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/******************************************************************** File: BinarySearchTree.h Author: blackboy blackboycpp@gmail.com Purpose: 二叉查找树， C实现，不支持重复元素。 使用递归的好例子。 Created: 2011-04-11 Modified: 2011-04-11 19:15 *********************************************************************/ #ifndef __BINARY_SEARCH_TREE_H__ #define __BINARY_SEARCH_TREE_H__ typedef int ElementType; struct _TreeNode; typedef struct _TreeNode TreeNode; typedef TreeNode* Position; typedef TreeNode* SearchTree; struct _TreeNode { ElementType Val; SearchTree Left; SearchTree Right; }; ////////////////////////////////////////////////////////////////////////// SearchTree MakeEmpty(SearchTree); Position Find(ElementType, SearchTree); Position FindMin(SearchTree); Position FindMax(SearchTree); SearchTree Insert(ElementType, SearchTree); SearchTree Delete(ElementType, SearchTree); ElementType GetAt(Position); void InOrder(SearchTree); // 中序遍历 #endif 

#include <stdlib.h> #include <stdio.h> #include “BinarySearchTree.h” SearchTree MakeEmpty(SearchTree T) { if(T != NULL) { MakeEmpty(T->Left); MakeEmpty(T->Right); free(T); } return NULL; } Position Find(ElementType X, SearchTree T) { if(T == NULL) return NULL; if(X < T->Val) return Find(X, T->Left); else if(X > T->Val) return Find(X, T->Right); else // 递归终止条件 return T; } Position FindMin(SearchTree T) { if(T == NULL) return NULL; else if(T->Left == NULL) return T; else return FindMin(T->Left); } Position FindMax(SearchTree T) { if(T == NULL) return NULL; else if(T->Right == NULL) return T; else return FindMax(T->Right); // 非递归实现 /* if(T != NULL) { while(T->Right != NULL) { T = T->Right; } } return T; */ } SearchTree Insert(ElementType X, SearchTree T) { if(T == NULL) // 递归终止条件 { T = (SearchTree)malloc(sizeof(TreeNode)); T->Left = T->Right = NULL; T->Val = X; } else if(X < T->Val) { T->Left = Insert(X, T->Left); } else if(X > T->Val) { T->Right = Insert(X, T->Right); } // else： 重复元素，不考虑。 return T; } // 搜索并删除右子树中最小的节点。 // D: 要删除的节点；T：递归用的树，初始值为D的右子树。 // 注意：此函数被调用时，D必有左、右两个儿子。 static SearchTree DeleteRightMin(SearchTree D, SearchTree T) { Position Temp; // 最小节点必定没有左儿子 if(T->Left == NULL) { Temp = T; D->Val = T->Val; T = T->Right; free(Temp); } else T->Left = DeleteRightMin(D, T->Left); // 很关键，且容易出错 return T; } SearchTree Delete(ElementType X, SearchTree T) { Position Temp; if(T == NULL) // 空树 return NULL; else if(X < T->Val) T->Left = Delete(X, T->Left); else if(X > T->Val) T->Right = Delete(X, T->Right); else if(T->Left && T->Right) // 两个儿子 { T->Right = DeleteRightMin(T, T->Right); // 也可以如下实现，但效率较低，因为遍历了两遍右子树 /* Temp = FindMin(T->Right); T->Val = Temp->Val; T->Right = Delete(T->Val, T->Right); */ } else // 单个儿子 { Temp = T; if(T->Left == NULL) T = T->Right; else if(T->Right == NULL) T = T->Left; free(Temp); } return T; } ElementType GetAt(Position Pos) { return Pos->Val; } // 中序遍历，输出节点值 void InOrder(SearchTree T) { if(T == NULL) return; InOrder(T->Left); printf(“%d “, T->Val); InOrder(T->Right); } 

#include <stdlib.h> #include <stdio.h> #include “BinarySearchTree.h” int main() { SearchTree Tree = NULL; Position Pos = NULL; Tree = Insert(5, Tree); Tree = Insert(2, Tree); Tree = Insert(8, Tree); Tree = Insert(1, Tree); Tree = Insert(3, Tree); Tree = Insert(6, Tree); Tree = Insert(4, Tree); InOrder(Tree); printf(“/n”); Pos = Find(3, Tree); printf(“Find 3: %d/n”, GetAt(Pos)); Pos = FindMax(Tree); printf(“FindMax: %d/n”, GetAt(Pos)); Pos = FindMin(Tree); printf(“FindMin: %d/n”, GetAt(Pos)); // 删除单儿子节点 Tree = Delete(3, Tree); InOrder(Tree); printf(“/n”); Tree = Insert(3, Tree); // 删除双儿子节点 Tree = Delete(2, Tree); InOrder(Tree); printf(“/n”); // 删除根节点 Tree = Delete(5, Tree); InOrder(Tree); printf(“/n”); Tree = MakeEmpty(Tree); InOrder(Tree); printf(“/n”); Tree = MakeEmpty(Tree); system(“PAUSE”); return 0; }