Two Sum in BST in DSA Go - Time & Space Complexity

Time Complexity: Two Sum in BST

O(n)

Understanding Time Complexity

We want to know how the time needed to find two numbers that add up to a target grows as the tree gets bigger.

How does the search time change when the number of nodes in the BST increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func findTarget(root *TreeNode, k int) bool {
    seen := make(map[int]bool)
    var dfs func(node *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)
}
    

This code searches the BST to find if there are two nodes whose values add up to k using a depth-first search and a map to track seen values.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Recursive traversal of each node in the BST.
• How many times: Each node is visited once during the DFS.

How Execution Grows With Input

As the number of nodes (n) grows, the function visits each node once, so the operations grow roughly in direct proportion to n.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The operations increase linearly as the tree size increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the two sum grows linearly with the number of nodes in the BST.

Common Mistake

[X] Wrong: "Because the tree is a BST, searching for pairs is O(log n)."

[OK] Correct: The code visits every node once to check pairs, so it must look at all nodes, making it linear, not logarithmic.

Interview Connect

Understanding this linear time complexity helps you explain how tree traversal and hash maps work together to solve problems efficiently.

Self-Check

"What if we used an in-order traversal to create a sorted list first, then used two pointers to find the sum? How would the time complexity change?"

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