LeetCode #3657 — MEDIUM

Find Loyal Customers

Move from brute-force thinking to an efficient approach using core interview patterns strategy.

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The Problem

Problem Statement

Table: customer_transactions

+------------------+---------+
| Column Name      | Type    | 
+------------------+---------+
| transaction_id   | int     |
| customer_id      | int     |
| transaction_date | date    |
| amount           | decimal |
| transaction_type | varchar |
+------------------+---------+
transaction_id is the unique identifier for this table.
transaction_type can be either 'purchase' or 'refund'.

Write a solution to find loyal customers. A customer is considered loyal if they meet ALL the following criteria:

  • Made at least 3 purchase transactions.
  • Have been active for at least 30 days.
  • Their refund rate is less than 20% .

Refund rate is the proportion of transactions that are refunds, calculated as the number of refund transactions divided by the total number of transactions (purchases plus refunds).

Return the result table ordered by customer_id in ascending order.

The result format is in the following example.

Example:

Input:

customer_transactions table:

+----------------+-------------+------------------+--------+------------------+
| transaction_id | customer_id | transaction_date | amount | transaction_type |
+----------------+-------------+------------------+--------+------------------+
| 1              | 101         | 2024-01-05       | 150.00 | purchase         |
| 2              | 101         | 2024-01-15       | 200.00 | purchase         |
| 3              | 101         | 2024-02-10       | 180.00 | purchase         |
| 4              | 101         | 2024-02-20       | 250.00 | purchase         |
| 5              | 102         | 2024-01-10       | 100.00 | purchase         |
| 6              | 102         | 2024-01-12       | 120.00 | purchase         |
| 7              | 102         | 2024-01-15       | 80.00  | refund           |
| 8              | 102         | 2024-01-18       | 90.00  | refund           |
| 9              | 102         | 2024-02-15       | 130.00 | purchase         |
| 10             | 103         | 2024-01-01       | 500.00 | purchase         |
| 11             | 103         | 2024-01-02       | 450.00 | purchase         |
| 12             | 103         | 2024-01-03       | 400.00 | purchase         |
| 13             | 104         | 2024-01-01       | 200.00 | purchase         |
| 14             | 104         | 2024-02-01       | 250.00 | purchase         |
| 15             | 104         | 2024-02-15       | 300.00 | purchase         |
| 16             | 104         | 2024-03-01       | 350.00 | purchase         |
| 17             | 104         | 2024-03-10       | 280.00 | purchase         |
| 18             | 104         | 2024-03-15       | 100.00 | refund           |
+----------------+-------------+------------------+--------+------------------+

Output:

+-------------+
| customer_id |
+-------------+
| 101         |
| 104         |
+-------------+

Explanation:

  • Customer 101:
    • Purchase transactions: 4 (IDs: 1, 2, 3, 4) 
    • Refund transactions: 0
    • Refund rate: 0/4 = 0% (less than 20%) 
    • Active period: Jan 5 to Feb 20 = 46 days (at least 30 days) 
    • Qualifies as loyal 
  • Customer 102:
    • Purchase transactions: 3 (IDs: 5, 6, 9) 
    • Refund transactions: 2 (IDs: 7, 8)
    • Refund rate: 2/5 = 40% (exceeds 20%) 
    • Not loyal 
  • Customer 103:
    • Purchase transactions: 3 (IDs: 10, 11, 12) 
    • Refund transactions: 0
    • Refund rate: 0/3 = 0% (less than 20%) 
    • Active period: Jan 1 to Jan 3 = 2 days (less than 30 days) 
    • Not loyal 
  • Customer 104:
    • Purchase transactions: 5 (IDs: 13, 14, 15, 16, 17) 
    • Refund transactions: 1 (ID: 18)
    • Refund rate: 1/6 = 16.67% (less than 20%) 
    • Active period: Jan 1 to Mar 15 = 73 days (at least 30 days) 
    • Qualifies as loyal 

The result table is ordered by customer_id in ascending order.

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: Table: customer_transactions +------------------+---------+ | Column Name | Type | +------------------+---------+ | transaction_id | int | | customer_id | int | | transaction_date | date | | amount | decimal | | transaction_type | varchar | +------------------+---------+ transaction_id is the unique identifier for this table. transaction_type can be either 'purchase' or 'refund'. Write a solution to find loyal customers. A customer is considered loyal if they meet ALL the following criteria: Made at least 3 purchase transactions. Have been active for at least 30 days. Their refund rate is less than 20% . Refund rate is the proportion of transactions that are refunds, calculated as the number of refund transactions divided by the total number of transactions (purchases plus refunds). Return the result table ordered by customer_id in ascending order. The result format is in the following

Baseline thinking

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

Pattern signal: General problem-solving

Example 1

{"headers":{"customer_transactions":["transaction_id","customer_id","transaction_date","amount","transaction_type"]},"rows":{"customer_transactions":[[1,101,"2024-01-05",150.00,"purchase"],[2,101,"2024-01-15",200.00,"purchase"],[3,101,"2024-02-10",180.00,"purchase"],[4,101,"2024-02-20",250.00,"purchase"],[5,102,"2024-01-10",100.00,"purchase"],[6,102,"2024-01-12",120.00,"purchase"],[7,102,"2024-01-15",80.00,"refund"],[8,102,"2024-01-18",90.00,"refund"],[9,102,"2024-02-15",130.00,"purchase"],[10,103,"2024-01-01",500.00,"purchase"],[11,103,"2024-01-02",450.00,"purchase"],[12,103,"2024-01-03",400.00,"purchase"],[13,104,"2024-01-01",200.00,"purchase"],[14,104,"2024-02-01",250.00,"purchase"],[15,104,"2024-02-15",300.00,"purchase"],[16,104,"2024-03-01",350.00,"purchase"],[17,104,"2024-03-10",280.00,"purchase"],[18,104,"2024-03-15",100.00,"refund"]]}}
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

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. 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
Upper-end input sizes
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 #3657: Find Loyal Customers
// Auto-generated Java example from py.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (py):
// # Accepted solution for LeetCode #3657: Find Loyal Customers
// import pandas as pd
// 
// 
// def find_loyal_customers(customer_transactions: pd.DataFrame) -> pd.DataFrame:
//     customer_transactions["transaction_date"] = pd.to_datetime(
//         customer_transactions["transaction_date"]
//     )
//     grouped = customer_transactions.groupby("customer_id")
//     agg_df = grouped.agg(
//         total_transactions=("transaction_type", "size"),
//         refund_count=("transaction_type", lambda x: (x == "refund").sum()),
//         min_date=("transaction_date", "min"),
//         max_date=("transaction_date", "max"),
//     ).reset_index()
//     agg_df["date_diff"] = (agg_df["max_date"] - agg_df["min_date"]).dt.days
//     agg_df["refund_ratio"] = agg_df["refund_count"] / agg_df["total_transactions"]
//     result = (
//         agg_df[
//             (agg_df["total_transactions"] >= 3)
//             & (agg_df["refund_ratio"] < 0.2)
//             & (agg_df["date_diff"] >= 30)
//         ][["customer_id"]]
//         .sort_values("customer_id")
//         .reset_index(drop=True)
//     )
//     return result
Step 06

Interactive Study Demo

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

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.