Data Structure Binary Search Tree: Inorder Successor in Binary Search Tree

struct node {
    int val;
    node *left;
    node *right;
    node *parent;
    node() : val(0), left(NULL), right(NULL) { }
    node(int v) : val(v), left(NULL), right(NULL) { }
};

node* insert(int n, node *root) {
    if (root == NULL) {
        root = new node(n);
        return root;
    }
    if (n < root->val) {
        if (root->left == NULL) {
            root->left = new node(n);
            return root->left;
        }
        else return insert(n, root->left);
    }
    if (n > root->val) {
        if (root->right == NULL) {
            root->right = new node(n);
            return root->right;
        }
        else return insert(n, root->right);
    }
}

//Variation: How would you find the sucessor of a node?
node* leftmost(node *n) {
    if (n == NULL) return NULL;
    while (n->left) n = n->left;
    return n;
}

node* findSuccessor(node* n) {
    if (n == NULL) return NULL;
    if (!n->parent || n->right) return leftmost(n->right);
    else {
        while (n->parent && n->parent->right == n) n = n->parent; 
        return n->parent;
    }
}

 下面是没有parent的代码

node *minvalue(node *root) {
    while (root->left) root = root->left;
    return root;
}

node* successor(node *root, node *n) {
    if (n->right) return minvalue(n->right);
    node *succ = NULL;
    while (root) {
        if (n->data < root->data) {
            succ = root;
            root = root->left;
        }
        else if (n->data > root->data) root = root->right;
        else break;
    }
    return succ;
}