制作二叉搜索树

Question

当我有一个包含100个元素的数组列表{3,2,6,7,...,99}时，如何创建一棵二叉搜索树(BST)？

- user472221

Answer 1

我相信TreeSet是二叉搜索树的一种实现。由于整数具有自然排序，因此您可以简单地循环遍历整数数组并将它们全部添加到TreeSet<Integer>中。

还请注意，有一个方法Arrays.binarySearch可在已排序的数组中进行二分查找。

int[] someInts = {3,2,6,7, /*...,*/ 99};

// use a TreeSet
TreeSet<Integer> ints = new TreeSet<Integer>();
for (int i : someInts)
    ints.add(i);

System.out.println(ints.contains(2)); // true      
System.out.println(ints.contains(5)); // false

// or sort the array and use Arrays.binarySearch
Arrays.sort(someInts);
System.out.println(Arrays.binarySearch(someInts, 2) >= 0); // true
System.out.println(Arrays.binarySearch(someInts, 5) >= 0); // false

- aioobe

---

如果它们没有自然排序，我的意思是像 {95,54,23,87,13,14,12} 这样，我也可以使用你的代码吗？ - user472221

我也不理解你的代码如何使用上述数组创建二叉搜索树!!! - user472221

当然可以。TreeSet 不会在乎您是否按顺序插入元素。 - aioobe

谢谢，但正如我之前提到的，我不明白TreeSet如何为我创建BST！您能否再解释一下，抱歉。 - user472221

@user472221 所有数字类型，如int都有自然排序，您不能使用未排序的集合执行二分搜索。在数组上执行二分搜索比使用TreeSet更快。唯一更快的是使用HashSet或使用TIntHashSet（最快的）。 - Peter Lawrey

Answer 2

我最近完成了一个项目，我们基本上就是要做这个。

你可以看一下这个类

编辑：这是C++，我看到你在编写Java，抱歉！

/**************************************
 *  Tree.cpp - Created by DT
 **************************************
 *
 *  Functions:
 *
 *  public:
 *      Tree();
 *      void addNode(int);
 *      bool findID(int);
 *      Node* findNode(int);
 *      Node* findParent(int);
 *      bool deleteID(int);
 *      Node* findMaximum(Node*);
 *      Node* findMinimum(Node*);
 *      void printInOrder();
 *      void printPreOrder();
 *      void printPostOrder();
 *      int recurseHeight(Node*);
 *      int getHeight();
 *      void inOrder(Node*);
 *      void preOrder(Node*);
 *      void postOrder(Node*);
 *
 ***************************************/
#include <iostream>
#include "Node.h"
#include "Tree.h"

using namespace std;

Tree::Tree() {
    root = NULL;
}
///////////////////////////////
// AddNode Function:
///////////////////////////////
void Tree::addNode(int id) {
    if(findNode(id)) {
        cout << "This ID already exists in the tree" << endl;
        return;
    }
    //if(id == 2147483647) {
    //  cout << "Overflow Detected: Did you enter a really big number?\n";
    //  cout << "This ID is being stored as 2147483647\n";
    //}
    Node *newNode = new Node();
    newNode->id = id;
    if(root == NULL) {
        root = newNode;
        return;
    }
    Node *nextNode = root;
    Node *lastNode = nextNode;
    while(nextNode != NULL) {
        if(id <= nextNode->id) {
            lastNode = nextNode;
            nextNode = nextNode->leftChild;
        }
        else {
            lastNode = nextNode;
            nextNode = nextNode->rightChild;
        }
    }
    if(id <= lastNode->id)
        lastNode->leftChild = newNode;
    else
        lastNode->rightChild = newNode;
}
///////////////////////////////
// FindID Function:
///////////////////////////////
bool Tree::findID(int id) {
    Node *finder = root;
    while(finder != NULL) {
        if(id == finder->id)
            return true;
        if(id <= finder->id)
            finder = finder->leftChild;
        else
            finder = finder->rightChild;
    }
    return false;
}
///////////////////////////////
// FindNode Helper Function:
///////////////////////////////
Node* Tree::findNode(int id) {
    Node *finder = root;
    while(finder != NULL) {
        if(id == finder->id)
            return finder;
        if(id <= finder->id)
            finder = finder->leftChild;
        else
            finder = finder->rightChild;
    }
    return NULL;
}
///////////////////////////////
// FindParent Helper Function:
///////////////////////////////
Node* Tree::findParent(int id) {
    Node *parent = NULL;
    Node *finder = root;
    while(finder != NULL) {
        if(id == finder->id)
            return parent;
        parent = finder;
        if(id <= finder->id)
            finder = finder->leftChild;
        else
            finder = finder->rightChild;
    }
    return NULL;
}
///////////////////////////////
// DeleteID Function:
///////////////////////////////
bool Tree::deleteID(int id) {
    if(root == NULL)
        return false;
    Node *toDelete = findNode(id);      //Find the node to delete
    if(toDelete == NULL)                //If we can't find it, return false
        return false;
    Node *parent = findParent(id);      //Find the parent of the node to delete
    Node *justInCase;                   //In case we are deleting the root node
    bool deletingRoot = false;          //This is a special case so handle it differently
    if(root->id == id) {                //If we're deleting the root node
        justInCase = new Node();        //Let's create a fake parent for the root
        justInCase->leftChild = root;   //Just to make sure that we can run checks on parents
        justInCase->rightChild = NULL;
        justInCase->id = 0;             //Later on in the code
        parent = justInCase;            //Set the parent of the root to our new fake node
        deletingRoot = true;            //Let the end of our function know we're deleting the root
    }
    bool deletingLeftChild = (parent->leftChild == toDelete);
    if(toDelete->leftChild == NULL && toDelete->rightChild == NULL) {
        if(toDelete == root)
            root = NULL;
        if(deletingLeftChild)
            parent->leftChild = NULL;
        else
            parent->rightChild = NULL;
        delete toDelete;
        return true;
    }
    if((toDelete->leftChild == NULL || toDelete->rightChild == NULL) && (parent != NULL && !deletingRoot)) {
        if(deletingLeftChild)
            parent->leftChild = (toDelete->leftChild == NULL) ? toDelete->rightChild : toDelete->leftChild;
        else
            parent->rightChild = (toDelete->leftChild == NULL) ? toDelete->rightChild : toDelete->leftChild;
        delete toDelete;
        return true;
    }
    Node *replacer = findMaximum(toDelete->leftChild);          //Replace the node we're deleting with the hightest LEFT Child
    if(replacer == NULL || replacer == toDelete)                //If we can't find a left child (in case of deleting root)
        replacer = findMinimum(toDelete->rightChild);           //Find the smallest RIGHT child
    Node *replacerParent = findParent(replacer->id);            //Find the parent of this child
    if(replacerParent != NULL) {                                //If this child has a parent
        if(replacerParent->leftChild == replacer) {             //If the child is to the left of the parent
            if(replacer->leftChild != NULL)                     //And the left child has a child of its own (in case of findMinimum/maximum)
                replacerParent->leftChild = replacer->leftChild;//set the parent's child to this child's node
            else
                replacerParent->leftChild = NULL;               //Otherwise, set the parent's child to NULL
        }
        else {                                                  //In the case of Right Child
            if(replacer->rightChild != NULL)                    //Do the same thing
                replacerParent->rightChild = replacer->rightChild;
            else
                replacerParent->rightChild = NULL;
        }
    }
    toDelete->id = replacer->id;                                //Swap the IDs of the nodes we're deleting
    delete replacer;                                            //And delete the minimum or maximum that we found
    return true;
}
///////////////////////////////
// FindMaximum Helper Function:
///////////////////////////////
Node* Tree::findMaximum(Node *theNode) {
    if(theNode == NULL)
        return NULL;
    Node *finder = theNode;
    Node *last = finder;
    while(finder != NULL) {
        last = finder;
        finder = finder->rightChild;
    }
    return last;
}
///////////////////////////////
// FindMinimum Helper Function:
///////////////////////////////
Node* Tree::findMinimum(Node *theNode) {
    if(theNode == NULL)
        return NULL;
    Node *finder = theNode;
    Node *last = finder;
    while(finder != NULL) {
        last = finder;
        finder = finder->leftChild;
    }
    return last;
}
///////////////////////////////
// PrintInOrder Function:
///////////////////////////////
void Tree::printInOrder() {
    inOrder(root);                                      //Recurse through our root
    cout << "\b " << endl;
}
///////////////////////////////
// PrintPostOrder Function:
///////////////////////////////
void Tree::printPostOrder() {
    postOrder(root);                                    //Recurse through our root
    cout << "\b " << endl;
}
///////////////////////////////
// PrintPreOrder Function:
///////////////////////////////
void Tree::printPreOrder() {
    preOrder(root);                                 //Recurse through our root
    cout << "\b " << endl;
}
///////////////////////////////
// RecurseHeight Function:
///////////////////////////////
int Tree::recurseHeight(Node *node) {
    if(node == NULL) return -1;
    return 1 + max(recurseHeight(node->leftChild),recurseHeight(node->rightChild));
}
///////////////////////////////
// GetHeight Function:
///////////////////////////////
int Tree::getHeight() { return recurseHeight(root); }   //Recurse through our root
///////////////////////////////
// InOrder Function:
///////////////////////////////
void Tree::inOrder(Node *cNode) {
    if(cNode == NULL)
        return;
    inOrder(cNode->leftChild);
    cout << cNode->id << "-";
    inOrder(cNode->rightChild);
}
///////////////////////////////
// PostOrder Function:
///////////////////////////////
void Tree::postOrder(Node *cNode) {
    if(cNode == NULL)
        return;
    postOrder(cNode->leftChild);
    postOrder(cNode->rightChild);
    cout << cNode->id << "-";
}
///////////////////////////////
// PreOrder Function:
///////////////////////////////
void Tree::preOrder(Node *cNode) {
    if(cNode == NULL)
        return;
    cout << cNode->id << "-";
    preOrder(cNode->leftChild);
    preOrder(cNode->rightChild);
}

节点类：

/**************************************
 *  Node.cpp - Created by DT
 **************************************
 *
 *  An incredibly simple class that
 *  apparently deserves its own header
 *
 ***************************************/
#include "Node.h"
#include <iostream>
Node::Node() {
    leftChild = NULL;
    rightChild = NULL;
    id = NULL;
}

- user1274820

Answer 3

首先对这个数组进行排序，然后使用二叉搜索树（BST）。

编辑

1- BST 适用于已排序的数组。

2- 使用此伪代码 在这里查看。

- TalentTuner

---

我不知道为什么无法打开网页，请您把伪代码放在这里好吗？谢谢。 - user472221

Answer 4

除非你想自己实现所有的东西（在这种情况下，你可能想要检查这里），否则你应该看一下 [Collections.binarySearch][2]。

[2]: http://download.oracle.com/javase/1.4.2/docs/api/java/util/Collections.html#binarySearch(java.util.List, java.lang.Object)

- npinti