二叉排序树

二叉排序树（Binary Sort Tree）：或者是一颗空树，或者是具有以下性质的树：（1）若它的左子树不空，则左子树上所以结点的值均小于它的根节点的值；（2）若它的右子树不空，则右子树上的所以结点的值均大于它的根节点的值；（3）它的左、右子树也分别是二叉排序树。

二叉排序树的基本操作均可以在O(h)时间内完成（算法导论p165）。

相关操作代码如下：

int InsertBST(BiTree &T, int key)//递归插入{if (T == NULL){T = new BiNode;T->data = key;T->lchild = T->rchild = NULL;return 1;}else{if (key == T->data)return 0;else if (key < T->data)return InsertBST(T->lchild, key);elsereturn InsertBST(T->rchild, key);}}int InsertBST_(BiTree &T, int key)//迭代插入{//find the insert positionBiNode *f = T, *p = T;while (p != NULL){if (key == p->data)return 0;f = p;//记录上一次访问的结点p = key < p->data ? p->lchild : p->rchild;}//分配新结点BiNode *q = new BiNode;q->lchild = q->rchild = NULL;q->data = key;//插入if (T == NULL)//若根为空{T = q;return 1;}if (key < f->data)f->lchild = q;elsef->rchild = q;return 1;}BiNode *SearchBST(BiTree T, int key)//递归搜索{if (!T)return NULL;else{if (key == T->data)return T;else if (key < T->data)return SearchBST(T->lchild, key);elsereturn SearchBST(T->rchild, key);}}BiNode* SearchBST_(BiTree T, int key)//迭代搜索{while (T != NULL){if (key == T->data)break;T = key < T->data ? T->lchild : T->rchild;}return T;}int DeleteNode(BiNode *&p){BiNode *q;//从二叉排序树中删除结点p，并重接它的的左或右子树if (p == NULL)return 0;if (p->lchild == NULL) //左子树空则只需重接右子树{q = p; p = p->rchild; delete q;}else if (p->rchild == NULL)  //右子树空则只需重接左子树{q = p; p = p->lchild; delete q;}else//左右子树均不空{BiNode *s;#if 0//用p的直接前驱代替p，然后删除p的直接前驱q = p; s = p->lchild;//转左，然后向右到尽头while (s->rchild){q = s; s = s->rchild;}p->data = s->data;//s指向被删除结点,q指向被删除结点的前驱if (q != p)q->rchild = s->lchild;//重接q的右子树elseq->lchild = s->lchild;//重接q的左子树#else//用p的直接后继代替p，然后删除p的直接后继q = p; s = p->rchild;while (s->lchild){q = s; s = s->lchild;}p->data = s->data;if (p != p)q->lchild = s->rchild;elseq->rchild = s->rchild;#endifdelete s;}return 1;}int DeleteBST(BiTree &T, int key){if (T == NULL)return 0;else{if (key == T->data)return DeleteNode(T);else if (key < T->data)return DeleteBST(T->lchild, key);elsereturn DeleteBST(T->rchild, key);}}void CreateBST(BiTree &T, int a[], int n){T = NULL;for (int i = 0; i < n; i++){InsertBST_(T, a[i]);}}void DestoryBST(BiTree &T){if (T == NULL)return;DestoryBST(T->lchild);DestoryBST(T->rchild);delete T; T = NULL;}void InOrderTraverse(BiTree T)//=O(n)时间复杂度{if (T == NULL)return;InOrderTraverse(T->lchild);cout << T->data << " ";InOrderTraverse(T->rchild);}

测试代码：

int main(){const int n = 10;int a[n] = {3, 2, 8, 6, 1, 4, 5, 7, 1, 3};BiTree T;CreateBST(T, a, n);InOrderTraverse(T);cout << endl;BiNode *p;for (int i = 1; i < 10; i++){p = SearchBST_(T, i);if (p != NULL)cout << p->data << endl;}int b[5]={0, 2, 6, 1, 7};int ret;for (int i = 0; i < 5; i++){ret = DeleteBST(T, b[i]);if (ret == 0)cout << "删除 " << b[i] << " 失败" << endl;else{cout << "删除 " << b[i] << " 后: " ;InOrderTraverse(T);cout << endl;}}DestoryBST(T);getchar();return 0;}

参考：数据结构C语言版、算法导论（关于删除结点操作，该书p173页有注记）