Path Sum Root to Leaf in Binary Tree in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

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

It asks whether there exists a path from the root node to any leaf node such that the sum of the node values along that path equals a given target sum.

beginner

In the context of the Path Sum problem, what is a leaf node?

A leaf node is a node in a binary tree that has no children (no left or right child).

intermediate

Why do we subtract the current node's value from the target sum when moving down the tree in the Path Sum problem?

Because we want to check if the remaining sum needed to reach the target can be found in the subtree below the current node. Subtracting the current node's value updates the remaining sum to find.

intermediate

What is the base case for the recursive solution to the Path Sum problem?

When the current node is null, return false because no path exists. When the current node is a leaf, check if its value equals the remaining sum; if yes, return true.

beginner

How does the Path Sum algorithm explore the binary tree?

It uses depth-first search (DFS), exploring each path from root to leaf, checking sums along the way.

What should the Path Sum function return if the binary tree is empty?

A true

B null

C false

D 0

If the tree is empty, there is no path, so the function returns false.

In the Path Sum problem, when do we check if the current node's value equals the remaining sum?

A At every node regardless

B When the node is a leaf node

C At the root only

D When the node has children

We check at leaf nodes because only complete root-to-leaf paths count.

Which traversal method is commonly used to solve the Path Sum problem?

A Inorder traversal

B Breadth-first search

C Level order traversal

D Depth-first search

Depth-first search explores each path fully, which fits the problem's need to check root-to-leaf paths.

If the target sum is 22 and the path is 5 -> 4 -> 11 -> 2, what should the Path Sum function return?

A true

B false

C null

D Depends on tree structure

The sum 5 + 4 + 11 + 2 equals 22, so the function returns true.

What happens if the Path Sum function finds a valid path early?

A It returns true immediately

B It continues searching all paths

C It returns false

D It restarts the search

Once a valid path is found, the function returns true without checking further.

Explain how you would use recursion to solve the Path Sum Root to Leaf problem in a binary tree.

Think about how to reduce the problem size at each step.

Describe the role of leaf nodes in determining if a path sum exists in a binary tree.

Focus on where the path ends.

Practice

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

easy

A. The maximum depth of the binary tree

B. If there exists a root-to-leaf path with a sum equal to a target value

C. The total number of nodes in the binary tree

D. The sum of all node values in the binary 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

   This is different from finding the maximum depth, counting nodes, or summing all nodes. It specifically checks for a path sum.

3. Final Answer:

   If there exists a root-to-leaf path with a sum equal to a target value -> Option B

4. Quick Check:

   Path sum means root-to-leaf sum check = A [OK]

Hint: Focus on root-to-leaf paths and their sums [OK]

Common Mistakes:

• Confusing path sum with total tree sum
• Checking any path, not just root-to-leaf
• Mixing depth or node count with sum

2. Which of the following Rust function signatures correctly represents a function to check path sum in a binary tree node defined as struct TreeNode { val: i32, left: Option, right: Option }?

easy

A. fn has_path_sum(root: Option<TreeNode>, sum: i32) -> bool

B. fn has_path_sum(root: TreeNode, sum: i32) -> i32

C. fn has_path_sum(root: Option, sum: i32) -> bool

D. fn has_path_sum(root: &TreeNode, sum: i32) -> Option<i32>

Solution

1. Step 1: Analyze the tree node ownership and option usage

   The tree nodes are wrapped in Option to allow for empty children and heap allocation. The function should accept Option to handle empty trees.

2. Step 2: Check return type and parameters

   The function returns a boolean indicating if a path sum exists. So the signature fn has_path_sum(root: Option, sum: i32) -> bool matches the problem.

3. Final Answer:

   fn has_path_sum(root: Option, sum: i32) -> bool -> Option C

4. Quick Check:

   Correct ownership and return type = D [OK]

Hint: Use Option for nullable tree nodes [OK]

Common Mistakes:

• Using TreeNode directly without Option or Box
• Wrong return type (not bool)
• Passing references incorrectly

3. Given the following Rust code, what is the output?

struct TreeNode {
    val: i32,
    left: Option,
    right: Option,
}

fn has_path_sum(root: Option, sum: i32) -> bool {
    match root {
        None => false,
        Some(node) => {
            if node.left.is_none() && node.right.is_none() {
                return node.val == sum;
            }
            has_path_sum(node.left, sum - node.val) || has_path_sum(node.right, sum - node.val)
        }
    }
}

fn main() {
    let leaf = TreeNode { val: 5, left: None, right: None };
    let root = TreeNode {
        val: 4,
        left: Some(Box::new(leaf)),
        right: None,
    };
    println!("{}", has_path_sum(Some(Box::new(root)), 9));
}

medium

A. Compilation error

B. false

C. Runtime panic

D. true

Solution

1. Step 1: Trace the path sum calculation

   The tree has root 4 with left child 5. The target sum is 9. The path 4 -> 5 sums to 9, so the function returns true.

2. Step 2: Confirm leaf node check and recursion

   At leaf node 5, it checks if 5 == 9 - 4 = 5, which is true, so returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   4 + 5 = 9 matches sum = true [OK]

Hint: Check leaf node sums carefully [OK]

Common Mistakes:

• Ignoring leaf node condition
• Subtracting sum incorrectly
• Confusing Option handling

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

fn has_path_sum(root: Option, sum: i32) -> bool {
    if root.is_none() {
        return false;
    }
    let node = root.unwrap();
    if node.left.is_none() && node.right.is_none() {
        return node.val == sum;
    }
    has_path_sum(node.left, sum - node.val) && has_path_sum(node.right, sum - node.val)
}

medium

A. Using && instead of || for recursive calls

B. Unwrapping Option without checking None

C. Not handling empty tree case

D. Incorrect sum subtraction

Solution

1. Step 1: Analyze recursive call logic

   The function uses logical AND (&&) to combine left and right subtree results, but the problem requires checking if any path exists, so logical OR (||) is correct.

2. Step 2: Understand impact of && vs ||

   Using && means both left and right paths must have the sum, which is incorrect. Only one path needs to match.

3. Final Answer:

   Using && instead of || for recursive calls -> Option A

4. Quick Check:

   Path sum needs OR (||), not AND (&&) [OK]

Hint: Use || to check any path, not all paths [OK]

Common Mistakes:

• Using && instead of ||
• Unwrapping Option without safe check
• Ignoring leaf node condition

5. You want to modify the path sum function to return all root-to-leaf paths where the sum equals the target. Which approach is best to implement this in Rust?

hard

A. Use backtracking with a mutable vector to store current path and a vector of vectors for results

B. Use a global variable to store paths and update it in recursion

C. Return a boolean and print paths inside the function

D. Use iterative BFS traversal without recursion

Solution

1. Step 1: Understand the requirement for all paths

   To find all root-to-leaf paths with a given sum, we need to explore all paths and store those matching the sum.

2. Step 2: Choose backtracking with mutable vectors

   Backtracking allows building paths step-by-step, storing current path in a mutable vector, and adding copies to results when sum matches.

3. Final Answer:

   Use backtracking with a mutable vector to store current path and a vector of vectors for results -> Option A

4. Quick Check:

   Backtracking with path storage = B [OK]

Hint: Backtrack paths, store copies when sum matches [OK]

Common Mistakes:

• Using global variables (not idiomatic in Rust)
• Printing instead of returning paths
• Trying BFS which is complex for path tracking