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Functions for Binary Trees, Hash Tables, and Heaps Implementation

This document outlines key functions for working with binary search trees (BST), hash tables, and heaps. It includes a method to return the number of internal nodes in a BST, find the minimum key in a BST, and display keys in descending order using recursive procedures. Additionally, the document details the construction of a minimum heap from an array and the merging of two minimum heaps. Lastly, it demonstrates how to manage hash tables using linear probing and calculates average search costs for inserted keys.

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Functions for Binary Trees, Hash Tables, and Heaps Implementation

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  1. CS 210 Revision 2Spring 2012 BST, Hash Tables, Heaps

  2. Write a function INTERNAL to return the number of internal nodes in a BST template <class keyType, class dataType> intbinaryTree<keyType, dataType>::INTERNAL() { NodePointeraRoot; aRoot = root; return INTERNAL2(aRoot); } template <class keyType, class dataType> intbinaryTree<keyType, dataType>::INTERNAL2(NodePointeraRoot) { if(aRoot != NULL) { if(aRoot->left != NULL || aRoot->right != NULL) return 1 + INTERNAL2(aRoot->left) + INTERNAL2(aRoot->right); return INTERNAL2(aRoot->left) + INTERNAL2(aRoot->right); } return 0; }

  3. Write a function MINPOS returns the minimum key in a BST template <class keyType, class dataType> keyTypebinaryTree<keyType, dataType>::MINPOS () { NodePointer cur = root; while(cur != NULL) { if(cur->left == NULL) return cur->key; cur = cur->left; } }

  4. Code a recursive procedure BACKTRAVERSE to display the keys in the nodes of a BST in descending order template <class keyType, class dataType> void binaryTree<keyType, dataType>::BACKTRAVERSE() { if(root != NULL) BACK (root); else cout << “Tree is empty” << endl; } template <class keyType, class dataType> void binaryTree<keyType, dataType>::BACK(NodePointeraRoot) { if (aRoot->right != NULL) BACK (aRoot->right); cout << aRoot->key << " " << aRoot->data << endl; if (aRoot->left != NULL) BACK (aRoot->left); }

  5. Hash Tables Show the hash table of size 11 after insertion of the following sequence of keys using linear probing: 25 , 42 , 95 , 108 , 109 , 162 , 198 , 37 , 66 , 223 , 124 Use a hash function F( key ) = ( key mod 10 ) mod 11 What is the average search cost per key in that table?

  6. 25 , 42 , 95 , 108 , 109 , 162 , 198 , 37 , 66 , 223 , 124

  7. Heaps Given the following array of keys : ( 4 , 4 , 13 , 6 , 12 , 15 , 9 ) Show the steps of building up a minimum heap for that array and the removal from the heap to sort the array.

  8. 1 1 1 1 1 1 2

  9. 4 4 2 2 1

  10. Write a function to merge two minimum heaps into one minimum heap void Merge2Heaps(PQ<int> & Heap1, PQ<int> & Heap2, PQ<int> & Heapm, int N, int M) { int i, x1, x2; int K = (M>N)?N:M; for (i = 1; i <= K; i++) { x1 = Heap1.remove(); x2 = Heap2.remove(); if(x1 < x2) // for efficiency { Heapm.insert(x1); Heapm.insert(x2); } else { Heapm.insert(x2); Heapm.insert(x1); } } if(N>M) for( ; i<=K+abs(N-M); i++) { x1 = Heap1.remove(); Heapm.insert(x1); } else for( ; i<=K+abs(N-M); i++) { x2 = Heap2.remove(); Heapm.insert(x2); } }

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