Minimum Flips to Match Expected Binary Values in a Tree

Problem Statement

You are given an undirected tree with tree_nodes nodes, numbered from 0 to tree_nodes - 1, and rooted at node 0. Each node initially has a binary value (0 or 1) given by the array initial, and an expected binary value given by the array expected.

You can perform the following operation any number of times:

• Pick a node and flip its value along with all nodes in the subtree of u where u % 2 == x % 2. Flipping a value means toggling between 0 and 1.

Find the minimum number of operations needed so that the final binary values match expected.

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Example 1

Input:

tree_nodes = 4  
tree_from = [0, 0, 1]  
tree_to = [1, 2, 3]  
initial = [0, 1, 1, 0]  
expected = [0, 1, 1, 1]  

Output:

2  

Explanation:

1. Pick node 0 and flip it → initial = [0, 1, 1, 1]
2. Pick node 3 and flip it → initial = [0, 1, 1, 0] (matches expected)

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Example 2

Input:

tree_nodes = 5  
tree_from = [0, 1, 2, 4]  
tree_to = [1, 2, 3, 1]  
initial = [1, 1, 0, 1, 0]  
expected = [1, 0, 1, 0, 1]  

Output:

3

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Problem Statement
You are given a list of products, where each product has a name, price, and weight. Your task is to determine how many duplicate products are in the list. A duplicate product is defined as a product that has the same name, price, and weight as another product in the list.

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Function Signature

public static int numDuplicates(List name, List price, List weight)

Parameters

• name: A list of strings where name[i] represents the name of the product at index i.
• price: A list of integers where price[i] represents the price of the product at index i.
• weight: A list of integers where weight[i] represents the weight of the product at index i.

Returns

• An integer denoting the number of duplicate products in the list.

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Constraints

• 1 ≤ n ≤ 10⁶
• 1 ≤ price[i], weight[i] ≤ 1000
• name[i] consists of lowercase English letters (a-z) and has at most 10 characters.

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Example 1

Input:

name = ["ball", "box", "ball", "ball", "box"]  
price = [2, 2, 2, 2, 2]  
weight = [1, 1, 1, 1, 3]  

Output:

2  

Explanation:

• Products at indices 0, 2, 3 have the same attributes (name = "ball", price = 2, weight = 1).
• There are 2 duplicates in this group.
• "box" at index 1, 4 have different weights, so they are unique.

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Example 2

Input:

name = ["ball", "box", "lamp", "brick", "pump"]  
price = [2, 2, 2, 2, 2]  
weight = [2, 2, 2, 2, 2]  

Output:

0  

Explanation:

Each product has unique attributes, so there are no duplicates.
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