Why Path Sum Root to Leaf in Binary Tree in DSA Go?

The Big Idea

What if you could instantly know if a path adds up to your target without checking every step yourself?

The Scenario

Imagine you have a family tree drawn on paper, and you want to find if there is a path from the oldest ancestor to a youngest family member where the ages add up to a certain number.

Doing this by hand means checking every possible path, adding numbers, and hoping you don't miss any.

The Problem

Manually adding numbers along every path is slow and easy to mess up, especially if the tree is big.

You might forget a path or add wrong numbers, making the whole process frustrating and error-prone.

The Solution

Using a program to check the tree automatically saves time and avoids mistakes.

The program walks down each path, keeps track of the sum, and tells you if any path matches the target sum.

Before vs After

✗ Before

func checkPathSum(root *Node, target int) bool {
    // Manually check each path by hand
    return false // too complex to do manually
}

✓ After

func hasPathSum(root *Node, targetSum int) bool {
    if root == nil {
        return false
    }
    if root.Left == nil && root.Right == nil {
        return root.Val == targetSum
    }
    return hasPathSum(root.Left, targetSum-root.Val) || hasPathSum(root.Right, targetSum-root.Val)
}

What It Enables

This lets you quickly find if any root-to-leaf path adds up to a target, even in huge trees.

Real Life Example

Checking if a route in a map adds up to a certain distance or cost, helping in navigation or planning.

Key Takeaways

Manual checking is slow and error-prone.

Recursive path sum checking automates and simplifies the task.

It helps find exact paths matching a sum quickly.

Practice

1. What does the "Path Sum Root to Leaf" problem ask you to find in a binary tree?

easy

A. If there exists a root-to-leaf path with a sum equal to a given target

B. The maximum depth of the binary tree

C. The total number of leaf nodes in the tree

D. The sum of all node values in the tree

Solution

1. Step 1: Understand the problem statement

   The problem asks if there is any path from the root node down to any leaf node where the sum of the node values equals a given target sum.

2. Step 2: Differentiate from other tree properties

   It is not about counting leaves, finding max depth, or summing all nodes, but specifically about a path sum from root to leaf.

3. Final Answer:

   If there exists a root-to-leaf path with a sum equal to a given target -> Option A

4. Quick Check:

   Path sum = target? [OK]

Hint: Focus on root-to-leaf paths, not entire tree sums [OK]

Common Mistakes:

• Confusing path sum with total tree sum
• Checking paths that don't end at leaf nodes
• Ignoring the root node in the sum

2. Which of the following Go function signatures correctly represents a function to check path sum in a binary tree node defined as type TreeNode struct { Val int; Left, Right *TreeNode }?

easy

A. func hasPathSum(root TreeNode, sum int) bool

B. func hasPathSum(root *TreeNode, sum int) bool

C. func hasPathSum(root *TreeNode, sum int) int

D. func hasPathSum(root TreeNode, sum int) int

Solution

1. Step 1: Identify correct parameter types

   The root node should be passed as a pointer to TreeNode to allow nil checks and avoid copying the entire node.

2. Step 2: Identify correct return type

   The function should return a boolean indicating if such a path exists, not an integer.

3. Final Answer:

   func hasPathSum(root *TreeNode, sum int) bool -> Option B

4. Quick Check:

   Pointer param + bool return = correct signature [OK]

Hint: Use pointer receiver and bool return for path existence [OK]

Common Mistakes:

• Passing TreeNode by value instead of pointer
• Returning int instead of bool
• Using incorrect parameter order

3. What is the output of the following Go code snippet?

package main

import "fmt"

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

func hasPathSum(root *TreeNode, sum int) bool {
  if root == nil {
    return false
  }
  if root.Left == nil && root.Right == nil {
    return root.Val == sum
  }
  return hasPathSum(root.Left, sum-root.Val) || hasPathSum(root.Right, sum-root.Val)
}

func main() {
  root := &TreeNode{5, &TreeNode{4, &TreeNode{11, &TreeNode{7, nil, nil}, &TreeNode{2, nil, nil}}, nil}, &TreeNode{8, &TreeNode{13, nil, nil}, &TreeNode{4, nil, &TreeNode{1, nil, nil}}}}
  fmt.Println(hasPathSum(root, 22))
}

medium

A. Compilation error

B. false

C. Runtime panic

D. true

Solution

1. Step 1: Trace the path sums in the tree

   Check if any root-to-leaf path sums to 22. One path is 5->4->11->2 = 22, so the function returns true.

2. Step 2: Confirm function logic correctness

   The function correctly checks leaf nodes and recursively subtracts node values from sum, returning true if any path matches.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Path 5+4+11+2 = 22 [OK]

Hint: Look for any root-to-leaf path summing to target [OK]

Common Mistakes:

• Ignoring leaf node condition
• Not subtracting node value from sum
• Assuming sum must be at root only

4. The following Go function is intended to check if a path sum exists but has a bug. What is the bug?

func hasPathSum(root *TreeNode, sum int) bool {
  if root == nil {
    return false
  }
  if root.Left == nil && root.Right == nil {
    return sum == root.Val
  }
  return hasPathSum(root.Left, sum-root.Val) && hasPathSum(root.Right, sum-root.Val)
}

medium

A. Using && instead of || causes incorrect results

B. Missing base case for nil root

C. Incorrect comparison order in leaf check

D. Not subtracting root.Val from sum in recursive calls

Solution

1. Step 1: Analyze recursive return condition

   The function uses logical AND (&&) to combine left and right subtree results, which requires both to be true.

2. Step 2: Understand correct logic for path sum

   We want to return true if either left or right subtree has a valid path, so logical OR (||) should be used instead.

3. Final Answer:

   Using && instead of || causes incorrect results -> Option A

4. Quick Check:

   Use OR (||) to find any valid path [OK]

Hint: Use OR (||) to combine subtree results, not AND (&&) [OK]

Common Mistakes:

• Using AND instead of OR in recursive calls
• Forgetting to check leaf nodes properly
• Not handling nil root correctly

5. Given a binary tree where node values can be negative, zero, or positive, which modification is necessary to correctly check for a path sum equal to a target value?

hard

A. Only consider paths with positive sums

B. Stop recursion early if sum becomes negative

C. No modification needed; the standard path sum check works for all values

D. Use breadth-first search instead of depth-first search

Solution

1. Step 1: Understand path sum logic with negative values

   The standard recursive approach subtracts node values from sum and checks leaf nodes; negative values do not break this logic.

2. Step 2: Evaluate unnecessary optimizations

   Stopping early on negative sums or ignoring negative paths can miss valid paths; BFS is not required for correctness.

3. Final Answer:

   No modification needed; the standard path sum check works for all values -> Option C

4. Quick Check:

   Standard DFS works with negatives [OK]

Hint: Standard DFS path sum works regardless of node values sign [OK]

Common Mistakes:

• Stopping recursion on negative sums
• Ignoring negative or zero values in paths
• Switching to BFS unnecessarily