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【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】

2014-04-08 16:54 375 查看
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++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.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

递归的方法：

test.cpp：
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118		#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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21		#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:
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89		#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);
}
}


                                            

                                        

                        
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