轉(zhuǎn)自：http://blog.csdn.net/lovesqcc/article/details/6246615

為了克服對樹結(jié)構(gòu)編程的恐懼感，決心自己實現(xiàn)一遍二叉查找樹，以便掌握關(guān)于樹結(jié)構(gòu)編程的一些技巧和方法。以下是基本思路：

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??????? [1] 關(guān)于容器與封裝。封裝，是一種非常重要的系統(tǒng)設(shè)計思想；無論是面向過程的函數(shù)，還是面向?qū)ο蟮膶ο?#xff0c;都是實現(xiàn)抽象和封裝的技術(shù)手段。要使系統(tǒng)更加安全更具可維護性，就應(yīng)當將封裝思想謹記心中。容器是封裝思想的絕好示例。用戶對容器的印象應(yīng)該簡潔地表達為：A. 可以存入指定的東西； B. 可以取出所期望的東西。 而至于這容器中究竟有什么機關(guān)，藏的是毒蛇還是黃金，都是對用戶不可見的。二叉查找樹就是這樣一個容器。面向?qū)ο缶幊讨?#xff0c;為實現(xiàn)樹結(jié)構(gòu)，自然要對樹結(jié)點對象進行建模。這里采用了內(nèi)部類；外部類對二叉查找樹進行建模，而樹結(jié)點作為內(nèi)部類實現(xiàn)。

?

?????? [2] 本程序盡量實現(xiàn)一個比較實用的二叉查找樹，其中包括動態(tài)的插入、刪除操作；查詢給定關(guān)鍵字、最小關(guān)鍵字、最大關(guān)鍵字；獲取二叉樹的有序列表（用于排序）等。因為我希望以后還能用到這個容器的，而不僅僅是編程練習(xí)。二叉查找樹操作的大部分算法參考了《算法導(dǎo)論2》第12章內(nèi)容，刪除操作略顯笨拙。程序中有錯誤之處，歡迎指出。

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????? [3]? 程序如下：

?

?????

[c-sharp]?view plaincopyprint?

/**?

?*?@author?shuqin1984??2011-3-13?

?*??

?*?此程序?qū)崿F(xiàn)一個二叉查找樹的功能，可以進行動態(tài)插入、刪除關(guān)鍵字；?

?*?查詢給定關(guān)鍵字、最小關(guān)鍵字、最大關(guān)鍵字；轉(zhuǎn)換為有序列表(用于排序)?

?*??

?*??

?*/??

package?datastructure.tree;??

import?java.util.ArrayList;??

import?java.util.List;??

??

public?class?BinarySearchTree?{??

??????

????//?樹的根結(jié)點??

????private?TreeNode?root?=?null;??

??????

????//?遍歷結(jié)點列表??

????private?List<TreeNode>?nodelist?=?new?ArrayList<TreeNode>();??

??????

????private?class?TreeNode?{??

??????????

????????private?int?key;??

????????private?TreeNode?leftChild;??

????????private?TreeNode?rightChild;??

????????private?TreeNode?parent;??

??????????

????????public?TreeNode(int?key,?TreeNode?leftChild,?TreeNode?rightChild,?TreeNode?parent)?{??

????????????this.key?=?key;??

????????????this.leftChild?=?leftChild;??

????????????this.rightChild?=?rightChild;??

????????????this.parent?=?parent;??

????????}?????

????????public?int?getKey()?{??

????????????return?key;??

????????}??

????????public?String?toString()??

????????{??

????????????String?leftkey?=?(leftChild?==?null???""?:?String.valueOf(leftChild.key));????

????????????String?rightkey?=?(rightChild?==?null???""?:?String.valueOf(rightChild.key));???

????????????return?"("?+?leftkey?+?"?,?"?+?key?+?"?,?"?+?rightkey?+?")";??

????????}??

??????????

????}??

??????

????/**?

?????*?isEmpty:?判斷二叉查找樹是否為空；若為空，返回?true?，否則返回?false?.??

?????*??

?????*/??

????public?boolean?isEmpty()??

????{??

????????if?(root?==?null)?{??

????????????return?true;??

????????}?else?{??

????????????return?false;??

????????}?????????????

????}??

??????

????/**?

?????*?TreeEmpty:?對于某些二叉查找樹操作(比如刪除關(guān)鍵字)來說，若樹為空，則拋出異常。?

?????*/??

????public?void?TreeEmpty()?throws?Exception???

????{??

????????if?(isEmpty())?{??

????????????throw?new?Exception("樹為空!");??

????????}??

????}??

??????

????/**?

?????*?search:?在二叉查找樹中查詢給定關(guān)鍵字??

?????*?@param?key?給定關(guān)鍵字?

?????*?@return?匹配給定關(guān)鍵字的樹結(jié)點?

?????*/??

????public?TreeNode?search(int?key)???

????{??

????????TreeNode?pNode?=?root;??

????????while?(pNode?!=?null?&&?pNode.key?!=?key)?{??

????????????if?(key?<?pNode.key)?{??

????????????????pNode?=?pNode.leftChild;??

????????????}??

????????????else?{??

????????????????pNode?=?pNode.rightChild;??

????????????}??

????????}??

????????return?pNode;??

????}??

??????

????/**?

?????*?minElemNode:?獲取二叉查找樹中的最小關(guān)鍵字結(jié)點?

?????*?@return?二叉查找樹的最小關(guān)鍵字結(jié)點?

?????*?@throws?Exception?若樹為空，則拋出異常?

?????*/??

????public?TreeNode?minElemNode(TreeNode?node)?throws?Exception??

????{??

????????if?(node?==?null)?{??

????????????throw?new?Exception("樹為空！");??

????????}??

????????TreeNode?pNode?=?node;??

????????while?(pNode.leftChild?!=?null)?{??

????????????pNode?=?pNode.leftChild;??

????????}??

????????return?pNode;??

????}??

??????

????/**?

?????*?maxElemNode:?獲取二叉查找樹中的最大關(guān)鍵字結(jié)點?

?????*?@return?二叉查找樹的最大關(guān)鍵字結(jié)點?

?????*?@throws?Exception?若樹為空，則拋出異常?

?????*/??

????public?TreeNode?maxElemNode(TreeNode?node)?throws?Exception???

????{??

????????if?(node?==?null)?{??

????????????throw?new?Exception("樹為空！");??

????????}??

????????TreeNode?pNode?=?node;??

????????while?(pNode.rightChild?!=?null)?{??

????????????pNode?=?pNode.rightChild;??

????????}??

????????return?pNode;??

????}??

??????

????/**?

?????*?successor:?獲取給定結(jié)點在中序遍歷順序下的后繼結(jié)點?

?????*?@param?node?給定樹中的結(jié)點?

?????*?@return?若該結(jié)點存在中序遍歷順序下的后繼結(jié)點，則返回其后繼結(jié)點；否則返回?null?

?????*?@throws?Exception??

?????*/??

????public?TreeNode?successor(TreeNode?node)?throws?Exception??

????{??

????????if?(node?==?null)?{??

????????????return?null;??

????????}??

??????????

????????//?若該結(jié)點的右子樹不為空，則其后繼結(jié)點就是右子樹中的最小關(guān)鍵字結(jié)點??

????????if?(node.rightChild?!=?null)?{???

????????????return?minElemNode(node.rightChild);??

????????}??

????????//?若該結(jié)點右子樹為空??

????????TreeNode?parentNode?=?node.parent;??

????????while?(parentNode?!=?null?&&?node?==?parentNode.rightChild)?{??

????????????node?=?parentNode;??

????????????parentNode?=?parentNode.parent;??

????????}??

????????return?parentNode;??

????}??

??????

??????

????/**?

?????*?precessor:?獲取給定結(jié)點在中序遍歷順序下的前趨結(jié)點?

?????*?@param?node?給定樹中的結(jié)點?

?????*?@return?若該結(jié)點存在中序遍歷順序下的前趨結(jié)點，則返回其前趨結(jié)點；否則返回?null?

?????*?@throws?Exception??

?????*/??

????public?TreeNode?precessor(TreeNode?node)?throws?Exception??

????{??

????????if?(node?==?null)?{??

????????????return?null;??

????????}??

??????????

????????//?若該結(jié)點的左子樹不為空，則其前趨結(jié)點就是左子樹中的最大關(guān)鍵字結(jié)點??

????????if?(node.leftChild?!=?null)?{???

????????????return?maxElemNode(node.leftChild);??

????????}??

????????//?若該結(jié)點左子樹為空??

????????TreeNode?parentNode?=?node.parent;??

????????while?(parentNode?!=?null?&&?node?==?parentNode.leftChild)?{??

????????????node?=?parentNode;??

????????????parentNode?=?parentNode.parent;??

????????}??

????????return?parentNode;??

????}??

??????

??????

????/**?

?????*?insert:?將給定關(guān)鍵字插入到二叉查找樹中?

?????*?@param?key?給定關(guān)鍵字?

?????*/??

????public?void?insert(int?key)??

????{??

????????TreeNode?parentNode?=?null;??

????????TreeNode?newNode?=?new?TreeNode(key,?null,?null,null);??

????????TreeNode?pNode?=?root;??

????????if?(root?==?null)?{??

????????????root?=?newNode;??

????????????return?;??

????????}??

????????while?(pNode?!=?null)?{??

????????????parentNode?=?pNode;??

????????????if?(key?<?pNode.key)?{?????

????????????????pNode?=?pNode.leftChild;??

????????????}??

????????????else?if?(key?>?pNode.key)?{??

????????????????pNode?=?pNode.rightChild;??

????????????}?else?{??

????????????????//?樹中已存在匹配給定關(guān)鍵字的結(jié)點，則什么都不做直接返回????????????????????

????????????????return?;??

????????????}??

????????}??

????????if?(key?<?parentNode.key)?{??

????????????parentNode.leftChild?=?newNode;??

????????????newNode.parent?=?parentNode;??

????????}??

????????else?{??

????????????parentNode.rightChild?=?newNode;??

????????????newNode.parent?=?parentNode;??

????????}?????????

??????????

????}??

??????

????/**?

?????*?insert:?從二叉查找樹中刪除匹配給定關(guān)鍵字相應(yīng)的樹結(jié)點?

?????*?@param?key?給定關(guān)鍵字?

?????*/??

????public?void?delete(int?key)?throws?Exception??

????{??

????????TreeNode?pNode?=?search(key);??

????????if?(pNode?==?null)?{??

????????????throw?new?Exception("樹中不存在要刪除的關(guān)鍵字!");??

????????}??

????????delete(pNode);??

????}??

??????

????/**?

?????*?delete:?從二叉查找樹中刪除給定的結(jié)點.?

?????*?@param?pNode?要刪除的結(jié)點?

?????*??

?????*?前置條件：?給定結(jié)點在二叉查找樹中已經(jīng)存在?

?????*?@throws?Exception??

?????*/??

????private?void?delete(TreeNode?pNode)?throws?Exception???

????{??

??????????if?(pNode?==?null)?{??

??????????????return?;??

??????????}??

??????????if?(pNode.leftChild?==?null?&&?pNode.rightChild?==?null)?{?//?該結(jié)點既無左孩子結(jié)點，也無右孩子結(jié)點??

??????????????TreeNode?parentNode?=?pNode.parent;??

??????????????if?(pNode?==?parentNode.leftChild)?{??

??????????????????parentNode.leftChild?=?null;??

??????????????}?else?{??

??????????????????parentNode.rightChild?=?null;??

??????????????}??

??????????????return?;??

??????????}??

??????????if?(pNode.leftChild?==?null?&&?pNode.rightChild?!=?null)?{?//?該結(jié)點左孩子結(jié)點為空，右孩子結(jié)點非空??

??????????????TreeNode?parentNode?=?pNode.parent;??

??????????????if?(pNode?==?parentNode.leftChild)?{??

??????????????????parentNode.leftChild?=?pNode.rightChild;??

??????????????????pNode.rightChild.parent?=?parentNode;??

??????????????}??

??????????????else?{??

??????????????????parentNode.rightChild?=?pNode.rightChild;??

??????????????????pNode.rightChild.parent?=?parentNode;??

??????????????}??

??????????????return?;??

??????????}??

??????????if?(pNode.leftChild?!=?null?&&?pNode.rightChild?==?null)?{?//?該結(jié)點左孩子結(jié)點非空，右孩子結(jié)點為空??

??????????????TreeNode?parentNode?=?pNode.parent;??

??????????????if?(pNode?==?parentNode.leftChild)?{??

??????????????????parentNode.leftChild?=?pNode.leftChild;??

??????????????????pNode.rightChild.parent?=?parentNode;??

??????????????}??

??????????????else?{??

??????????????????parentNode.rightChild?=?pNode.leftChild;??

??????????????????pNode.rightChild.parent?=?parentNode;??

??????????????}??

??????????????return?;??

??????????}??

??????????//?該結(jié)點左右孩子結(jié)點均非空，則刪除該結(jié)點的后繼結(jié)點，并用該后繼結(jié)點取代該結(jié)點??

??????????TreeNode?successorNode?=?successor(pNode);??

??????????delete(successorNode);??

??????????pNode.key?=?successorNode.key;??

????}??

??????

????/**?

?????*?inOrderTraverseList:?獲得二叉查找樹的中序遍歷結(jié)點列表?

?????*?@return?二叉查找樹的中序遍歷結(jié)點列表?

?????*/??

????public?List<TreeNode>?inOrderTraverseList()??

????{??

????????if?(nodelist?!=?null)?{??

???????????nodelist.clear();??

????????}??

????????inOrderTraverse(root);??

????????return?nodelist;??

????}??

??????

????/**?

?????*?inOrderTraverse:?對給定二叉查找樹進行中序遍歷?

?????*?@param?root?給定二叉查找樹的根結(jié)點?

?????*/??

????private?void?inOrderTraverse(TreeNode?root)??

????{??

????????if?(root?!=?null)?{??

????????????inOrderTraverse(root.leftChild);??

????????????nodelist.add(root);??

????????????inOrderTraverse(root.rightChild);??

????????}??

????}??

??????

????/**?

?????*?toStringOfOrderList:?獲取二叉查找樹中關(guān)鍵字的有序列表?

?????*?@return?二叉查找樹中關(guān)鍵字的有序列表?

?????*/??

????public?String?toStringOfOrderList()??

????{??

????????StringBuilder?sbBuilder?=?new?StringBuilder("?[?");??

????????for?(TreeNode?p:?inOrderTraverseList())?{??

????????????sbBuilder.append(p.key);??

????????????sbBuilder.append("?");??

????????}??

????????sbBuilder.append("]");??

????????return?sbBuilder.toString();??

????}??

??????

????/**?

?????*?獲取該二叉查找樹的字符串表示?

?????*/??

????public?String?toString()??

????{??

????????StringBuilder?sbBuilder?=?new?StringBuilder("?[?");??

????????for?(TreeNode?p:?inOrderTraverseList())?{??

????????????sbBuilder.append(p);??

????????????sbBuilder.append("?");??

????????}??

????????sbBuilder.append("]");??

????????return?sbBuilder.toString();??

????}??

????public?TreeNode?getRoot()?{??

????????return?root;??

????}??

??????

????public?static?void?testNode(BinarySearchTree?bst,?TreeNode?pNode)?throws?Exception?{??

????????System.out.println("本結(jié)點:?"?+?pNode);??

????????System.out.println("前趨結(jié)點:?"?+?bst.precessor(pNode));??

????????System.out.println("后繼結(jié)點:?"?+?bst.successor(pNode));??

????}??

??????

????public?static?void?testTraverse(BinarySearchTree?bst)?{??

????????System.out.println("二叉樹遍歷："?+?bst);??

????????System.out.println("二叉查找樹轉(zhuǎn)換為有序列表:?"?+?bst.toStringOfOrderList());??

????}??

??????

????public?static?void?main(String[]?args)???

????{??

????????try?{??

????????????BinarySearchTree?bst?=?new?BinarySearchTree();??

????????????System.out.println("查找樹是否為空？?"?+?(bst.isEmpty()???"是"?:?"否"));??

????????????int[]?keys?=?new?int[]?{15,?6,?18,?3,?7,?13,?20,?2,?9,?4};??

????????????for?(int?key:?keys)?{??

????????????????bst.insert(key);??

????????????}??

????????????System.out.println("查找樹是否為空？?"?+?(bst.isEmpty()???"是"?:?"否"));??

??????????????

????????????TreeNode?minkeyNode?=?bst.minElemNode(bst.getRoot());??

????????????System.out.println("最小關(guān)鍵字：?"?+?minkeyNode.getKey());??

????????????testNode(bst,?minkeyNode);??

??????????????

????????????TreeNode?maxKeyNode?=?bst.maxElemNode(bst.getRoot());??

????????????System.out.println("最大關(guān)鍵字：?"?+?maxKeyNode.getKey());??

????????????testNode(bst,?maxKeyNode);??

??????????????

????????????System.out.println("根結(jié)點關(guān)鍵字：?"?+?bst.getRoot().getKey());??

????????????testNode(bst,?bst.getRoot());??

????????????testTraverse(bst);??

??????????????

????????????System.out.println("******************************?");??

??????????????

????????????System.out.println("查找?7?:?"?+?(bst.search(7)?!=?null???"查找成功!"?:?"查找失敗，不存在該關(guān)鍵字!"));??

????????????bst.delete(7);??

????????????System.out.println("查找?7?:?"?+?(bst.search(7)?!=?null???"查找成功!"?:?"查找失敗，不存在該關(guān)鍵字!"));??

????????????System.out.println("查找?12?:?"?+?(bst.search(12)?!=?null???"查找成功!"?:?"查找失敗，不存在該關(guān)鍵字!"));??

????????????bst.insert(12);??

????????????System.out.println("查找?12?:?"?+?(bst.search(12)?!=?null???"查找成功!"?:?"查找失敗，不存在該關(guān)鍵字!"));??

??????????????

????????????testTraverse(bst);??

??????????????

????????????System.out.println("******************************?");??

??????????????

????????????bst.insert(16);??

????????????bst.delete(6);??

????????????bst.delete(4);??

??????????????

????????????testTraverse(bst);??

??????????????

????????}?catch?(Exception?e)?{??

????????????System.out.println(e.getMessage());??

????????????e.printStackTrace();??

????????}??

????}??

??????

??????

} ??

?

轉(zhuǎn)載于:https://www.cnblogs.com/cugwx/p/3664306.html

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