[LeetCode] 1008. Construct Binary Search Tree from Preorder Traversal 從先序遍歷重建二叉搜索樹

Return the root node of a binary search tree that matches the given preorder traversal.

(Recall that a binary search tree is a binary tree where for every node, any descendant of node.left has a value < node.val, and any descendant of node.right has a value > node.val.  Also recall that a preorder traversal displays the value of the node first, then traverses node.left, then traverses node.right.)

It's guaranteed that for the given test cases there is always possible to find a binary search tree with the given requirements.

Example 1:

Input: [8,5,1,7,10,12]
Output: [8,5,10,1,7,null,12]

Constraints:

• 1 <= preorder.length <= 100
• 1 <= preorder[i] <= 10^8
• The values of preorder are distinct.

這道題讓我們從一個數組來重建一棵二叉搜索樹，同時說明了這個數組是先序遍歷二叉樹后得到的。首先要明白的是二叉搜索樹的性質，是左子結點值小於根結點小於右子結點，正是因為有這樣的特點，才使得從一種遍歷順序上重建變的可能。若是普通的二叉樹，則至少需要兩種遍歷順序的數組，比如之前的 Construct Binary Tree from Preorder and Postorder Traversal，Construct Binary Tree from Inorder and Postorder Traversal，和 Construct Binary Tree from Preorder and Inorder Traversal。再來分析下這個先序數組有什么特點，先序是根左右的順序，則第一個結點肯定是根結點，而根據二叉搜索樹的特點，接下來第一個大於根結點值的數一定是右子結點，而中間的數字都是左子樹中的值，這樣就可以將左右子樹分開了，再分別調用遞歸函數就可以建成整個樹了。有了思路，代碼就很好寫了，先對 preorder 判空，若不為空則用第一個數字建立一個根結點，然后遍歷數組，找到第一個大於根結點值的數字，將左右子樹的數組提取來，分別調用遞歸函數，連接到根結點的左右子結點即可，參見代碼如下：

class Solution {
public:
    TreeNode* bstFromPreorder(vector<int>& preorder) {
        if (preorder.empty()) return nullptr;
        TreeNode *node = new TreeNode(preorder[0]);
        int i = 0, n = preorder.size();
        for (i = 1; i < n; ++i) {
            if (preorder[i] > preorder[0]) break;
        }
        vector<int> left(preorder.begin() + 1, preorder.begin() + i);
        vector<int> right(preorder.begin() + i, preorder.end());
        node->left = bstFromPreorder(left);
        node->right = bstFromPreorder(right);
        return node;
    }
};

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1008

類似題目：

Construct Binary Tree from Preorder and Postorder Traversal

Construct Binary Tree from Inorder and Postorder Traversal

Construct Binary Tree from Preorder and Inorder Traversal

參考資料：

https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/

https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/discuss/252754/Java-Stack-Iterative-Solution

https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/discuss/252232/JavaC%2B%2BPython-O(N)-Solution

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