问题描述

提示：求一颗二叉搜索树的高度

给一个BST求其高度

难点分析：

提示：这里直接递归就好

递归的思路是每次把当前节点当成子树，求其左分支和右分支的最大高度，就这样递归下去，得到其子树的累加和，最后的左子树和右子树中累加和最高的就是BST的高度

代码：

提示：这里也可以用栈或者线性表来替代一下

import java.util.*;public class Lab25_01 {public static void main(String[] args) {BSTWithHeight<String> tree = new BSTWithHeight<>();System.out.print("The height of an empty tree is " + tree.height());tree.insert("Green");System.out.print("\nThe height of the tree with one node is " + tree.height());tree.insert("Red");System.out.print("\nThe height of the tree with two nodes is " + tree.height());Scanner input = new Scanner(System.in);System.out.print("\nEnter six strings: ");for (int i = 0; i < 6; i++) {String s = input.next();tree.insert(s.trim());}System.out.print("The height of tree is " + tree.height());BSTWithHeight<String> tree1 = new BSTWithHeight<>(new String[]{"Tom", "George", "Jean", "Jane", "Kevin", "Peter", "Susan","Jen", "Kim", "Michael", "Michelle"});System.out.print("\nThe height of tree1 is " + tree1.height());BSTWithHeight<Integer> tree2 =new BSTWithHeight<>(new Integer[]{50, 45, 35, 48, 59, 51, 58});
//        BSTWithHeight<Integer> tree2 =
//                new BSTWithHeight<>(new Integer[]{50, 45, 59, 35, 48, 47, 46});int temp = tree2.height();System.out.print("\nThe height of tree2 is " + temp);}
}interface Tree<E> extends Collection<E> {/*** Return true if the element is in the tree*/public boolean search(E e);/*** Insert element o into the binary tree* Return true if the element is inserted successfully*/public boolean insert(E e);/*** Delete the specified element from the tree* Return true if the element is deleted successfully*/public boolean delete(E e);/*** Get the number of nodes in the tree*/public int getSize();/*** Inorder traversal from the root*/public default void inorder() {}/*** Postorder traversal from the root*/public default void postorder() {}/*** Preorder traversal from the root*/public default void preorder() {}@Override/** Return true if the tree is empty */public default boolean isEmpty() {return size() == 0;};@Overridepublic default boolean contains(Object e) {return search((E) e);}@Overridepublic default boolean add(E e) {return insert(e);}@Overridepublic default boolean remove(Object e) {return delete((E) e);}@Overridepublic default int size() {return getSize();}@Overridepublic default boolean containsAll(Collection<?> c) {// Left as an exercisereturn false;}@Overridepublic default boolean addAll(Collection<? extends E> c) {// Left as an exercisereturn false;}@Overridepublic default boolean removeAll(Collection<?> c) {// Left as an exercisereturn false;}@Overridepublic default boolean retainAll(Collection<?> c) {// Left as an exercisereturn false;}@Overridepublic default Object[] toArray() {// Left as an exercisereturn null;}@Overridepublic default <T> T[] toArray(T[] array) {// Left as an exercisereturn null;}
}class BST<E> implements Tree25_02<E> {protected TreeNode<E> root;protected int size = 0;protected Comparator<E> c;/*** Create a default BST with a natural order comparator*/public BST() {this.c = new Comparator<E>() {public int compare(E e1, E e2) {return ((Comparable<E>) e1).compareTo(e2);}};}/*** Create a BST with a specified comparator*/public BST(Comparator<E> c) {this.c = c;}/*** Create a binary tree from an array of objects*/public BST(E[] objects) {this();for (int i = 0; i < objects.length; i++)add(objects[i]);}@Override/** Returns true if the element is in the tree */public boolean search(E e) {TreeNode<E> current = root; // Start from the rootwhile (current != null) {if (c.compare(e, current.element) < 0) {current = current.left;} else if (c.compare(e, current.element) > 0) {current = current.right;} else // element matches current.elementreturn true; // Element is found}return false;}@Override/** Insert element e into the binary tree* Return true if the element is inserted successfully */public boolean insert(E e) {if (root == null)root = createNewNode(e); // Create a new rootelse {// Locate the parent nodeTreeNode<E> parent = null;TreeNode<E> current = root;while (current != null)if (c.compare(e, current.element) < 0) {parent = current;current = current.left;} else if (c.compare(e, current.element) > 0) {parent = current;current = current.right;} elsereturn false; // Duplicate node not inserted// Create the new node and attach it to the parent nodeif (c.compare(e, parent.element) < 0)parent.left = createNewNode(e);elseparent.right = createNewNode(e);}size++;return true; // Element inserted successfully}protected TreeNode<E> createNewNode(E e) {return new TreeNode<>(e);}@Override/** Inorder traversal from the root */public void inorder() {inorder(root);}/*** Inorder traversal from a subtree*/protected void inorder(TreeNode<E> root) {if (root == null) return;inorder(root.left);System.out.print(root.element + " ");inorder(root.right);}@Override/** Postorder traversal from the root */public void postorder() {postorder(root);}/*** Postorder traversal from a subtree*/protected void postorder(TreeNode<E> root) {if (root == null) return;postorder(root.left);postorder(root.right);System.out.print(root.element + " ");}@Override/** Preorder traversal from the root */public void preorder() {preorder(root);}/*** Preorder traversal from a subtree*/protected void preorder(TreeNode<E> root) {if (root == null) return;System.out.print(root.element + " ");preorder(root.left);preorder(root.right);}/*** This inner class is static, because it does not access* any instance members defined in its outer class*/public static class TreeNode<E> {protected E element;protected TreeNode<E> left;protected TreeNode<E> right;public TreeNode(E e) {element = e;}}@Override/** Get the number of nodes in the tree */public int getSize() {return size;}/*** Returns the root of the tree*/public TreeNode<E> getRoot() {return root;}/*** Returns a path from the root leading to the specified element*/public ArrayList<TreeNode<E>> path(E e) {ArrayList<TreeNode<E>> list =new ArrayList<>();TreeNode<E> current = root; // Start from the rootwhile (current != null) {list.add(current); // Add the node to the listif (c.compare(e, current.element) < 0) {current = current.left;} else if (c.compare(e, current.element) > 0) {current = current.right;} elsebreak;}return list; // Return an array list of nodes}@Override/** Delete an element from the binary tree.* Return true if the element is deleted successfully* Return false if the element is not in the tree */public boolean delete(E e) {// Locate the node to be deleted and also locate its parent nodeTreeNode<E> parent = null;TreeNode<E> current = root;while (current != null) {if (c.compare(e, current.element) < 0) {parent = current;current = current.left;} else if (c.compare(e, current.element) > 0) {parent = current;current = current.right;} elsebreak; // Element is in the tree pointed at by current}if (current == null)return false; // Element is not in the tree// Case 1: current has no left childif (current.left == null) {// Connect the parent with the right child of the current nodeif (parent == null) {root = current.right;} else {if (c.compare(e, parent.element) < 0)parent.left = current.right;elseparent.right = current.right;}} else {// Case 2: The current node has a left child// Locate the rightmost node in the left subtree of// the current node and also its parentTreeNode<E> parentOfRightMost = current;TreeNode<E> rightMost = current.left;while (rightMost.right != null) {parentOfRightMost = rightMost;rightMost = rightMost.right; // Keep going to the right}// Replace the element in current by the element in rightMostcurrent.element = rightMost.element;// Eliminate rightmost nodeif (parentOfRightMost.right == rightMost)parentOfRightMost.right = rightMost.left;else// Special case: parentOfRightMost == currentparentOfRightMost.left = rightMost.left;}size--; // Reduce the size of the treereturn true; // Element deleted successfully}@Override/** Obtain an iterator. Use inorder. */public Iterator<E> iterator() {return new InorderIterator();}// Inner class InorderIteratorprivate class InorderIterator implements Iterator<E> {// Store the elements in a listprivate ArrayList<E> list =new ArrayList<>();private int current = 0; // Point to the current element in listpublic InorderIterator() {inorder(); // Traverse binary tree and store elements in list}/*** Inorder traversal from the root*/private void inorder() {inorder(root);}/*** Inorder traversal from a subtree*/private void inorder(TreeNode<E> root) {if (root == null) return;inorder(root.left);list.add(root.element);inorder(root.right);}@Override/** More elements for traversing? */public boolean hasNext() {if (current < list.size())return true;return false;}@Override/** Get the current element and move to the next */public E next() {return list.get(current++);}@Override // Remove the element returned by the last next()public void remove() {if (current == 0) // next() has not been called yetthrow new IllegalStateException();delete(list.get(--current));list.clear(); // Clear the listinorder(); // Rebuild the list}}@Override/** Remove all elements from the tree */public void clear() {root = null;size = 0;}
}// BEGIN REVEL SUBMISSION
class BSTWithHeight<E> extends BST25_15<E> {/*** Create a default BST with a natural order comparator*/public BSTWithHeight() {super();}/*** Create a BST with a specified comparator*/public BSTWithHeight(Comparator<E> c) {super(c);}/*** Create a binary tree from an array of objects*/public BSTWithHeight(E[] objects) {super(objects);}/*** Returns the height of this binary tree.*/public int height() {return height(root);}private int height(TreeNode<E> root) {// WRITE YOUR CODE HEREif (root == null) return -1;return Math.max(height(root.left), height(root.right)) + 1;}
}
// END REVEL SUBMISSION

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java黑皮书25.1----（树的高度）

问题描述

难点分析：

代码：

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