LeetCode #3764 — HARD

Most Common Course Pairs

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

The Problem

Problem Statement

Table: course_completions

+-------------------+---------+
| Column Name       | Type    | 
+-------------------+---------+
| user_id           | int     |
| course_id         | int     |
| course_name       | varchar |
| completion_date   | date    |
| course_rating     | int     |
+-------------------+---------+
(user_id, course_id) is the combination of columns with unique values for this table.
Each row represents a completed course by a user with their rating (1-5 scale).

Write a solution to identify skill mastery pathways by analyzing course completion sequences among top-performing students:

Consider only top-performing students (those who completed at least 5 courses with an average rating of 4 or higher).
For each top performer, identify the sequence of courses they completed in chronological order.
Find all consecutive course pairs (Course A → Course B) taken by these students.
Return the pair frequency, identifying which course transitions are most common among high achievers.

Return the result table ordered by pair frequency in descending order and then by first course name and second course name in ascending order.

The result format is in the following example.

Example:

Input:

course_completions table:

+---------+-----------+------------------+-----------------+---------------+
| user_id | course_id | course_name      | completion_date | course_rating |
+---------+-----------+------------------+-----------------+---------------+
| 1       | 101       | Python Basics    | 2024-01-05      | 5             |
| 1       | 102       | SQL Fundamentals | 2024-02-10      | 4             |
| 1       | 103       | JavaScript       | 2024-03-15      | 5             |
| 1       | 104       | React Basics     | 2024-04-20      | 4             |
| 1       | 105       | Node.js          | 2024-05-25      | 5             |
| 1       | 106       | Docker           | 2024-06-30      | 4             |
| 2       | 101       | Python Basics    | 2024-01-08      | 4             |
| 2       | 104       | React Basics     | 2024-02-14      | 5             |
| 2       | 105       | Node.js          | 2024-03-20      | 4             |
| 2       | 106       | Docker           | 2024-04-25      | 5             |
| 2       | 107       | AWS Fundamentals | 2024-05-30      | 4             |
| 3       | 101       | Python Basics    | 2024-01-10      | 3             |
| 3       | 102       | SQL Fundamentals | 2024-02-12      | 3             |
| 3       | 103       | JavaScript       | 2024-03-18      | 3             |
| 3       | 104       | React Basics     | 2024-04-22      | 2             |
| 3       | 105       | Node.js          | 2024-05-28      | 3             |
| 4       | 101       | Python Basics    | 2024-01-12      | 5             |
| 4       | 108       | Data Science     | 2024-02-16      | 5             |
| 4       | 109       | Machine Learning | 2024-03-22      | 5             |
+---------+-----------+------------------+-----------------+---------------+

Output:

+------------------+------------------+------------------+
| first_course     | second_course    | transition_count |
+------------------+------------------+------------------+
| Node.js          | Docker           | 2                |
| React Basics     | Node.js          | 2                |
| Docker           | AWS Fundamentals | 1                |
| JavaScript       | React Basics     | 1                |
| Python Basics    | React Basics     | 1                |
| Python Basics    | SQL Fundamentals | 1                |
| SQL Fundamentals | JavaScript       | 1                |
+------------------+------------------+------------------+

Explanation:

User 1: Completed 6 courses with average rating 4.5 (qualifies as top performer)
User 2: Completed 5 courses with average rating 4.4 (qualifies as top performer)
User 3: Completed 5 courses but average rating is 2.8 (does not qualify)
User 4: Completed only 3 courses (does not qualify)
Course Pairs Among Top Performers:
- User 1: Python Basics → SQL Fundamentals → JavaScript → React Basics → Node.js → Docker
- User 2: Python Basics → React Basics → Node.js → Docker → AWS Fundamentals
- Most common transitions: Node.js → Docker (2 times), React Basics → Node.js (2 times)

Results are ordered by transition_count in descending order, then by first_course in ascending order, and then by second_course in ascending order.

Step 01

Brute Force Baseline

Problem summary: Table: course_completions +-------------------+---------+ | Column Name | Type | +-------------------+---------+ | user_id | int | | course_id | int | | course_name | varchar | | completion_date | date | | course_rating | int | +-------------------+---------+ (user_id, course_id) is the combination of columns with unique values for this table. Each row represents a completed course by a user with their rating (1-5 scale). Write a solution to identify skill mastery pathways by analyzing course completion sequences among top-performing students: Consider only top-performing students (those who completed at least 5 courses with an average rating of 4 or higher). For each top performer, identify the sequence of courses they completed in chronological order. Find all consecutive course pairs (Course A → Course B) taken by these students. Return the pair frequency, identifying which course

Baseline thinking

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

Pattern signal: General problem-solving

Example 1

{"headers":{"course_completions":["user_id","course_id","course_name","completion_date","course_rating"]},"rows":{"course_completions":[[1,101,"Python Basics","2024-01-05",5],[1,102,"SQL Fundamentals","2024-02-10",4],[1,103,"JavaScript","2024-03-15",5],[1,104,"React Basics","2024-04-20",4],[1,105,"Node.js","2024-05-25",5],[1,106,"Docker","2024-06-30",4],[2,101,"Python Basics","2024-01-08",4],[2,104,"React Basics","2024-02-14",5],[2,105,"Node.js","2024-03-20",4],[2,106,"Docker","2024-04-25",5],[2,107,"AWS Fundamentals","2024-05-30",4],[3,101,"Python Basics","2024-01-10",3],[3,102,"SQL Fundamentals","2024-02-12",3],[3,103,"JavaScript","2024-03-18",3],[3,104,"React Basics","2024-04-22",2],[3,105,"Node.js","2024-05-28",3],[4,101,"Python Basics","2024-01-12",5],[4,108,"Data Science","2024-02-16",5],[4,109,"Machine Learning","2024-03-22",5]]}}

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 #3764: Most Common Course Pairs
// Auto-generated Java example from py.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (py):
// # Accepted solution for LeetCode #3764: Most Common Course Pairs
// import pandas as pd
// 
// 
// def topLearnerCourseTransitions(course_completions: pd.DataFrame) -> pd.DataFrame:
//     grp = course_completions.groupby("user_id")
//     top_students = grp.filter(
//         lambda df: df.shape[0] >= 5 and df["course_rating"].mean() >= 4
//     )["user_id"].unique()
// 
//     df = course_completions[course_completions["user_id"].isin(top_students)].copy()
//     df = df.sort_values(["user_id", "completion_date"])
//     df["second_course"] = df.groupby("user_id")["course_name"].shift(-1)
//     df["first_course"] = df["course_name"]
// 
//     pairs = df[df["second_course"].notna()][["first_course", "second_course"]]
// 
//     result = (
//         pairs.groupby(["first_course", "second_course"])
//         .size()
//         .reset_index(name="transition_count")
//         .sort_values(
//             ["transition_count", "first_course", "second_course"],
//             ascending=[False, True, True],
//             key=lambda col: col.str.lower() if col.dtype == "object" else col,
//         )
//         .reset_index(drop=True)
//     )
// 
//     return result

// Accepted solution for LeetCode #3764: Most Common Course Pairs
// Auto-generated Go example from py.
func exampleSolution() {
}
// Reference (py):
// # Accepted solution for LeetCode #3764: Most Common Course Pairs
// import pandas as pd
// 
// 
// def topLearnerCourseTransitions(course_completions: pd.DataFrame) -> pd.DataFrame:
//     grp = course_completions.groupby("user_id")
//     top_students = grp.filter(
//         lambda df: df.shape[0] >= 5 and df["course_rating"].mean() >= 4
//     )["user_id"].unique()
// 
//     df = course_completions[course_completions["user_id"].isin(top_students)].copy()
//     df = df.sort_values(["user_id", "completion_date"])
//     df["second_course"] = df.groupby("user_id")["course_name"].shift(-1)
//     df["first_course"] = df["course_name"]
// 
//     pairs = df[df["second_course"].notna()][["first_course", "second_course"]]
// 
//     result = (
//         pairs.groupby(["first_course", "second_course"])
//         .size()
//         .reset_index(name="transition_count")
//         .sort_values(
//             ["transition_count", "first_course", "second_course"],
//             ascending=[False, True, True],
//             key=lambda col: col.str.lower() if col.dtype == "object" else col,
//         )
//         .reset_index(drop=True)
//     )
// 
//     return result

# Accepted solution for LeetCode #3764: Most Common Course Pairs
import pandas as pd


def topLearnerCourseTransitions(course_completions: pd.DataFrame) -> pd.DataFrame:
    grp = course_completions.groupby("user_id")
    top_students = grp.filter(
        lambda df: df.shape[0] >= 5 and df["course_rating"].mean() >= 4
    )["user_id"].unique()

    df = course_completions[course_completions["user_id"].isin(top_students)].copy()
    df = df.sort_values(["user_id", "completion_date"])
    df["second_course"] = df.groupby("user_id")["course_name"].shift(-1)
    df["first_course"] = df["course_name"]

    pairs = df[df["second_course"].notna()][["first_course", "second_course"]]

    result = (
        pairs.groupby(["first_course", "second_course"])
        .size()
        .reset_index(name="transition_count")
        .sort_values(
            ["transition_count", "first_course", "second_course"],
            ascending=[False, True, True],
            key=lambda col: col.str.lower() if col.dtype == "object" else col,
        )
        .reset_index(drop=True)
    )

    return result

// Accepted solution for LeetCode #3764: Most Common Course 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 #3764: Most Common Course Pairs
// import pandas as pd
// 
// 
// def topLearnerCourseTransitions(course_completions: pd.DataFrame) -> pd.DataFrame:
//     grp = course_completions.groupby("user_id")
//     top_students = grp.filter(
//         lambda df: df.shape[0] >= 5 and df["course_rating"].mean() >= 4
//     )["user_id"].unique()
// 
//     df = course_completions[course_completions["user_id"].isin(top_students)].copy()
//     df = df.sort_values(["user_id", "completion_date"])
//     df["second_course"] = df.groupby("user_id")["course_name"].shift(-1)
//     df["first_course"] = df["course_name"]
// 
//     pairs = df[df["second_course"].notna()][["first_course", "second_course"]]
// 
//     result = (
//         pairs.groupby(["first_course", "second_course"])
//         .size()
//         .reset_index(name="transition_count")
//         .sort_values(
//             ["transition_count", "first_course", "second_course"],
//             ascending=[False, True, True],
//             key=lambda col: col.str.lower() if col.dtype == "object" else col,
//         )
//         .reset_index(drop=True)
//     )
// 
//     return result

// Accepted solution for LeetCode #3764: Most Common Course Pairs
// Auto-generated TypeScript example from py.
function exampleSolution(): void {
}
// Reference (py):
// # Accepted solution for LeetCode #3764: Most Common Course Pairs
// import pandas as pd
// 
// 
// def topLearnerCourseTransitions(course_completions: pd.DataFrame) -> pd.DataFrame:
//     grp = course_completions.groupby("user_id")
//     top_students = grp.filter(
//         lambda df: df.shape[0] >= 5 and df["course_rating"].mean() >= 4
//     )["user_id"].unique()
// 
//     df = course_completions[course_completions["user_id"].isin(top_students)].copy()
//     df = df.sort_values(["user_id", "completion_date"])
//     df["second_course"] = df.groupby("user_id")["course_name"].shift(-1)
//     df["first_course"] = df["course_name"]
// 
//     pairs = df[df["second_course"].notna()][["first_course", "second_course"]]
// 
//     result = (
//         pairs.groupby(["first_course", "second_course"])
//         .size()
//         .reset_index(name="transition_count")
//         .sort_values(
//             ["transition_count", "first_course", "second_course"],
//             ascending=[False, True, True],
//             key=lambda col: col.str.lower() if col.dtype == "object" else col,
//         )
//         .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.