BST Inorder Successor in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Find the inorder successor in a BST with right subtree

What is the output of the inorder successor function for node 15 in the given BST?

DSA Go

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

func inorderSuccessor(root, p *TreeNode) *TreeNode {
    if p.Right != nil {
        curr := p.Right
        for curr.Left != nil {
            curr = curr.Left
        }
        return curr
    }
    var succ *TreeNode
    curr := root
    for curr != nil {
        if p.Val < curr.Val {
            succ = curr
            curr = curr.Left
        } else if p.Val > curr.Val {
            curr = curr.Right
        } else {
            break
        }
    }
    return succ
}

// BST structure:
//        20
//       /  \
//     10    30
//       \     \
//       15    40

// Call: inorderSuccessor(root, node with Val=15)

A Node with Val=20

B Node with Val=30

C Node with Val=40

D Node with Val=15

💡 Hint

Remember, if the node has a right child, the successor is the leftmost node in the right subtree.

Since node 15 has no right child, the successor is the lowest ancestor whose left child is also an ancestor of 15. That is node 20.

❓ Predict Output

intermediate

Inorder successor when node has no right subtree

What is the output of the inorder successor function for node 10 in the BST below?

DSA Go

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

func inorderSuccessor(root, p *TreeNode) *TreeNode {
    var succ *TreeNode
    curr := root
    for curr != nil {
        if p.Val < curr.Val {
            succ = curr
            curr = curr.Left
        } else if p.Val > curr.Val {
            curr = curr.Right
        } else {
            break
        }
    }
    return succ
}

// BST structure:
//        20
//       /  \
//     10    30
//    /  
//   5

// Call: inorderSuccessor(root, node with Val=10)

A Node with Val=30

B Node with Val=5

C Node with Val=20

D Node with Val=10

💡 Hint

If the node has no right child, the successor is the lowest ancestor whose left child is also an ancestor of the node.

Node 10 has no right subtree, so the successor is the ancestor node 20 which is the next bigger value.

🔧 Debug

advanced

Identify the error in inorder successor code

What error will this code produce when finding the inorder successor of node 25 in the BST below?

DSA Go

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

func inorderSuccessor(root, p *TreeNode) *TreeNode {
    if p.Right != nil {
        curr := p.Right
        for curr.Right != nil {
            curr = curr.Right
        }
        return curr
    }
    var succ *TreeNode
    curr := root
    for curr != nil {
        if p.Val < curr.Val {
            succ = curr
            curr = curr.Left
        } else if p.Val > curr.Val {
            curr = curr.Right
        } else {
            break
        }
    }
    return succ
}

// BST structure:
//        20
//       /  \
//     10    30
//           / \
//         25   40

// Call: inorderSuccessor(root, node with Val=25)

A Returns nil

B Returns node with Val=30

C Returns node with Val=25

D Returns node with Val=40

💡 Hint

Check the traversal inside the right subtree for the successor.

The code incorrectly traverses to the rightmost node in the right subtree instead of the leftmost. The successor of 25 is 30, and the code correctly returns it since 25 has no right subtree.

🧠 Conceptual

advanced

Inorder successor when node is the maximum element

What is the inorder successor of the maximum node in a BST?

A The minimum node in the BST

B The root node

C The parent of the maximum node

D Nil (no successor)

💡 Hint

Think about the inorder traversal order and what comes after the largest value.

The maximum node has no inorder successor because it is the last node in the inorder traversal.

🚀 Application

expert

Find inorder successor in BST without parent pointer

Given a BST and a node p without parent pointers, which approach correctly finds the inorder successor of p?

A Traverse from root, keep track of potential successor when moving left, return last recorded successor

B Traverse from p to root using parent pointers to find successor

C Return the right child of p if exists, else return p itself

D Traverse the entire tree inorder and return the node after p

💡 Hint

Without parent pointers, you must start from the root to find the successor.

Since p has no parent pointer, we start from root and move down. When moving left, we update successor. This finds the lowest ancestor whose left child is also ancestor of p.

Practice

1. What is the inorder successor of a node in a Binary Search Tree (BST)?

easy

A. The node with the largest key smaller than the given node's key

B. The node with the smallest key greater than the given node's key

C. The root node of the BST

D. The left child of the given node

Solution

1. Step 1: Understand inorder traversal order

   Inorder traversal visits nodes in ascending order of their keys in a BST.

2. Step 2: Define inorder successor

   The inorder successor of a node is the next node visited after it in inorder traversal, which is the smallest node with a key greater than the current node's key.

3. Final Answer:

   The node with the smallest key greater than the given node's key -> Option B

4. Quick Check:

   Inorder successor = next larger node [OK]

Hint: Inorder successor is next bigger node in BST [OK]

Common Mistakes:

• Confusing successor with predecessor
• Thinking successor is always right child
• Assuming successor is parent node

2. Which of the following Go function signatures correctly represents a function to find the inorder successor of a BST node?

easy

A. func inorderSuccessor(root *Node, p *Node) *Node

B. func inorderSuccessor(p *Node) *Node

C. func inorderSuccessor(root Node, p Node) Node

D. func inorderSuccessor(root *Node) int

Solution

1. Step 1: Analyze function parameters

   To find the inorder successor, we need the BST root and the target node pointer, both as pointers to Node structs.

2. Step 2: Check return type

   The function should return a pointer to the successor node, so return type is *Node.

3. Final Answer:

   func inorderSuccessor(root *Node, p *Node) *Node -> Option A

4. Quick Check:

   Function needs root and target node pointers, returns node pointer [OK]

Hint: Function needs root and target node pointers [OK]

Common Mistakes:

• Passing nodes by value instead of pointer
• Returning int instead of node pointer
• Missing root parameter

3. Given the following BST and code snippet, what will be printed?

type Node struct {
    Val   int
    Left  *Node
    Right *Node
}

func inorderSuccessor(root, p *Node) *Node {
    var successor *Node
    for root != nil {
        if p.Val < root.Val {
            successor = root
            root = root.Left
        } else {
            root = root.Right
        }
    }
    return successor
}

// BST structure:
//       20
//      /  \
//    10    30
//      \
//      15

p := &Node{Val: 15}
succ := inorderSuccessor(root, p)
if succ != nil {
    fmt.Println(succ.Val)
} else {
    fmt.Println("nil")
}

medium

A. 20

B. 30

C. 15

D. nil

Solution

1. Step 1: Trace inorderSuccessor function for p=15

   Start at root=20: 15 < 20, successor=20, move left to 10. At 10: 15 >= 10, move right to 15. At 15: 15 >= 15, move right (nil). Loop ends.

2. Step 2: Return successor node

   Successor is 20, so succ.Val = 20 is printed.

3. Final Answer:

   20 -> Option A

4. Quick Check:

   Next bigger node after 15 is 20 [OK]

Hint: Successor is smallest node bigger than p [OK]

Common Mistakes:

• Returning p itself as successor
• Returning nil when right subtree is empty
• Confusing successor with predecessor

4. The following Go code tries to find the inorder successor of a node in a BST but has a bug. What is the bug?

func inorderSuccessor(root, p *Node) *Node {
    if p.Right != nil {
        curr := p.Right
        for curr.Left != nil {
            curr = curr.Left
        }
        return curr
    }
    var successor *Node
    for root != nil {
        if p.Val < root.Val {
            successor = root
            root = root.Left
        } else {
            root = root.Right
        }
    }
    return successor
}

medium

A. It does not handle the case when p has no right child

B. It incorrectly returns p.Right when p.Right is nil

C. It does not update successor when p.Val equals root.Val

D. It assumes root is always the BST root, which may not be true

Solution

1. Step 1: Understand the logic for successor search

   The code tries to find successor by checking right subtree or walking from root to find successor.

2. Step 2: Identify the bug in root traversal

   The code assumes root is the BST root, but if root is not the actual BST root or p is not reachable from root, the successor found may be incorrect.

3. Final Answer:

   It assumes root is always the BST root, which may not be true -> Option D

4. Quick Check:

   Root must be BST root to find correct successor [OK]

Hint: Ensure root is BST root, not arbitrary node [OK]

Common Mistakes:

• Passing a root that is not the BST root
• Not checking if p.Right is nil before access
• Ignoring case when p has no right subtree

5. You have a BST where each node has a parent pointer in addition to left and right children. How can you find the inorder successor of a node p efficiently using this parent pointer? Choose the correct approach.

hard

A. Always move to the root and perform full inorder traversal to find successor

B. If p has left child, successor is rightmost node in left subtree; else move down to left child

C. If p has right child, successor is leftmost node in right subtree; else move up using parent until node is left child of its parent

D. Successor is always the parent node regardless of children

Solution

1. Step 1: Check if p has right child

   If yes, successor is the leftmost node in p's right subtree.

2. Step 2: If no right child, move up using parent pointer

   Keep moving up until current node is left child of its parent; that parent is the successor.

3. Final Answer:

   If p has right child, successor is leftmost node in right subtree; else move up using parent until node is left child of its parent -> Option C

4. Quick Check:

   Use right subtree or climb parents to find successor [OK]

Hint: Use right subtree or climb parents via left child check [OK]

Common Mistakes:

• Confusing left and right subtree roles
• Always returning parent as successor
• Performing full traversal instead of using parent pointer