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A collection of Tree Programming Interview Questions Solved in C++

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Key < tk->key_)) // search key < next level link's key { if (k < x->size_) // is curr lev allowed for this node? { // insert: x->next_[k] = tk;// new node's successor is tk t->next_[k] = x; // t'successor is x #ifdef DEBUG std::cerr << "\tdone inserted key=" << key << " value=" << x->val_ << std::endl; #endif } if (k == 0) // level 0 return; // return // k >= x->size__ // insert down a level insert__(t, x, k - 1); return; } // k > tk->key_ insert__(tk, x, k); // stay in the same level } public: Skiplist(num lgNmax = 5) : head_(new node(default_key_, default_val_, lgNmax + 1)), lgN_(0), lgNmax_(lgNmax) {}; ~Skiplist(){ remove_all__(head_, lgN_); }; // search a key and get a val // start from head_ and current level reached lgN_ inline Tval search(const Tkey key) const { return search__(head_, key, lgN_); }; // insert a key and a val // start from head_ and // the new randomized node with // j=rand_sl_gen() links built with // probability 1/t^j current level is lgN_ // inline void insert(const Tkey key, const Tval val) { insert__(head_, new node(key, val, rand_sl_gen__()), lgN_); }; inline void remove(Tkey key) { remove__(head_, key, lgN_ -1); } }; // end class Skiplist }; // end namespace Tree #endif Complexity The table here below provides space complexity for the average and the worst cases, by reporting also space and time complexity for search, insert and delete.

Insert: x->next_[k] = tk;// new node's successor is tk t->next_[k] = x; // t'successor is x #ifdef DEBUG std::cerr << "\tdone inserted key=" << key << " value=" << x->val_ << std::endl; #endif } if (k == 0) // level 0 return; // return // k >= x->size__ // insert down a level insert__(t, x, k - 1); return; } // k > tk->key_ insert__(tk, x, k); // stay in the same level } public: Skiplist(num lgNmax = 5) : head_(new node(default_key_, default_val_, lgNmax + 1)), lgN_(0), lgNmax_(lgNmax) {}; ~Skiplist(){ remove_all__(head_, lgN_); }; // search a key and get a val // start from head_ and current level reached lgN_ inline Tval search(const Tkey key) const { return search__(head_, key, lgN_); }; // insert a key and a val // start from head_ and // the new randomized node with // j=rand_sl_gen() links built with // probability 1/t^j current level is lgN_ // inline void insert(const Tkey key, const Tval val) { insert__(head_, new node(key, val, rand_sl_gen__()), lgN_); }; inline void remove(Tkey key) { remove__(head_, key, lgN_ -1); } }; // end class Skiplist }; // end namespace Tree #endif Complexity The table here below provides space complexity for the average and the worst cases, by reporting also space and time complexity for search, insert and delete.

If it is found, the process returns. Otherwise if the search reaches a null node, the key is inserted in that position. The process can be either recursive or iterative. root) return NULL; return ((root->v__ < k) ? find(root->right, k) : (root->v__ > k ? root) { root = new binaryTree(k); return; } if (root->v__ < k) insert(root->right, k); else if (root->v__ > k) insert(root->left, k); } Complexity Average time complexity of “insert” and “find” is) , where expresses the number of nodes in the tree.

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