What is the Passing Values Down (State) pattern?

The Passing Values Down (State) is a common coding interview pattern in Depth First Search problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use Passing Values Down (State)?

Use the Passing Values Down (State) pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is Passing Values Down (State) asked in FAANG interviews?

Yes, Passing Values Down (State) is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Depth-First Search

Medium

Passing Values Down (State)

Learn how to pass information (state) from parents to children in DFS.

10 min read

Solve on LeetCode

Examples

Input:root = [3,1,4,3,null,1,5]

Output:4

Explain:

Good nodes are in bold: [3,1,4,3,null,1,5].
Path 3->1->3: Node 3 is good because 3 >= 3.
Path 3->4->5: Node 5 is good because 5 >= 4.

Problem Understanding

We need to count the Good Nodes in a binary tree.

A node is Good if, in the path from the Root to that Node, there are no nodes with a value greater than the node itself.

In simpler terms: Is this node result the largest (or equal largest) value we've seen so far on this path?

Algorithm Strategy (Top-Down State)

We use Pre-order DFS (Top-Down) to solve this.

We need to pass the Maximum Value Seen So Far down to children. This 'state' allows each child to decide if it is 'good' without looking back up the tree.

State: maxVal (the maximum value encountered on the current path).
Check: If node.val >= maxVal, the node is Good. Increment count.
Update: New state for children is max(maxVal, node.val).
Recurse: Call DFS on left and right children with the updated state.

Interactive Visualization

Step 1 / 6

Good

Node 3. Max So Far: 3. 3 >= 3 ? YES (+1).

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