#1740MediumPremium on LC~35 min

Find Distance in a Binary Tree

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() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int findDistance(TreeNode* root, int p, int q) {
        return iter_dfs(root, p, q);
    }

private:
    int iter_dfs(TreeNode *node, int p, int q) {
        int result = 0, dist = -1;
        vector<tuple<int, TreeNode *, unique_ptr<int>, unique_ptr<int>, int*>> stk;
        stk.emplace_back(1, node, nullptr,  nullptr, &dist);
        while (!empty(stk)) {
            const auto [step, node, ret1, ret2, ret] = move(stk.back()); stk.pop_back();
            if (step == 1) {
                if (!node) {
                    continue;
                }
                auto ret1 = make_unique<int>(-1), ret2 = make_unique<int>(-1);
                auto p1 = ret1.get(), p2 = ret2.get();
                stk.emplace_back(2, node, move(ret1), move(ret2), ret);
                stk.emplace_back(1, node->right, nullptr, nullptr, p2);
                stk.emplace_back(1, node->left, nullptr, nullptr, p1);
            } else if (step == 2) {
                if (node->val == p || node->val == q) {
                    if (*ret1 == -1 && *ret2 == -1) {
                        *ret = 0;
                    }
                    result = (*ret1 != -1) ? *ret1 + 1 : *ret2 + 1;
                } else if (*ret1 != -1 && *ret2 != -1) {
                    result = *ret1 + *ret2 + 2;
                } else if (*ret1 != -1) {
                    *ret = *ret1 + 1;
                } else if (*ret2 != -1) {
                    *ret = *ret2 + 1;
                }
            }
        }
        return result;
    }
};

// Time:  O(n)
// Space: O(h)
class Solution2 {
public:
    int findDistance(TreeNode* root, int p, int q) {
        int result = 0;
        dfs(root, p, q, &result);
        return result;
    }

private:
    int dfs(TreeNode *node, int p, int q, int *result) {
        if (!node) {
            return -1;
        }
        auto left = dfs(node->left, p, q, result);
        auto right = dfs(node->right, p, q, result);
        if (node->val == p || node->val == q) {
            if (left == -1 && right == -1) {
                return 0;
            }
            *result = (left != -1) ? left + 1 : right + 1;
        } else if (left != -1 && right != -1) {
            *result = left + right + 2;
        } else if (left != -1) {
            return left + 1;
        } else if (right != -1) {
            return right + 1;
        }
        return -1;
    }
};

Beginner Explanation

What is Find Distance in a Binary Tree?

Find Distance in a Binary Tree (LeetCode #1740) is a Medium problem that primarily trains depth first search.

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 dfs backtracking.
Only then translate the idea into code.

Why this problem matters

It sits in the sweet spot of interview difficulty: multiple valid approaches, clear trade-offs.

AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.

Interview Walkthrough

Interview approach for Find Distance in a Binary Tree

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 dfs backtracking.

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: dfs backtracking

Use the pattern as a checklist:

dfs backtracking — 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 Find Distance in a Binary Tree

Skipping edge cases — empty collections, single-element inputs, max constraints.
Wrong invariant for dfs backtracking — 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 dfs backtracking:

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: depth first search.

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 Find Distance in a Binary Tree in a second language (cpp, python).
Drill 3–5 more problems tagged depth first search.
Teach the solution out loud in under 5 minutes.
Add this problem to your revision calendar in 3 days and 14 days.

Visualization

Conceptual diagram for Find Distance in a Binary Tree: show input structure (depth first search), highlight the moving parts of the dfs backtracking approach, and annotate each step with the maintained invariant and complexity.

Study checklist

Read the official problem statement on LeetCode
Solve on paper / whiteboard first
Implement the dfs backtracking 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

Find Distance in a Binary Tree (#1740) — Medium. Pattern: dfs backtracking. Complexity: O(n) time / O(h) space. Re-derive the invariant before coding.

FAQs

What is the time complexity of Find Distance in a Binary Tree?+

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 Find Distance in a Binary Tree use?+

It primarily maps to dfs backtracking, within the broader topic of depth first search.

Is Find Distance in a Binary Tree good for interviews?+

Yes — as a Medium 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/find-distance-in-a-binary-tree/

#	Title	Difficulty	Topics
113	Path Sum II	Medium	depth first search
199	Binary Tree Right Side View	Medium	depth first search
236	Lowest Common Ancestor of a Binary Tree	Medium	depth first search
247	Strobogrammatic Number II	Medium	depth first search
250	Count Univalue Subtrees	Medium	depth first search
364	Nested List Weight Sum II	Medium	depth first search
366	Find Leaves of Binary Tree	Medium	depth first search
417	Pacific Atlantic Water Flow	Medium	depth first search