算法导论：c++实现二叉搜索树

struct TreeNode_p {
    int val;
    TreeNode_p *left;
    TreeNode_p *right;
    TreeNode_p *parent;
    TreeNode_p(int x) : val(x), left(NULL), right(NULL),parent(NULL) {}
};

二叉搜索树搜索

TreeNode_p *tree_search(TreeNode_p * tree,int k) {
    if (tree == NULL || k == tree->val) {
        return tree;
    }
    if(k<tree->val)
    {
        tree_search(tree->left, k);
    }
    else
    {
        tree_search(tree->right, k);
    }
}

int main()
{
    TreeNode_p *r1 = new TreeNode_p(15);
    TreeNode_p *r2 = new TreeNode_p(6);
    TreeNode_p *r3 = new TreeNode_p(18);
    TreeNode_p *r4 = new TreeNode_p(3);
    TreeNode_p *r5 = new TreeNode_p(7);

    r1->left = r2;
    r1->right = r3;
    r2->parent = r1;
    r2->left = r4;
    r2->right = r5;
    r3->parent = r1;

    r4->parent = r2;
    r5->parent = r2;

    TreeNode_p *result = tree_search(r1, 18);
    cout << result->val;
}

最大最小结点

/*求二叉搜索树最小结点*/
TreeNode_p *tree_minimum(TreeNode_p * tree) {
    if (tree->left == NULL) {
        return tree;
    }
    tree_minimum(tree->left);
}
/*求二叉搜索树最大结点*/
TreeNode_p *tree_maximum(TreeNode_p * tree) {
    if (tree->right == NULL) {
        return tree;
    }
    tree_maximum(tree->right);
}

后继查找

/*求二叉搜索树后继结点*/
TreeNode_p *tree_successor(TreeNode_p * tree) {
    if (tree->right != NULL) {
        return tree_minimum(tree->right);   //右子树非空，则后继为右子树最小结点
    }
    TreeNode_p *y = tree->parent;
    while(y != NULL && tree==y->right) {
        tree = y;
        y = tree->parent;
    }
    return y;

}

前驱节点

若一个节点有左子树，那么该节点的前驱节点是其左子树中val值最大的节点（也就是左子树中所谓的rightMostNode）
若一个节点没有左子树，那么判断该节点和其父节点的关系
2.1 若该节点是其父节点的右边孩子，那么该节点的前驱结点即为其父节点。
2.2 若该节点是其父节点的左边孩子，那么需要沿着其父亲节点一直向树的顶端寻找，直到找到一个节点P，P节点是其父节点Q的右边孩子，那么Q就是该节点的后继节点

/*求二叉搜索树后继结点*/
TreeNode_p *tree_presuccessor(TreeNode_p * tree) {
    if (tree->left != NULL) {
        return tree_maximum(tree->left);    //右子树非空，则后继为右子树最小结点
    }
    TreeNode_p *y = tree->parent;
    while (y != NULL && tree == y->left) {
        tree = y;
        y = tree->parent;
    }
    return y;

}

增加节点

void tree_insert(TreeNode_p * tree, TreeNode_p * node) {
    TreeNode_p *y = NULL;   //y标记node的父指针
    TreeNode_p *x = tree;   //x用于向下探测
    while (x!=NULL)
    {
        y = x;
        if (node->val < x->val) {
            x = x->left;
        }
        else
        {
            x = x->right;
        }
    }
    node->parent = y;
    if (y == NULL) {
        tree = node;
    }
    else if(node->val<y->val)
    {
        y->left = node;
    }
    else
    {
        y->right = node;
    }

}
int main()
{
    TreeNode_p *r1 = new TreeNode_p(15);
    TreeNode_p *r2 = new TreeNode_p(6);
    TreeNode_p *r3 = new TreeNode_p(18);
    TreeNode_p *r4 = new TreeNode_p(3);
    TreeNode_p *r5 = new TreeNode_p(7);

    r1->left = r2;
    r1->right = r3;
    r2->parent = r1;
    r2->left = r4;
    r2->right = r5;
    r3->parent = r1;

    r4->parent = r2;
    r5->parent = r2;

    TreeNode_p *in = new TreeNode_p(4);

    tree_insert(r1, in);
}

删除节点

必须分三种情况进行讨论。

//v子树替换u子树,tree是根节点
void transplant(TreeNode_p * tree, TreeNode_p * u, TreeNode_p *v) 
{
    if (u->parent == NULL) {
        tree = v;
    }
    else if (u->parent->left ==u) //更新父节点的孩子
    {
        u->parent->left = v;
    }
    else
    {
        u->parent->right = v;
    }
    if (v != NULL) {
        v->parent = u->parent;
    }
}
/*二叉搜索树删除*/
void tree_delete(TreeNode_p * tree, TreeNode_p * node) {
    if (node->left == NULL) //左子树空
    {
        transplant(tree, node, node->right);

    }
    else if(node->right==NULL) //右子树空
    {
        transplant(tree, node, node->left);
    }
    else
    {
        TreeNode_p *y =  tree_minimum(node->right);;//寻找后继
        if (y->parent != node) 
        {
            transplant(tree, y, y->right);
            y->right = node->right;
            y->right->parent = y;
        }
        transplant(tree, node, y);//后继是待删除节点的子树，直接替换删除节点，并把后继左子树替换为删除节点左子树
        y->left = node->left;   //拼接左孩子
        y->left->parent =y;
    }
}

测试：

int main()
{
    TreeNode_p *r1 = new TreeNode_p(15);
    TreeNode_p *r2 = new TreeNode_p(6);
    TreeNode_p *r3 = new TreeNode_p(18);
    TreeNode_p *r4 = new TreeNode_p(3);
    TreeNode_p *r5 = new TreeNode_p(7);

    r1->left = r2;
    r1->right = r3;
    r2->parent = r1;
    r2->left = r4;
    r2->right = r5;
    r3->parent = r1;

    r4->parent = r2;
    r5->parent = r2;
    tree_delete(r1, r2);
}