【二叉查找树】04根据升序数组构造二叉查找树【Convert Sorted Array to Binary Search Tree】

2023年11月1日 418次阅读来源: z陵

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给定一个升序的数组，把他转换成一个高度平衡的二叉查找树

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Given an array where elements are sorted in ascending order, convert it to a height balanced BST.

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递归的方法：

test.cpp：

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#include <iostream>
#include <cstdio>
#include <stack>
#include <vector>
#include “BinaryTree.h”

using namespace std;

/**
* Definition for binary tree
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
TreeNode *tobst(vector< int> num, int begin, int end)
{

     if(begin > end)
    {
         return NULL;
    }
     if(begin == end)
    {
         return new TreeNode(num[begin]);
    }
     int mid = begin + (end – begin) / 2;
    TreeNode *tmp = new TreeNode(num[mid]);
    tmp->left = tobst(num, begin, mid – 1);
    tmp->right = tobst(num, mid + 1, end);
     return tmp;
}

TreeNode *sortedArrayToBST(vector< int> &num)
{
return tobst(num, 0, num.size() – 1);
}

vector<vector< int> > levelOrder(TreeNode *root)
{

    vector<vector< int> > matrix;
     if(root == NULL)
    {
         return matrix;
    }
    vector< int> temp;
    temp.push_back(root->val);
    matrix.push_back(temp);

vector<TreeNode *> path;
path.push_back(root);

     int count = 1;
     while(!path.empty())
    {
        TreeNode *tn = path.front();
         if(tn->left)
        {
            path.push_back(tn->left);
        }
         if(tn->right)
        {
            path.push_back(tn->right);
        }
        path.erase(path.begin());
        count–;

         if(count == 0)
        {
            vector< int> tmp;
            vector<TreeNode *>::iterator it = path.begin();
             for(; it != path.end(); ++it)
            {
                tmp.push_back((*it)->val);
            }
             if(tmp.size() > 0)
            {
                matrix.push_back(tmp);
            }
            count = path.size();
        }
    }
     return matrix;
}

// 树中结点含有分叉，
//                  4
//              /       \
//             2         6
//           /   \      /  \
//          1     3    5    7
int main()
{
     int arr[ 7] = { 1, 2, 3, 4, 5, 6, 7};
    vector< int> num(arr, arr + 7);

TreeNode *root = sortedArrayToBST(num);

vector<vector< int> > ans = levelOrder(root);

     for ( int i = 0; i < ans.size(); ++i)
    {
         for ( int j = 0; j < ans[i].size(); ++j)
        {
            cout << ans[i][j] << ” “;
        }
    }
    cout << endl;
    DestroyTree(root);
     return 0;
}

结果输出：

4 2 6 1 3 5 7

BinaryTree.h:

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#ifndef _BINARY_TREE_H_
#define _BINARY_TREE_H_

struct TreeNode
{
     int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode( int x) : val(x), left( NULL), right( NULL) {}
};

TreeNode *CreateBinaryTreeNode( int value);
void ConnectTreeNodes(TreeNode *pParent,
TreeNode *pLeft, TreeNode *pRight);
void PrintTreeNode(TreeNode *pNode);
void PrintTree(TreeNode *pRoot);
void DestroyTree(TreeNode *pRoot);

#endif /*_BINARY_TREE_H_*/

BinaryTree.cpp:

#include <iostream>
#include <cstdio>
#include “BinaryTree.h”

using namespace std;

/**
* Definition for binary tree
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/

//创建结点
TreeNode *CreateBinaryTreeNode( int value)
{
TreeNode *pNode = new TreeNode(value);

return pNode;
}

//连接结点
void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight)
{
     if(pParent != NULL)
    {
        pParent->left = pLeft;
        pParent->right = pRight;
    }
}

//打印节点内容以及左右子结点内容
void PrintTreeNode(TreeNode *pNode)
{
     if(pNode != NULL)
    {
        printf( “value of this node is: %d\n”, pNode->val);

         if(pNode->left != NULL)
            printf( “value of its left child is: %d.\n”, pNode->left->val);
         else
            printf( “left child is null.\n”);

         if(pNode->right != NULL)
            printf( “value of its right child is: %d.\n”, pNode->right->val);
         else
            printf( “right child is null.\n”);
    }
     else
    {
        printf( “this node is null.\n”);
    }

printf( “\n”);
}

//前序遍历递归方法打印结点内容
void PrintTree(TreeNode *pRoot)
{
PrintTreeNode(pRoot);

     if(pRoot != NULL)
    {
         if(pRoot->left != NULL)
            PrintTree(pRoot->left);

         if(pRoot->right != NULL)
            PrintTree(pRoot->right);
    }
}

void DestroyTree(TreeNode *pRoot)
{
     if(pRoot != NULL)
    {
        TreeNode *pLeft = pRoot->left;
        TreeNode *pRight = pRoot->right;

delete pRoot;
pRoot = NULL;

        DestroyTree(pLeft);
        DestroyTree(pRight);
    }
}

    原文作者：z陵
    原文地址: http://www.cnblogs.com/codemylife/p/3652368.html
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