Two Sum IV - Input is a BST
Time O(n) · Space O(h) · Official statement on LeetCode
Solutions
// Time: O(n)
// Space: O(h)
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
public:
bool findTarget(TreeNode* root, int k) {
if (!root) {
return false;
}
BSTIterator left(root, true), right(root, false);
while (*left < *right) {
if (*left + *right == k) {
return true;
} else if (*left + *right < k) {
++left;
} else {
++right;
}
}
return false;
}
private:
class BSTIterator {
public:
BSTIterator(TreeNode *root, bool forward) :
node_(root),
forward_(forward) {
++(*this);
};
int operator*() {
return cur_;
}
void operator++() {
while (node_ || !s_.empty()) {
if (node_) {
s_.emplace(node_);
node_ = forward_ ? node_->left : node_->right;
} else {
node_ = s_.top();
s_.pop();
cur_ = node_->val;
node_ = forward_ ? node_->right : node_->left;
break;
}
}
}
private:
TreeNode* node_;
bool forward_;
stack<TreeNode*> s_;
int cur_;
};
};
Beginner Explanation
What is Two Sum IV - Input is a BST?
Two Sum IV - Input is a BST (LeetCode #653) is a Easy problem that primarily trains tree.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with two pointers.
- Only then translate the idea into code.
Why this problem matters
It builds core muscle memory you will reuse on harder variants. Official solution notes mention: Two Pointers.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Two Sum IV - Input is a BST
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to two pointers.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n)) and space (O(h)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n) time and O(h) space.
Pattern focus: two pointers
Use the pattern as a checklist:
- two pointers — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n) |
| Space | O(h) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Two Sum IV - Input is a BST
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for two pointers — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to two pointers:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: tree.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Two Sum IV - Input is a BST in a second language (cpp, python).
- Drill 3–5 more problems tagged tree.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the two pointers approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Two Sum IV - Input is a BST (#653) — Easy. Pattern: two pointers. Complexity: O(n) time / O(h) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Two Sum IV - Input is a BST?+
The reference solutions aim for O(n) time and O(h) space. Always re-derive complexity from the code you write in the interview.
What pattern does Two Sum IV - Input is a BST use?+
It primarily maps to two pointers, within the broader topic of tree.
Is Two Sum IV - Input is a BST good for interviews?+
Yes — as a Easy problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/two-sum-iv-input-is-a-bst/