What is the brute force approach and complexity for Path Sum II?

Pass the path by value, so every call copies the whole path built so far with time complexity O(N · H) and space complexity O(H²).

What is the optimal approach and complexity for Path Sum II?

Push and pop one vector as we walk; copy it into the answers at matching leaves with optimal time complexity O(N + A · H) and space complexity O(H).

How do you identify the pattern for Path Sum II?

Look for key signals in the prompt: "all root-to-leaf paths" indicates Visit every leaf with a full DFS. The answer is a list of paths, not a single yes or no.; "values add up to targetSum" indicates Carry the remaining amount down, as in Path Sum.; "return the paths" indicates The path values are state we must keep, not just one number..

Path Sum II

Medium·LeetCode #113 Pro OnlyMedium

LeetCode

Problem Statement

You are given the root of a binary tree and a number targetSum.

Find every root-to-leaf path whose values add up to targetSum. A root-to-leaf path starts at the root and ends at a leaf (a node with no children). Return each matching path as a list of its node values, not as node references.

Input

The root of a binary tree (it can be empty) and an integer targetSum.

Output

A list of every matching path. Each path is a list of values from the root down to a leaf.

Example 1

Input: root = [5, 4, 8, 11, null, 13, 4, 7, 2, null, null, 5, 1], targetSum = 22

Output: [[5, 4, 11, 2], [5, 8, 4, 5]]

5 + 4 + 11 + 2 = 22 and 5 + 8 + 4 + 5 = 22. The path 4 → 11 → 7 also adds to 22, but it does not start at the root, so it does not count.

Example 2

Input: root = [1, 2, 3], targetSum = 5

Output: []

The two paths add to 3 and 4. Neither is 5.

Example 3

Input: root = [1, 2], targetSum = 0

Output: []

The only path, 1 → 2, adds to 3.

Constraints

• The tree has between 0 and 5000 nodes.
• −1000 ≤ Node.val ≤ 1000
• −1000 ≤ targetSum ≤ 1000

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“all root-to-leaf paths”

→ Visit every leaf with a full DFS. The answer is a list of paths, not a single yes or no.

“values add up to targetSum”

→ Carry the remaining amount down, as in Path Sum.

“return the paths”

→ The path values are state we must keep, not just one number.

Approach Complexity Ladder

Brute Force — copy the path into every callO(N · H)O(H²)

Pass the path by value, so every call copies the whole path built so far

Optimal — one shared path, copy only at answersO(N + A · H)O(H)

Push and pop one vector as we walk; copy it into the answers at matching leaves

Brute Force Intuition

Give each call its own vector of values. A call adds its node to the vector it was given, and passes a full copy of that vector to each child. When a leaf matches, its vector is an answer.

Recognition rule for this sub-pattern:

Carry information down the path (current sum, max so far, direction). Check it at leaves.

Remember this · Tree DFS

Trigger

Paths, heights, diameters, validating structure, ancestors, anything "for every subtree".

Think

If my left and right children already gave me their answers, how do I build mine?

Key question

What does my recursive function return, and what do I pass down?

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