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We can utilize the properties of a BST to perform a recursive traversal. The strategy here involves:
low, we need to trim the left subtree and consider the right subtree.high, we trim the right subtree and consider the left subtree.low, high], we recursively trim both subtrees.Time Complexity: O(n), where n is the number of nodes in the tree, since each node is processed once.
Space Complexity: O(h), where h is the height of the tree, representing the recursion stack.
1#include <iostream>
2using namespace std;
3
4struct TreeNode {
5 int val;
6 TreeNode *left;
7 TreeNode *right;
8 TreeNode(int x) : val(x), left(NULL), right(NULL) {}
9};
10
11TreeNode* trimBST(TreeNode* root, int low, int high) {
12 if (!root) return NULL;
13 if (root->val < low) return trimBST(root->right, low, high);
14 if (root->val > high) return trimBST(root->left, low, high);
15 root->left = trimBST(root->left, low, high);
16 root->right = trimBST(root->right, low, high);
17 return root;
18}The function trimBST is similar to its C counterpart, using the BST properties to recursively adjust subtrees.
This iterative approach uses a stack to traverse the tree. The main idea is to mimic the recursive depth-first search using an explicit stack.
Time Complexity: O(n), as each node is processed once.
Space Complexity: O(h), where h is the height of the tree, due to the stack usage.
1import java.util.Stack;
This Java example shows an iterative approach using a stack to maintain the modified tree's structure while keeping nodes within bounds. Each node is processed, ensuring valid nodes are stacked for later traversal.