【本文链接】
http://www.cnblogs.com/hellogiser/p/query-min-max-successor-of-bst.html
【代码】
C++ Code
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/*
version: 1.0 author: hellogiser blog: http://www.cnblogs.com/hellogiser date: 2014/9/18 */ // binary tree node struct struct BinaryTreeNode { int value; BinaryTreeNode *parent; // for rank of bst BinaryTreeNode *left; BinaryTreeNode *right; int size; // for kmin of bst // x.size = x.left.size + x.right.size +1 }; int node_size(BinaryTreeNode *node) { // get node size of node if (node == NULL) return 0; node->size = node_size(node->left) + node_size(node->right) + 1; return node->size; } int left_size(BinaryTreeNode *node) { // get left size of node in o(1) return node->left != NULL ? node->left->size : 0; } //================================================= // BST Tree kmin //================================================= BinaryTreeNode *kmin_bst(BinaryTreeNode *root, int k) { if (root == NULL) return NULL; int pk = left_size(root) + 1; // get node rank first if (k == pk) { return root; } else if (k < pk) { return kmin_bst(root->left, k); } else // k>pk { return kmin_bst(root->right, k - pk); } } BinaryTreeNode *Kmin_of_BST(BinaryTreeNode *root, int k) { if (root == NULL) return NULL; // get node size of bst first int nodes = node_size(root); if (k < 1 || k > nodes) return NULL; // use node size info to get kmin of bst return kmin_bst(root, k); } //================================================= // BST Tree querying //================================================= BinaryTreeNode *Search_of_BST(BinaryTreeNode *root, int key) { if (root == NULL) return NULL; if (key == root->value) return root; else if(key < root->value) return Search_of_BST(root->left, key); else return Search_of_BST(root->right, key); } BinaryTreeNode *Search_of_BST2(BinaryTreeNode *root, int key) { BinaryTreeNode *node = root; while (node != NULL && key != node->value) { if (key < node->value) node = node->left; else node = node->right; } return node; } BinaryTreeNode *Min_of_BST(BinaryTreeNode *root) { if (root == NULL) return NULL; BinaryTreeNode *node = root; while(node->left != NULL) node = node->left; return node; } BinaryTreeNode *Max_of_BST(BinaryTreeNode *root) { if(root == NULL) return NULL; BinaryTreeNode *node = root; while(node->right != NULL) node = node->right; return node; } /* x has right child ===> Min(x.right) (case 1) else px = x.parent (case 2) if px.right == x ===> go up until px==null (case 2.2) else px.left ==x ===> px (case 2.1) */ BinaryTreeNode *Successor(BinaryTreeNode *x) { if(x == NULL) return NULL; // case 1 if (x->right != NULL) return Min_of_BST(x->right); // case 2 BinaryTreeNode *px = x->parent; if(px == NULL) return NULL; // case 2.1 if (px->left == x) return px; // case 2.2 while(px != NULL && px->right == x) { x = px; px = px->parent; } return px; } /* px px / x x */ /* get all node size first rank = leftsize(x)+1 px = x.parent if px.right ==x ====> rank += leftsize(px)+1, go up else rank += 0 */ int Rank_of_BST(BinaryTreeNode *root, BinaryTreeNode *x) { if(root == NULL || x == NULL) return -1; // get node size first node_size(root); int rank = left_size(x) + 1; // parent's left or right child ? BinaryTreeNode *px = x->parent; while(px != NULL) { if (px->right == x) { // px's right child rank += left_size(px) + 1; } px = px->parent; } return rank; } |