二叉排序树

• 二叉排序树是一个基础的树的数据结构。应用许多。
• 它的特性就是，左孩子小于parent。右孩子大于parent.

寻找节点

寻找节点就是直接依据数值的大小。从root节点開始遍历，大于当前遍历节点就向它的右子树查找，相反则查找它的左子树。

然后返回。

查找最大最小节点

直接依据root节点，遍历到最右就是最大节点，遍历到最左，就是最小节点。

插入节点

插入节点我这里插入的节点都会成为叶子节点。依据大小的关系向下遍历，遍历到最后的节点，然后插入就能够了。

删除节点

这里删除节点是相对麻烦一点的。在删除的节点是一个叶子节点的时候。或者仅仅有一个孩子的时候，那么直接把当前节点删除让孩子取代自己的位置就能够了，在被删除的节点左右孩子都存在的时候，要删除当前节点，就须要用自己右子树的最小节点来取代被删除的节点。

代码例如以下

//
//  main.cpp
//  BSTree
//
//  Created by Alps on 14-7-31.
//  Copyright (c) 2014年 chen. All rights reserved.
//#include <iostream>
#define ElementType intusing namespace std;struct Node;
typedef Node* PtrToNode;
typedef PtrToNode TreeNode;TreeNode makeEmpty(TreeNode T);
int isEmpty(TreeNode T);
TreeNode findTree(ElementType X,TreeNode T);
TreeNode findMin(TreeNode T);
TreeNode findMax(TreeNode T);
TreeNode insertTree(ElementType X, TreeNode T);
TreeNode deleteTree(ElementType X, TreeNode T);struct Node{ElementType element;TreeNode left;TreeNode right;
};TreeNode makeEmpty(TreeNode T){if (T != NULL) {makeEmpty(T->left);makeEmpty(T->right);free(T);}return NULL;
}int isEmpty(TreeNode T){return T == NULL;
}TreeNode findTree(ElementType X,TreeNode T){if (T == NULL) {return NULL;}if (X < T->element) {return findTree(X, T->left);}else if(X > T->element){return findTree(X, T->right);}else{return T;}
}TreeNode findMin(TreeNode T){if (T == NULL) {return NULL;}if (T->left == NULL) {return T;}else{return findMin(T->left);}
//    return NULL;
}TreeNode findMax(TreeNode T){if (T == NULL) {return NULL;}if (T->right  == NULL) {return T;}else{return findMax(T->right);}
//    return NULL;
}TreeNode insertTree(ElementType X, TreeNode T){if (T == NULL) {T = (TreeNode)malloc(sizeof(Node));T->element = X;T->left = NULL;T->right = NULL;}else if(X > T->element){T->right = insertTree(X, T->right);}else if(X < T->element){T->left = insertTree(X, T->left);}return T;
}TreeNode deleteTree(ElementType X, TreeNode T){TreeNode XNode = findTree(X, T);if (XNode == NULL || T == NULL) {printf("can't find the node is : %d",X);exit(1);}if (X > T->element) {T->right = deleteTree(X, T->right);}else if(X < T->element){T->left = deleteTree(X, T->left);}else{TreeNode tmp;if (T->left && T->right) {tmp = findMin(T->right);T->element = tmp->element;T->right = deleteTree( T->element, T->right);}else{tmp = T;if (T->left == NULL) {T = T->right;}elseif (T->right == NULL) {T = T->left;}free(tmp);}}return T;
}void PreOrderTree(TreeNode T){if (T != NULL) {printf("%d ",T->element);PreOrderTree(T->left);PreOrderTree(T->right);}
}int main(int argc, const char * argv[])
{TreeNode T = (TreeNode)malloc(sizeof(Node));T = makeEmpty(T);T = insertTree(6, T);T = insertTree(2, T);T =insertTree(8, T);T =insertTree(1, T);T = insertTree(5, T);T =insertTree(3, T);T = insertTree(4, T);
//    printf("%d\n",T->element);PreOrderTree(T);printf("\n");TreeNode tmp;tmp = findTree(2, T);printf("%d\n",tmp->element);T = deleteTree(2, T);PreOrderTree(T);printf("\n");tmp = findMax(T);printf("%d\n",tmp->element);tmp = findMin(T);printf("%d\n",tmp->element);
//    std::cout << "Hello, World!\n";return 0;
}