Search Range in Binary Search Tree
Question (LC.11)
Given two values k1 and k2 (k1 < k2) and a pointer to the root of a BST. Find all the keys of tree in range [k1, k2] or k1<=x<=k2. Return all the keys in ascending order.
Example
root20
/ \
8 22
/ \
4 12
Input: k1 = 10, k2 = 22
Return: [12, 20, 22]
Analysis
Do a binary search. If the root is in the search interval (low < root.val < high), search both left and right subtree. If the root.val < low, search right subtree. If the root.val > high, search left subtree.
Traverse Code
public ArrayList<Integer> searchRange(TreeNode root, int k1, int k2) {
ArrayList<Integer> results = new ArrayList<>();
bsearchRange(results, root, k1, k2);
Collections.sort(results);
return results;
}
private void bsearchRange(ArrayList<Integer> results, TreeNode root, int low, int high) {
if (root == null) {
return;
}
if (root.val >= low && root.val <= high) {
results.add(root.val);
bsearchRange(results, root.left, low, high);
bsearchRange(results, root.right, low, high);
} else if (root.val < low) {
bsearchRange(results, root.right, low, high);
} else {
bsearchRange(results, root.left, low, high);
}
}
We don't need to sort it. We can take advantaged of the binary search tree property - sorted. We can add in the nodes in a sorted order.
private void bsearchRange(ArrayList<Integer> results, TreeNode root, int low, int high) {
if (root == null) {
return;
}
if (root.val < low) {
bsearchRange(results, root.right, low, high);
} else if (root.val > low && root.val < high) {
results.add(root.val);
bsearchRange(results, root.left, low, high);
bsearchRange(results, root.right, low, high);
} else {
bsearchRange(results, root.left, low, high);
}
}
D&C Code
def searchRange(self, root: TreeNode, k1: int, k2: int) -> List[int]:
# base
if root is None:
return []
# divide
left_vals = []
if k1 < root.val:
left_vals = self.searchRange(root.left, k1, k2)
right_vals = []
if k2 > root.val:
right_vals = self.searchRange(root.right, k1, k2)
# merge
cur_vals = []
if root.val >= k1 and root.val <= k2:
cur_vals = [root.val]
return left_vals + cur_vals + right_vals
Worst case O(n) but can prune some searches outside of the search interval
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