leetcode 108. Convert Sorted Array to Binary Search Tree

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 every node 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

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def sortedArrayToBST(self, nums):
        """
        :type nums: List[int]
        :rtype: TreeNode
        """
        def build_bst(arr, i, j):
            if i > j:
                return None
            mid = (i+j)>>1
            node = TreeNode(arr[mid])
            node.left = build_bst(arr, i, mid-1)
            node.right = build_bst(arr, mid+1, j)
            return node            
        
        return build_bst(nums, 0, len(nums)-1)    

 

迭代解法，本质上是先序遍历：

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def sortedArrayToBST(self, nums):
        """
        :type nums: List[int]
        :rtype: TreeNode
        """        
        if not nums: return None
        q = [(0, len(nums)-1)]
        ans = TreeNode(0)
        nodes = [ans]
        while q:
            i, j = q.pop()
            mid = (i+j)>>1
            node = nodes.pop()
            node.val = nums[mid]
            if mid+1 <= j:
                node.right = TreeNode(0)
                q.append((mid+1, j))
                nodes.append(node.right)
            if mid-1 >= i:
                node.left = TreeNode(0)
                q.append((i, mid-1))
                nodes.append(node.left)
        return ans