[LeetCode] 108.Convert Sorted Array to Binary Search Tree 將有序數(shù)組轉(zhuǎn)為二叉搜索樹

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

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of everynode never differ by more than 1.

Example:

Given the sorted array: [-10,-3,0,5,9],

One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST:

      0
/ \
-3   9
/   /
-10  5 

這道題是要將有序數(shù)組轉(zhuǎn)為二叉搜索樹，所謂二叉搜索樹，是一種始終滿足左<根<右的特性，如果將二叉搜索樹按中序遍歷的話，得到的就是一個有序數(shù)組了。那么反過來，我們可以得知，根節(jié)點應(yīng)該是有序數(shù)組的中間點，從中間點分開為左右兩個有序數(shù)組，在分別找出其中間點作為原中間點的左右兩個子節(jié)點，這不就是是二分查找法的核心思想么。所以這道題考的就是二分查找法，代碼如下：

解法一：

class Solution {
public:
    TreeNode* sortedArrayToBST(vector<int>& nums) {
        return helper(nums, 0 , (int)nums.size() - 1);
    }
    TreeNode* helper(vector<int>& nums, int left, int right) {
        if (left > right) return NULL;
        int mid = left + (right - left) / 2;
        TreeNode *cur = new TreeNode(nums[mid]);
        cur->left = helper(nums, left, mid - 1);
        cur->right = helper(nums, mid + 1, right);
        return cur;
    }
};

我們也可以不使用額外的遞歸函數(shù)，而是在原函數(shù)中完成遞歸，由于原函數(shù)的參數(shù)是一個數(shù)組，所以當(dāng)把輸入數(shù)組的中間數(shù)字取出來后，需要把所有兩端的數(shù)組組成一個新的數(shù)組，并且分別調(diào)用遞歸函數(shù)，并且連到新創(chuàng)建的cur結(jié)點的左右子結(jié)點上面，參見代碼如下：

解法二：

class Solution {
public:
    TreeNode* sortedArrayToBST(vector<int>& nums) {
        if (nums.empty()) return NULL;
        int mid = nums.size() / 2;
        TreeNode *cur = new TreeNode(nums[mid]);
        vector<int> left(nums.begin(), nums.begin() + mid), right(nums.begin() + mid + 1, nums.end());
        cur->left = sortedArrayToBST(left);
        cur->right = sortedArrayToBST(right);
        return cur;
    }
};

類似題目：

Convert Sorted List to Binary Search Tree

參考資料：

https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/

https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/discuss/35220/My-Accepted-Java-Solution

https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/discuss/35394/6-lines-Java-Accepted-Solution

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