LeetCode #3617 — HARD

Find Students with Study Spiral Pattern

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

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The Problem

Problem Statement

Table: students

+--------------+---------+
| Column Name  | Type    |
+--------------+---------+
| student_id   | int     |
| student_name | varchar |
| major        | varchar |
+--------------+---------+
student_id is the unique identifier for this table.
Each row contains information about a student and their academic major.

Table: study_sessions

+---------------+---------+
| Column Name   | Type    |
+---------------+---------+
| session_id    | int     |
| student_id    | int     |
| subject       | varchar |
| session_date  | date    |
| hours_studied | decimal |
+---------------+---------+
session_id is the unique identifier for this table.
Each row represents a study session by a student for a specific subject.

Write a solution to find students who follow the Study Spiral Pattern - students who consistently study multiple subjects in a rotating cycle.

  • A Study Spiral Pattern means a student studies at least 3 different subjects in a repeating sequence
  • The pattern must repeat for at least 2 complete cycles (minimum 6 study sessions)
  • Sessions must be consecutive dates with no gaps longer than 2 days between sessions
  • Calculate the cycle length (number of different subjects in the pattern)
  • Calculate the total study hours across all sessions in the pattern
  • Only include students with cycle length of at least 3 subjects

Return the result table ordered by cycle length in descending order, then by total study hours in descending order.

The result format is in the following example.

Example:

Input:

students table:

+------------+--------------+------------------+
| student_id | student_name | major            |
+------------+--------------+------------------+
| 1          | Alice Chen   | Computer Science |
| 2          | Bob Johnson  | Mathematics      |
| 3          | Carol Davis  | Physics          |
| 4          | David Wilson | Chemistry        |
| 5          | Emma Brown   | Biology          |
+------------+--------------+------------------+

study_sessions table:

+------------+------------+------------+--------------+---------------+
| session_id | student_id | subject    | session_date | hours_studied |
+------------+------------+------------+--------------+---------------+
| 1          | 1          | Math       | 2023-10-01   | 2.5           |
| 2          | 1          | Physics    | 2023-10-02   | 3.0           |
| 3          | 1          | Chemistry  | 2023-10-03   | 2.0           |
| 4          | 1          | Math       | 2023-10-04   | 2.5           |
| 5          | 1          | Physics    | 2023-10-05   | 3.0           |
| 6          | 1          | Chemistry  | 2023-10-06   | 2.0           |
| 7          | 2          | Algebra    | 2023-10-01   | 4.0           |
| 8          | 2          | Calculus   | 2023-10-02   | 3.5           |
| 9          | 2          | Statistics | 2023-10-03   | 2.5           |
| 10         | 2          | Geometry   | 2023-10-04   | 3.0           |
| 11         | 2          | Algebra    | 2023-10-05   | 4.0           |
| 12         | 2          | Calculus   | 2023-10-06   | 3.5           |
| 13         | 2          | Statistics | 2023-10-07   | 2.5           |
| 14         | 2          | Geometry   | 2023-10-08   | 3.0           |
| 15         | 3          | Biology    | 2023-10-01   | 2.0           |
| 16         | 3          | Chemistry  | 2023-10-02   | 2.5           |
| 17         | 3          | Biology    | 2023-10-03   | 2.0           |
| 18         | 3          | Chemistry  | 2023-10-04   | 2.5           |
| 19         | 4          | Organic    | 2023-10-01   | 3.0           |
| 20         | 4          | Physical   | 2023-10-05   | 2.5           |
+------------+------------+------------+--------------+---------------+

Output:

+------------+--------------+------------------+--------------+-------------------+
| student_id | student_name | major            | cycle_length | total_study_hours |
+------------+--------------+------------------+--------------+-------------------+
| 2          | Bob Johnson  | Mathematics      | 4            | 26.0              |
| 1          | Alice Chen   | Computer Science | 3            | 15.0              |
+------------+--------------+------------------+--------------+-------------------+

Explanation:

  • Alice Chen (student_id = 1):
    • Study sequence: Math → Physics → Chemistry → Math → Physics → Chemistry
    • Pattern: 3 subjects (Math, Physics, Chemistry) repeating for 2 complete cycles
    • Consecutive dates: Oct 1-6 with no gaps > 2 days
    • Cycle length: 3 subjects
    • Total hours: 2.5 + 3.0 + 2.0 + 2.5 + 3.0 + 2.0 = 15.0 hours
  • Bob Johnson (student_id = 2):
    • Study sequence: Algebra → Calculus → Statistics → Geometry → Algebra → Calculus → Statistics → Geometry
    • Pattern: 4 subjects (Algebra, Calculus, Statistics, Geometry) repeating for 2 complete cycles
    • Consecutive dates: Oct 1-8 with no gaps > 2 days
    • Cycle length: 4 subjects
    • Total hours: 4.0 + 3.5 + 2.5 + 3.0 + 4.0 + 3.5 + 2.5 + 3.0 = 26.0 hours
  • Students not included:
    • Carol Davis (student_id = 3): Only 2 subjects (Biology, Chemistry) - doesn't meet minimum 3 subjects requirement
    • David Wilson (student_id = 4): Only 2 study sessions with a 4-day gap - doesn't meet consecutive dates requirement
    • Emma Brown (student_id = 5): No study sessions recorded

The result table is ordered by cycle_length in descending order, then by total_study_hours in descending 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: students +--------------+---------+ | Column Name | Type | +--------------+---------+ | student_id | int | | student_name | varchar | | major | varchar | +--------------+---------+ student_id is the unique identifier for this table. Each row contains information about a student and their academic major. Table: study_sessions +---------------+---------+ | Column Name | Type | +---------------+---------+ | session_id | int | | student_id | int | | subject | varchar | | session_date | date | | hours_studied | decimal | +---------------+---------+ session_id is the unique identifier for this table. Each row represents a study session by a student for a specific subject. Write a solution to find students who follow the Study Spiral Pattern - students who consistently study multiple subjects in a rotating cycle. A Study Spiral Pattern means a student studies at least 3 different

Baseline thinking

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

Pattern signal: General problem-solving

Example 1

{"headers":{"students":["student_id","student_name","major"],"study_sessions":["session_id","student_id","subject","session_date","hours_studied"]},"rows":{"students":[[1,"Alice Chen","Computer Science"],[2,"Bob Johnson","Mathematics"],[3,"Carol Davis","Physics"],[4,"David Wilson","Chemistry"],[5,"Emma Brown","Biology"]],"study_sessions":[[1,1,"Math","2023-10-01",2.5],[2,1,"Physics","2023-10-02",3.0],[3,1,"Chemistry","2023-10-03",2.0],[4,1,"Math","2023-10-04",2.5],[5,1,"Physics","2023-10-05",3.0],[6,1,"Chemistry","2023-10-06",2.0],[7,2,"Algebra","2023-10-01",4.0],[8,2,"Calculus","2023-10-02",3.5],[9,2,"Statistics","2023-10-03",2.5],[10,2,"Geometry","2023-10-04",3.0],[11,2,"Algebra","2023-10-05",4.0],[12,2,"Calculus","2023-10-06",3.5],[13,2,"Statistics","2023-10-07",2.5],[14,2,"Geometry","2023-10-08",3.0],[15,3,"Biology","2023-10-01",2.0],[16,3,"Chemistry","2023-10-02",2.5],[17,3,"Biology","2023-10-03",2.0],[18,3,"Chemistry","2023-10-04",2.5],[19,4,"Organic","2023-10-01",3.0],[20,4,"Physical","2023-10-05",2.5]]}}
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

  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
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 #3617: Find Students with Study Spiral Pattern
// Auto-generated Java example from py.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (py):
// # Accepted solution for LeetCode #3617: Find Students with Study Spiral Pattern
// import pandas as pd
// from datetime import timedelta
// 
// 
// def find_study_spiral_pattern(
//     students: pd.DataFrame, study_sessions: pd.DataFrame
// ) -> pd.DataFrame:
//     # Convert session_date to datetime
//     study_sessions["session_date"] = pd.to_datetime(study_sessions["session_date"])
// 
//     result = []
// 
//     # Group study sessions by student
//     for student_id, group in study_sessions.groupby("student_id"):
//         # Sort sessions by date
//         group = group.sort_values("session_date").reset_index(drop=True)
// 
//         temp = []  # Holds current contiguous segment
//         last_date = None
// 
//         for idx, row in group.iterrows():
//             if not temp:
//                 temp.append(row)
//             else:
//                 delta = (row["session_date"] - last_date).days
//                 if delta <= 2:
//                     temp.append(row)
//                 else:
//                     # Check the previous contiguous segment
//                     if len(temp) >= 6:
//                         _check_pattern(student_id, temp, result)
//                     temp = [row]
//             last_date = row["session_date"]
// 
//         # Check the final segment
//         if len(temp) >= 6:
//             _check_pattern(student_id, temp, result)
// 
//     # Build result DataFrame
//     df_result = pd.DataFrame(
//         result, columns=["student_id", "cycle_length", "total_study_hours"]
//     )
// 
//     if df_result.empty:
//         return pd.DataFrame(
//             columns=[
//                 "student_id",
//                 "student_name",
//                 "major",
//                 "cycle_length",
//                 "total_study_hours",
//             ]
//         )
// 
//     # Join with students table to get name and major
//     df_result = df_result.merge(students, on="student_id")
// 
//     df_result = df_result[
//         ["student_id", "student_name", "major", "cycle_length", "total_study_hours"]
//     ]
// 
//     return df_result.sort_values(
//         by=["cycle_length", "total_study_hours"], ascending=[False, False]
//     ).reset_index(drop=True)
// 
// 
// def _check_pattern(student_id, sessions, result):
//     subjects = [row["subject"] for row in sessions]
//     hours = sum(row["hours_studied"] for row in sessions)
// 
//     n = len(subjects)
// 
//     # Try possible cycle lengths from 3 up to half of the sequence
//     for cycle_len in range(3, n // 2 + 1):
//         if n % cycle_len != 0:
//             continue
// 
//         # Extract the first cycle
//         first_cycle = subjects[:cycle_len]
//         is_pattern = True
// 
//         # Compare each following cycle with the first
//         for i in range(1, n // cycle_len):
//             if subjects[i * cycle_len : (i + 1) * cycle_len] != first_cycle:
//                 is_pattern = False
//                 break
// 
//         # If a repeated cycle is detected, store the result
//         if is_pattern:
//             result.append(
//                 {
//                     "student_id": student_id,
//                     "cycle_length": cycle_len,
//                     "total_study_hours": hours,
//                 }
//             )
//             break  # Stop at the first valid cycle found
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.