Largest BST Subtree

要點：

• http://articles.leetcode.com/largest-binary-search-tree-bst-in
• 這題重點是理解題意，還有道類似題 Largest Binary Search Tree (BST) in a Binary Tree – LeetCode( http://articles.leetcode.com/largest-binary-search-tree-bst-in_22
• 兩題的區別：
  • 本題with all descendants：需要所有left/right子樹都是bst，并且和root構成bst。而另一題是如果left or right不是bst，root還可以是（這里注意即使不要求所有descendants，結點仍需要連接的才構成bst）
  • 顯然如果all descendants，需要檢查到最底才能決定，所以bottom up方法。而另一題要從上到下擴展，所以top-down。
• return value和args：
  • 本題用bottom up的方法，所有min/max是return的，并且要return子樹的判定狀態和結點個數：-1表示子樹不是bst，0個結點還是可以的。其他個數要比較min/max和root。
    • 通過檢查-1/0來ignore返回的max/min：所以可以返回0/0作為max/min
  • 另一題return的個數是0或者實際個數，另外如果不能擴展了，要以這個子樹為root重新計數

錯誤點：

• 不能因為left子樹不符合就提前返回，仍然要遍歷right子樹來找到其他root對應的bst subtree

https://repl.it/Cb9Z/2

# Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it.# Note: # A subtree must include all of its descendants. # Here's an example: # 10 # / \ # 5 15 # / \ \ # 1 8 7 # The Largest BST Subtree in this case is the highlighted one. # The return value is the subtree's size, which is 3. # Hint:# You can recursively use algorithm similar to 98. Validate Binary Search Tree at each node of the tree, which will result in O(nlogn) time complexity. # Follow up: # Can you figure out ways to solve it with O(n) time complexity?# Definition for a binary tree node. # class TreeNode(object): # def __init__(self, x): # self.val = x # self.left = None # self.right = Noneclass Solution(object):def largestBSTSubtree(self, root):""":type root: TreeNode:rtype: int"""def bfs(root):if not root:return 0,0,0isBST = Trueleftnodes, maxl, minl = bfs(root.left)if leftnodes==-1 or (leftnodes!=0 and root.val<maxl):isBST = Falseif leftnodes==0:minl = root.valrightnodes, maxr, minr = bfs(root.right)if rightnodes==-1 or (rightnodes!=0 and root.val>minr):isBST = Falseif rightnodes==0:maxr = root.valif isBST:self.maxLen = max(self.maxLen, leftnodes+rightnodes+1)return leftnodes+rightnodes+1, maxr, minlreturn -1, 0, 0self.maxLen = 0bfs(root)return self.maxLen

轉載于:https://www.cnblogs.com/absolute/p/5815850.html

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