Two Sum in BST in DSA Go - Execution Trace

Concept Flow - Two Sum in BST

Start at root

↓

Initialize empty set

↓

Inorder traversal node

↓

Check if complement exists in set

↓

Return true

↓

Move to next node

↓

Repeat until all nodes visited or found

↓

Return false if no pair found

Traverse the BST in order, check if complement of current node value exists in a set, return true if found, else add value and continue.

Execution Sample

DSA Go

func findTarget(root *TreeNode, k int) bool {
    set := make(map[int]bool)
    var inorder func(*TreeNode) bool
    inorder = func(node *TreeNode) bool {
        if node == nil { return false }
        if inorder(node.Left) { return true }
        if set[k - node.Val] { return true }
        set[node.Val] = true
        return inorder(node.Right)
    }
    return inorder(root)
}

This code checks if there exist two nodes in BST whose values sum to k using inorder traversal and a set.

Execution Table

Step	Operation	Current Node Value	Set Contents	Check Complement	Action	Visual State
1	Start at root	5	{}	Check if 9 - 5 = 4 in set	4 not in set, add 5	5
2	Go left	3	{5}	Check if 9 - 3 = 6 in set	6 not in set, add 3	3 -> 5
3	Go left	2	{3,5}	Check if 9 - 2 = 7 in set	7 not in set, add 2	2 -> 3 -> 5
4	Left nil	nil	{2,3,5}	N/A	Return false	2 -> 3 -> 5
5	Back to 2	2	{2,3,5}	Already processed	Go right	2 -> 3 -> 5
6	Right nil	nil	{2,3,5}	N/A	Return false	2 -> 3 -> 5
7	Back to 3	3	{2,3,5}	Already processed	Go right	2 -> 3 -> 5
8	Go right	4	{2,3,5}	Check if 9 - 4 = 5 in set	5 found! Return true	4 -> 3 -> 5
9	Found pair (4,5)	N/A	{2,3,5}	N/A	Stop traversal	4 -> 3 -> 5

💡 Found complement 5 for node 4, sum 9 achieved, traversal stops.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 8	Final
Current Node	root (5)	3	2	4	4	N/A
Set Contents	{}	{5}	{3,5}	{2,3,5}	{2,3,5}	{2,3,5}
Return Value	false	false	false	false	true	true

Key Moments - 3 Insights

Why do we check if complement exists before adding current node value to the set?

Because checking complement first avoids pairing a node with itself. See step 8 in execution_table where complement 5 is found before adding 4.

Why do we use inorder traversal for this problem?

Inorder traversal visits nodes in ascending order, but here it mainly ensures all nodes are visited systematically. The set handles complement checks. See steps 1-9 for traversal order.

What happens if the BST is empty?

The traversal immediately returns false since root is nil, no nodes to check. This is implied at step 4 when node is nil and returns false.

Visual Quiz - 3 Questions

Look at the execution_table, what is the set contents after step 3?

A {}

B {5}

C {3,5}

D {2,3,5}

💡 Hint

Check the 'Set Contents' column at step 3 in execution_table.

At which step does the traversal find the pair that sums to 9?

A Step 4

B Step 6

C Step 8

D Step 9

💡 Hint

Look for the step where 'Check if 9 - 4 = 5 in set' is true in execution_table.

If the target sum was 7 instead of 9, what would happen to the execution?

A Pair found earlier than step 8

B No pair found, traversal completes all nodes

C Traversal stops at step 3

D Set remains empty

💡 Hint

Consider how complement checks depend on target k and see variable_tracker for set contents.

Concept Snapshot

Two Sum in BST:
- Traverse BST inorder
- Use a set to store visited values
- For each node, check if (target - node.Val) in set
- If yes, return true
- Else add node.Val to set
- Return false if no pair found

Full Transcript

This visualization shows how to find two numbers in a BST that add up to a target sum. We start at the root and traverse the tree in order. At each node, we check if the complement (target minus current node value) is already in a set of visited values. If it is, we found a pair and return true. If not, we add the current node value to the set and continue. The traversal stops early if a pair is found. The execution table tracks each step, the current node, the set contents, and actions taken. Variable tracker shows how the current node and set change over time. Key moments clarify why we check complement before adding the node value and why inorder traversal is used. The quiz tests understanding of set contents and when the pair is found.

Practice

1. What is the main goal of the Two Sum in BST problem?

easy

A. Find the maximum value in the BST.

B. Find two nodes in the BST whose values add up to a given target sum.

C. Count the total number of nodes in the BST.

D. Check if the BST is balanced.

Solution

1. Step 1: Understand the problem statement

   The problem asks to find two nodes in a Binary Search Tree (BST) such that their values add up to a given target sum.

2. Step 2: Identify the goal

   The goal is to check if such a pair exists, not to find max, count nodes, or check balance.

3. Final Answer:

   Find two nodes in the BST whose values add up to a given target sum. -> Option B

4. Quick Check:

   Two Sum in BST = Find pair with target sum [OK]

Hint: Look for two values that add up to target in BST [OK]

Common Mistakes:

• Confusing with finding max or min value
• Trying to count nodes instead of finding pairs
• Checking BST balance instead of sum pairs

2. Which of the following Go function signatures is correct for a function that checks if two sum exists in a BST?

easy

A. func findTarget(root *TreeNode, k int) bool

B. func findTarget(root TreeNode, k string) int

C. func findTarget(root *TreeNode, k float64) string

D. func findTarget(root TreeNode, k bool) *TreeNode

Solution

1. Step 1: Understand function parameters and return type

   The function should take a pointer to the root node of BST and an integer target sum, returning a boolean indicating if pair exists.

2. Step 2: Match correct signature

   func findTarget(root *TreeNode, k int) bool matches: pointer to TreeNode, integer target, returns bool.

3. Final Answer:

   func findTarget(root *TreeNode, k int) bool -> Option A

4. Quick Check:

   Correct function signature = func findTarget(root *TreeNode, k int) bool [OK]

Hint: Function takes *TreeNode and int, returns bool [OK]

Common Mistakes:

• Using wrong parameter types like string or bool
• Passing TreeNode by value instead of pointer
• Returning wrong type like int or string

3. What will be the output of the following Go code snippet for Two Sum in BST?

type TreeNode struct {
    Val int
    Left, Right *TreeNode
}

func findTarget(root *TreeNode, k int) bool {
    seen := make(map[int]bool)
    var dfs func(*TreeNode) bool
    dfs = func(node *TreeNode) bool {
        if node == nil {
            return false
        }
        if seen[k - node.Val] {
            return true
        }
        seen[node.Val] = true
        return dfs(node.Left) || dfs(node.Right)
    }
    return dfs(root)
}

root := &TreeNode{Val:5, Left:&TreeNode{Val:3}, Right:&TreeNode{Val:6}}
result := findTarget(root, 9)
fmt.Println(result)

medium

A. true

B. false

C. Compilation error

D. Runtime panic

Solution

1. Step 1: Trace the DFS traversal and map usage

   The function uses DFS to traverse nodes. It checks if (target - current node value) is in the map. For root 5, seen is empty, adds 5. Goes left to 3, checks if 9-3=6 in seen (no), adds 3. Goes right to 6, checks if 9-6=3 in seen (yes), returns true.

2. Step 2: Confirm output

   Since pair (3,6) sums to 9, function returns true and prints true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   Pair found (3+6=9) = true [OK]

Hint: Check if complement exists in map during DFS [OK]

Common Mistakes:

• Not checking complement before adding current value
• Returning false too early
• Ignoring nil node checks causing panic

4. Identify the bug in this Go code for Two Sum in BST and choose the fix:

func findTarget(root *TreeNode, k int) bool {
    seen := make(map[int]bool)
    var dfs func(*TreeNode) bool
    dfs = func(node *TreeNode) bool {
        if node == nil {
            return false
        }
        seen[node.Val] = true
        if seen[k - node.Val] {
            return true
        }
        return dfs(node.Left) || dfs(node.Right)
    }
    return dfs(root)
}

medium

A. Add a nil check after adding to map.

B. Remove the map and use a slice instead.

C. Change return type to int instead of bool.

D. Check complement before adding current node value to map.

Solution

1. Step 1: Analyze the order of operations in DFS

   The code adds current node value to map before checking if complement exists. This causes the complement check to always find current value, leading to false positives.

2. Step 2: Correct the order

   Check if complement exists in map before adding current node value to avoid matching the same node twice.

3. Final Answer:

   Check complement before adding current node value to map. -> Option D

4. Quick Check:

   Complement check before map insert fixes bug [OK]

Hint: Check complement before adding current value [OK]

Common Mistakes:

• Adding current value before checking complement
• Using wrong data structure for lookup
• Ignoring nil node checks

5. Given a BST with nodes [4, 2, 6, 1, 3, 5, 7], which pairs sum to 9? Select the correct output of a Two Sum in BST function that returns all pairs.

func findAllPairs(root *TreeNode, k int) [][2]int {
    seen := make(map[int]bool)
    pairs := [][2]int{}
    var dfs func(*TreeNode)
    dfs = func(node *TreeNode) {
        if node == nil {
            return
        }
        complement := k - node.Val
        if seen[complement] {
            pairs = append(pairs, [2]int{complement, node.Val})
        }
        seen[node.Val] = true
        dfs(node.Left)
        dfs(node.Right)
    }
    dfs(root)
    return pairs
}

hard

A. [[5,4],[6,3],[7,2]]

B. [[1,8],[2,7],[3,6]]

C. [[3,6],[4,5],[2,7]]

D. [[1,7],[2,6],[3,5]]

Solution

1. Step 1: Identify all pairs in BST that sum to 9

   Nodes are 1,2,3,4,5,6,7. Pairs summing to 9 are (2,7), (3,6), (4,5).

2. Step 2: Match pairs with function output format

   The function appends pairs as [complement, node.Val] during preorder traversal: at 6 finds 3 in seen, appends [3,6]; at 5 finds 4, [4,5]; at 7 finds 2, [2,7].

3. Final Answer:

   [[3,6],[4,5],[2,7]] -> Option C

4. Quick Check:

   Pairs summing to 9 in traversal order = [[3,6],[4,5],[2,7]] [OK]

Hint: List pairs where values sum to target k [OK]

Common Mistakes:

• Including pairs with values not in BST
• Reversing pair order incorrectly
• Missing valid pairs