LeetCode #3554 — HARD

Find Category Recommendation Pairs

Break down a hard problem into reliable checkpoints, edge-case handling, and complexity trade-offs.

The Problem

Problem Statement

Table: ProductPurchases

+-------------+------+
| Column Name | Type | 
+-------------+------+
| user_id     | int  |
| product_id  | int  |
| quantity    | int  |
+-------------+------+
(user_id, product_id) is the unique identifier for this table. 
Each row represents a purchase of a product by a user in a specific quantity.

Table: ProductInfo

+-------------+---------+
| Column Name | Type    | 
+-------------+---------+
| product_id  | int     |
| category    | varchar |
| price       | decimal |
+-------------+---------+
product_id is the unique identifier for this table.
Each row assigns a category and price to a product.

Amazon wants to understand shopping patterns across product categories. Write a solution to:

Find all category pairs (where category1 < category2)
For each category pair, determine the number of unique customers who purchased products from both categories

A category pair is considered reportable if at least 3 different customers have purchased products from both categories.

Return the result table of reportable category pairs ordered by customer_count in descending order, and in case of a tie, by category1 in ascending order lexicographically, and then by category2 in ascending order.

The result format is in the following example.

Example:

Input:

ProductPurchases table:

+---------+------------+----------+
| user_id | product_id | quantity |
+---------+------------+----------+
| 1       | 101        | 2        |
| 1       | 102        | 1        |
| 1       | 201        | 3        |
| 1       | 301        | 1        |
| 2       | 101        | 1        |
| 2       | 102        | 2        |
| 2       | 103        | 1        |
| 2       | 201        | 5        |
| 3       | 101        | 2        |
| 3       | 103        | 1        |
| 3       | 301        | 4        |
| 3       | 401        | 2        |
| 4       | 101        | 1        |
| 4       | 201        | 3        |
| 4       | 301        | 1        |
| 4       | 401        | 2        |
| 5       | 102        | 2        |
| 5       | 103        | 1        |
| 5       | 201        | 2        |
| 5       | 202        | 3        |
+---------+------------+----------+

ProductInfo table:

+------------+-------------+-------+
| product_id | category    | price |
+------------+-------------+-------+
| 101        | Electronics | 100   |
| 102        | Books       | 20    |
| 103        | Books       | 35    |
| 201        | Clothing    | 45    |
| 202        | Clothing    | 60    |
| 301        | Sports      | 75    |
| 401        | Kitchen     | 50    |
+------------+-------------+-------+

Output:

+-------------+-------------+----------------+
| category1   | category2   | customer_count |
+-------------+-------------+----------------+
| Books       | Clothing    | 3              |
| Books       | Electronics | 3              |
| Clothing    | Electronics | 3              |
| Electronics | Sports      | 3              |
+-------------+-------------+----------------+

Explanation:

Books-Clothing:
- User 1 purchased products from Books (102) and Clothing (201)
- User 2 purchased products from Books (102, 103) and Clothing (201)
- User 5 purchased products from Books (102, 103) and Clothing (201, 202)
- Total: 3 customers purchased from both categories
Books-Electronics:
- User 1 purchased products from Books (102) and Electronics (101)
- User 2 purchased products from Books (102, 103) and Electronics (101)
- User 3 purchased products from Books (103) and Electronics (101)
- Total: 3 customers purchased from both categories
Clothing-Electronics:
- User 1 purchased products from Clothing (201) and Electronics (101)
- User 2 purchased products from Clothing (201) and Electronics (101)
- User 4 purchased products from Clothing (201) and Electronics (101)
- Total: 3 customers purchased from both categories
Electronics-Sports:
- User 1 purchased products from Electronics (101) and Sports (301)
- User 3 purchased products from Electronics (101) and Sports (301)
- User 4 purchased products from Electronics (101) and Sports (301)
- Total: 3 customers purchased from both categories
Other category pairs like Clothing-Sports (only 2 customers: Users 1 and 4) and Books-Kitchen (only 1 customer: User 3) have fewer than 3 shared customers and are not included in the result.

The result is ordered by customer_count in descending order. Since all pairs have the same customer_count of 3, they are ordered by category1 (then category2) in ascending order.

Step 01

Brute Force Baseline

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: General problem-solving

Example 1

{"headers":{"ProductPurchases":["user_id","product_id","quantity"],"ProductInfo":["product_id","category","price"]},"rows":{"ProductPurchases":[[1,101,2],[1,102,1],[1,201,3],[1,301,1],[2,101,1],[2,102,2],[2,103,1],[2,201,5],[3,101,2],[3,103,1],[3,301,4],[3,401,2],[4,101,1],[4,201,3],[4,301,1],[4,401,2],[5,102,2],[5,103,1],[5,201,2],[5,202,3]],"ProductInfo":[[101,"Electronics",100],[102,"Books",20],[103,"Books",35],[201,"Clothing",45],[202,"Clothing",60],[301,"Sports",75],[401,"Kitchen",50]]}}

Step 02

Core Insight

What unlocks the optimal approach

No official hints in dataset. Start from constraints and look for a monotonic or reusable state.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Largest constraint values

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// Auto-generated Java example from py.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (py):
// # Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// import pandas as pd
// 
// 
// def find_category_recommendation_pairs(
//     product_purchases: pd.DataFrame, product_info: pd.DataFrame
// ) -> pd.DataFrame:
//     df = product_purchases[["user_id", "product_id"]].merge(
//         product_info[["product_id", "category"]], on="product_id", how="inner"
//     )
//     user_category = df.drop_duplicates(subset=["user_id", "category"])
//     pair_per_user = (
//         user_category.merge(user_category, on="user_id")
//         .query("category_x < category_y")
//         .rename(columns={"category_x": "category1", "category_y": "category2"})
//     )
//     pair_counts = (
//         pair_per_user.groupby(["category1", "category2"])["user_id"]
//         .nunique()
//         .reset_index(name="customer_count")
//     )
//     result = (
//         pair_counts.query("customer_count >= 3")
//         .sort_values(
//             ["customer_count", "category1", "category2"], ascending=[False, True, True]
//         )
//         .reset_index(drop=True)
//     )
//     return result

// Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// Auto-generated Go example from py.
func exampleSolution() {
}
// Reference (py):
// # Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// import pandas as pd
// 
// 
// def find_category_recommendation_pairs(
//     product_purchases: pd.DataFrame, product_info: pd.DataFrame
// ) -> pd.DataFrame:
//     df = product_purchases[["user_id", "product_id"]].merge(
//         product_info[["product_id", "category"]], on="product_id", how="inner"
//     )
//     user_category = df.drop_duplicates(subset=["user_id", "category"])
//     pair_per_user = (
//         user_category.merge(user_category, on="user_id")
//         .query("category_x < category_y")
//         .rename(columns={"category_x": "category1", "category_y": "category2"})
//     )
//     pair_counts = (
//         pair_per_user.groupby(["category1", "category2"])["user_id"]
//         .nunique()
//         .reset_index(name="customer_count")
//     )
//     result = (
//         pair_counts.query("customer_count >= 3")
//         .sort_values(
//             ["customer_count", "category1", "category2"], ascending=[False, True, True]
//         )
//         .reset_index(drop=True)
//     )
//     return result

# Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
import pandas as pd


def find_category_recommendation_pairs(
    product_purchases: pd.DataFrame, product_info: pd.DataFrame
) -> pd.DataFrame:
    df = product_purchases[["user_id", "product_id"]].merge(
        product_info[["product_id", "category"]], on="product_id", how="inner"
    )
    user_category = df.drop_duplicates(subset=["user_id", "category"])
    pair_per_user = (
        user_category.merge(user_category, on="user_id")
        .query("category_x < category_y")
        .rename(columns={"category_x": "category1", "category_y": "category2"})
    )
    pair_counts = (
        pair_per_user.groupby(["category1", "category2"])["user_id"]
        .nunique()
        .reset_index(name="customer_count")
    )
    result = (
        pair_counts.query("customer_count >= 3")
        .sort_values(
            ["customer_count", "category1", "category2"], ascending=[False, True, True]
        )
        .reset_index(drop=True)
    )
    return result

// Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// Rust example auto-generated from py reference.
// Replace the signature and local types with the exact LeetCode harness for this problem.
impl Solution {
    pub fn rust_example() {
        // Port the logic from the reference block below.
    }
}

// Reference (py):
// # Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// import pandas as pd
// 
// 
// def find_category_recommendation_pairs(
//     product_purchases: pd.DataFrame, product_info: pd.DataFrame
// ) -> pd.DataFrame:
//     df = product_purchases[["user_id", "product_id"]].merge(
//         product_info[["product_id", "category"]], on="product_id", how="inner"
//     )
//     user_category = df.drop_duplicates(subset=["user_id", "category"])
//     pair_per_user = (
//         user_category.merge(user_category, on="user_id")
//         .query("category_x < category_y")
//         .rename(columns={"category_x": "category1", "category_y": "category2"})
//     )
//     pair_counts = (
//         pair_per_user.groupby(["category1", "category2"])["user_id"]
//         .nunique()
//         .reset_index(name="customer_count")
//     )
//     result = (
//         pair_counts.query("customer_count >= 3")
//         .sort_values(
//             ["customer_count", "category1", "category2"], ascending=[False, True, True]
//         )
//         .reset_index(drop=True)
//     )
//     return result

// Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// Auto-generated TypeScript example from py.
function exampleSolution(): void {
}
// Reference (py):
// # Accepted solution for LeetCode #3554: Find Category Recommendation Pairs
// import pandas as pd
// 
// 
// def find_category_recommendation_pairs(
//     product_purchases: pd.DataFrame, product_info: pd.DataFrame
// ) -> pd.DataFrame:
//     df = product_purchases[["user_id", "product_id"]].merge(
//         product_info[["product_id", "category"]], on="product_id", how="inner"
//     )
//     user_category = df.drop_duplicates(subset=["user_id", "category"])
//     pair_per_user = (
//         user_category.merge(user_category, on="user_id")
//         .query("category_x < category_y")
//         .rename(columns={"category_x": "category1", "category_y": "category2"})
//     )
//     pair_counts = (
//         pair_per_user.groupby(["category1", "category2"])["user_id"]
//         .nunique()
//         .reset_index(name="customer_count")
//     )
//     result = (
//         pair_counts.query("customer_count >= 3")
//         .sort_values(
//             ["customer_count", "category1", "category2"], ascending=[False, True, True]
//         )
//         .reset_index(drop=True)
//     )
//     return result

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.