LeetCode #3421 — MEDIUM

Find Students Who Improved

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

The Problem

Problem Statement

Table: Scores

+-------------+---------+
| Column Name | Type    |
+-------------+---------+
| student_id  | int     |
| subject     | varchar |
| score       | int     |
| exam_date   | varchar |
+-------------+---------+
(student_id, subject, exam_date) is the primary key for this table.
Each row contains information about a student's score in a specific subject on a particular exam date. score is between 0 and 100 (inclusive).

Write a solution to find the students who have shown improvement. A student is considered to have shown improvement if they meet both of these conditions:

Have taken exams in the same subject on at least two different dates
Their latest score in that subject is higher than their first score

Return the result table ordered by student_id, subject in ascending order.

The result format is in the following example.

Example:

Input:

Scores table:

+------------+----------+-------+------------+
| student_id | subject  | score | exam_date  |
+------------+----------+-------+------------+
| 101        | Math     | 70    | 2023-01-15 |
| 101        | Math     | 85    | 2023-02-15 |
| 101        | Physics  | 65    | 2023-01-15 |
| 101        | Physics  | 60    | 2023-02-15 |
| 102        | Math     | 80    | 2023-01-15 |
| 102        | Math     | 85    | 2023-02-15 |
| 103        | Math     | 90    | 2023-01-15 |
| 104        | Physics  | 75    | 2023-01-15 |
| 104        | Physics  | 85    | 2023-02-15 |
+------------+----------+-------+------------+

Output:

+------------+----------+-------------+--------------+
| student_id | subject  | first_score | latest_score |
+------------+----------+-------------+--------------+
| 101        | Math     | 70          | 85           |
| 102        | Math     | 80          | 85           |
| 104        | Physics  | 75          | 85           |
+------------+----------+-------------+--------------+

Explanation:

Student 101 in Math: Improved from 70 to 85
Student 101 in Physics: No improvement (dropped from 65 to 60)
Student 102 in Math: Improved from 80 to 85
Student 103 in Math: Only one exam, not eligible
Student 104 in Physics: Improved from 75 to 85

Result table is ordered by student_id, subject.

Step 01

Brute Force Baseline

Problem summary: Table: Scores +-------------+---------+ | Column Name | Type | +-------------+---------+ | student_id | int | | subject | varchar | | score | int | | exam_date | varchar | +-------------+---------+ (student_id, subject, exam_date) is the primary key for this table. Each row contains information about a student's score in a specific subject on a particular exam date. score is between 0 and 100 (inclusive). Write a solution to find the students who have shown improvement. A student is considered to have shown improvement if they meet both of these conditions: Have taken exams in the same subject on at least two different dates Their latest score in that subject is higher than their first score Return the result table ordered by student_id, subject in ascending order. The result format is in the following example.

Baseline thinking

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

Pattern signal: General problem-solving

Example 1

{"headers":{"Scores":["student_id","subject","score","exam_date"]},"rows":{"Scores":[[101,"Math",70,"2023-01-15"],[101,"Math",85,"2023-02-15"],[101,"Physics",65,"2023-01-15"],[101,"Physics",60,"2023-02-15"],[102,"Math",80,"2023-01-15"],[102,"Math",85,"2023-02-15"],[103,"Math",90,"2023-01-15"],[104,"Physics",75,"2023-01-15"],[104,"Physics",85,"2023-02-15"]]}}

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

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 #3421: Find Students Who Improved
// Auto-generated Java example from rust.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (rust):
// // Accepted solution for LeetCode #3421: Find Students Who Improved
// pub fn sql_example() -> &'static str {
//     r#"
// -- Accepted solution for LeetCode #3421: Find Students Who Improved
// WITH
//     RankedScores AS (
//         SELECT
//             student_id,
//             subject,
//             score,
//             exam_date,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date ASC
//             ) AS rn_first,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date DESC
//             ) AS rn_latest
//         FROM Scores
//     ),
//     FirstAndLatestScores AS (
//         SELECT
//             f.student_id,
//             f.subject,
//             f.score AS first_score,
//             l.score AS latest_score
//         FROM
//             RankedScores f
//             JOIN RankedScores l ON f.student_id = l.student_id AND f.subject = l.subject
//         WHERE f.rn_first = 1 AND l.rn_latest = 1
//     )
// SELECT
//     *
// FROM FirstAndLatestScores
// WHERE latest_score > first_score
// ORDER BY 1, 2;
// "#
// }

// Accepted solution for LeetCode #3421: Find Students Who Improved
// Auto-generated Go example from rust.
func exampleSolution() {
}
// Reference (rust):
// // Accepted solution for LeetCode #3421: Find Students Who Improved
// pub fn sql_example() -> &'static str {
//     r#"
// -- Accepted solution for LeetCode #3421: Find Students Who Improved
// WITH
//     RankedScores AS (
//         SELECT
//             student_id,
//             subject,
//             score,
//             exam_date,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date ASC
//             ) AS rn_first,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date DESC
//             ) AS rn_latest
//         FROM Scores
//     ),
//     FirstAndLatestScores AS (
//         SELECT
//             f.student_id,
//             f.subject,
//             f.score AS first_score,
//             l.score AS latest_score
//         FROM
//             RankedScores f
//             JOIN RankedScores l ON f.student_id = l.student_id AND f.subject = l.subject
//         WHERE f.rn_first = 1 AND l.rn_latest = 1
//     )
// SELECT
//     *
// FROM FirstAndLatestScores
// WHERE latest_score > first_score
// ORDER BY 1, 2;
// "#
// }

# Accepted solution for LeetCode #3421: Find Students Who Improved
# Auto-generated Python example from rust.
def example_solution() -> None:
    return
# Reference (rust):
# // Accepted solution for LeetCode #3421: Find Students Who Improved
# pub fn sql_example() -> &'static str {
#     r#"
# -- Accepted solution for LeetCode #3421: Find Students Who Improved
# WITH
#     RankedScores AS (
#         SELECT
#             student_id,
#             subject,
#             score,
#             exam_date,
#             ROW_NUMBER() OVER (
#                 PARTITION BY student_id, subject
#                 ORDER BY exam_date ASC
#             ) AS rn_first,
#             ROW_NUMBER() OVER (
#                 PARTITION BY student_id, subject
#                 ORDER BY exam_date DESC
#             ) AS rn_latest
#         FROM Scores
#     ),
#     FirstAndLatestScores AS (
#         SELECT
#             f.student_id,
#             f.subject,
#             f.score AS first_score,
#             l.score AS latest_score
#         FROM
#             RankedScores f
#             JOIN RankedScores l ON f.student_id = l.student_id AND f.subject = l.subject
#         WHERE f.rn_first = 1 AND l.rn_latest = 1
#     )
# SELECT
#     *
# FROM FirstAndLatestScores
# WHERE latest_score > first_score
# ORDER BY 1, 2;
# "#
# }

// Accepted solution for LeetCode #3421: Find Students Who Improved
pub fn sql_example() -> &'static str {
    r#"
-- Accepted solution for LeetCode #3421: Find Students Who Improved
WITH
    RankedScores AS (
        SELECT
            student_id,
            subject,
            score,
            exam_date,
            ROW_NUMBER() OVER (
                PARTITION BY student_id, subject
                ORDER BY exam_date ASC
            ) AS rn_first,
            ROW_NUMBER() OVER (
                PARTITION BY student_id, subject
                ORDER BY exam_date DESC
            ) AS rn_latest
        FROM Scores
    ),
    FirstAndLatestScores AS (
        SELECT
            f.student_id,
            f.subject,
            f.score AS first_score,
            l.score AS latest_score
        FROM
            RankedScores f
            JOIN RankedScores l ON f.student_id = l.student_id AND f.subject = l.subject
        WHERE f.rn_first = 1 AND l.rn_latest = 1
    )
SELECT
    *
FROM FirstAndLatestScores
WHERE latest_score > first_score
ORDER BY 1, 2;
"#
}

// Accepted solution for LeetCode #3421: Find Students Who Improved
// Auto-generated TypeScript example from rust.
function exampleSolution(): void {
}
// Reference (rust):
// // Accepted solution for LeetCode #3421: Find Students Who Improved
// pub fn sql_example() -> &'static str {
//     r#"
// -- Accepted solution for LeetCode #3421: Find Students Who Improved
// WITH
//     RankedScores AS (
//         SELECT
//             student_id,
//             subject,
//             score,
//             exam_date,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date ASC
//             ) AS rn_first,
//             ROW_NUMBER() OVER (
//                 PARTITION BY student_id, subject
//                 ORDER BY exam_date DESC
//             ) AS rn_latest
//         FROM Scores
//     ),
//     FirstAndLatestScores AS (
//         SELECT
//             f.student_id,
//             f.subject,
//             f.score AS first_score,
//             l.score AS latest_score
//         FROM
//             RankedScores f
//             JOIN RankedScores l ON f.student_id = l.student_id AND f.subject = l.subject
//         WHERE f.rn_first = 1 AND l.rn_latest = 1
//     )
// SELECT
//     *
// FROM FirstAndLatestScores
// WHERE latest_score > first_score
// ORDER BY 1, 2;
// "#
// }

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.