333 Largest BST Subtree
333. Largest BST Subtree
1. Question
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.
Follow up: Can you figure out ways to solve it with O(n) time complexity?
2. Implementation
(1) Post-order Traversal
思路: 在后序遍历的过程中利用validate binary search tree的思想,对每个node的值,与它的leftSubTree最大值和rightSubtree最小值比较,如果node.val 小于等于leftSubTree的最大值或者大于等于rightSubTree的最小值,或者树的size是-1,则以该node作为root构成的树不是binary search tree. 然后每个node遍历完后返回一个数组,其中数组第一个元素存储的是以该node作为树的最小值,第二个元素存储的是以该node作为树最大值,第三个元素存储的是树的size。
class Solution {
public int largestBSTSubtree(TreeNode root) {
int[] maxSize = new int[1];
dfs(root, maxSize);
return maxSize[0];
}
public long[] dfs(TreeNode node, int[] maxSize) {
if (node == null) {
return new long[] {Integer.MAX_VALUE, Integer.MIN_VALUE, 0};
}
long[] left = dfs(node.left, maxSize);
long[] right = dfs(node.right, maxSize);
if (left[2] == -1 || right[2] == -1 || node.val <= left[1] || node.val >= right[0]) {
return new long[] {0, 0, -1};
}
int count = (int)(left[2] + right[2] + 1);
maxSize[0] = Math.max(maxSize[0], count);
return new long[] {Math.min(left[0], node.val), Math.max(right[1], node.val), count};
}
}
3. Time & Space Complexity
Post-order Traversal: 时间复杂度: O(n), 空间复杂度: O(h)
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