c_cpp 二叉树的继承者。假设每个节点都有一个父字段。 root的父字段为null。

Posted 2021-05-14

// =================== HAS PARENT POINTER ================================
// =======================================================================
// idea: if a node n has nonempty right subtree, return the leftmost node in the right subtree.
// if not, keep traversing parent till we find a node that is a left child of its parent. Then the parent is n's successor. If
//      we reach the root, then n is the last node in inorder walk, and thus has no successor.

// very concise and elegant! Have parent pointer!
TreeNode *successor_in_binary_tree_with_parent(TreeNode *r) {
    if(!r) return NULL;
    if(r->right) {
        TreeNode *p = r->right;             // find leftmost node in r's right subtree
        while(p->left) p = p->left;
        return p;
    } 
    while(r->parent && r->parent->right == r) // find the first parent whose left child contains r
        r = r->parent;
    return r->parent;                         // return NULL means r has no successor
}

// ========================== NO PARENT POINTER ==========================
// =======================================================================
// successor in BST without parent pointer!!!
// Note, BST!!!!
TreeNode* successor_in_BST_without_parent(TreeNode *root, TreeNode *n) {
    if(!root || !n) return NULL;
    if(n->right) {
        TreeNode *p = n->right;
        while(p->left) p = p->left;
        return p;
    }
    TreeNode *cur = root, *p = NULL;
    while(cur) {
        if(n->val < cur->val) {
            p = cur;
            cur = cur->left;
        }
        else if(n->val > cur->val) {
            p = cur;
            cur = cur->right;
        }
        else break;
    }
    return p;
}

// ========================== NO PARENT POINTER ==========================
// =======================================================================
// find successor for general binary tree without parent!!! 
// now that there is no parent, we can save a parent on fly! VERY ELEGANT!
// refer: http://algorithmsgeek.blogspot.com/2013/06/algo2-inorder-successor-in-binary-tree.html

Treenode* successor_in_BT_without_parent(TreeNode *root, TreeNode *parent, TreeNode *n) {
  if(!root) return NULL;
  if(root == n) {
    if(root->right) {
      TreeNode *p = root->right;
      while(p->left) p = p->left;
      return p;
    }
    else return parent; // gist!
  }
  else { 
    TreeNode *L = successor_in_BT_without_parent(root->left, root, n);
    if(L) return L;
    else return successor_in_BT_without_parent(root->right, root, n);
  }
}

TreeNode* FUN(TreeNode *root, TreeNode *n) {
  return successor_in_BT_without_parent(root, NULL, n);
}