應要刪除的節點。// tree的左右孩子都非空if ((tree.left!=null) && (tree.right!=null)) {if (height(tree.left) > height(tree.right)) {// 假設tree的左子樹比右子樹高；// 則(01)找出tree的左子樹中的最大節點// (02)將該最大節點的值賦值給tree。// (03)刪除該最大節點。// 這相似于用"tree的左子樹中最大節點"做"tree"的替身；// 採用這樣的方式的優點是：刪除"tree的左子樹中最大節點"之后，AVL樹仍然是平衡的。AVLTreeNode<T> max = maximum(tree.left);tree.key = max.key;tree.left = remove(tree.left, max);} else {// 假設tree的左子樹不比右子樹高(即它們相等，或右子樹比左子樹高1)// 則(01)找出tree的右子樹中的最小節點// (02)將該最小節點的值賦值給tree。// (03)刪除該最小節點。// 這相似于用"tree的右子樹中最小節點"做"tree"的替身；// 採用這樣的方式的優點是：刪除"tree的右子樹中最小節點"之后，AVL樹仍然是平衡的。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);}/* * 銷毀AVL樹*/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"二叉查找樹"** key -- 節點的鍵值 * direction -- 0，表示該節點是根節點;* -1，表示該節點是它的父結點的左孩子;* 1，表示該節點是它的父結點的右孩子。*/private void print(AVLTreeNode<T> tree, T key, int direction) {if(tree != null) {if(direction==0) // tree是根節點System.out.printf("%2d is root\n", tree.key, key);else // tree是分支節點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

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