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2683-design-de-projetos

design-de-projetos

B Difficulty

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# 2683 - Design de Projetos | **Version**: 0.5
`design-de-projetos` | Difficulty: **B** | **Updated**: 2026-05-16 13:44:01

**Sync Status:** ✅ Local: OK | ❌ Maratona: Not in DB | ❌ API: Not in DB

## Overview
Encontre e otimize duas Árvores Geradoras em um só grafo (MST e MaxST) utilizando o Algoritmo de Kruskal e Bucket Sort.

## Metadata
- **Author**: Unknown
- **Editorial**: Este é o problema clássico de se descobrir a Minimum Spanning Tree (MST)
e a Maximum Spanning Tree (MaxST) num grafo para orçamentos.
A sacada aqui não é só Kruskal. Como temos 1 MILHÃO de arestas, o 
QSort do Kruskal custaria O(E log E), que ainda passaria porque 2 segundos
é alto, mas pode ser apertado em linguagens mais lentas.
Porém, os pesos w <= 200!!
Então basta usar Counting Sort/Bucket Sort de O(E), 
juntando os vetores nas 200 gavetas e depois varrendo
do menor pro maior (para MST) ou do maior pro menor (para MaxST),
junto ao seu bom e velho Union-Find.

- **Success Msg**: Dominar MST usando Bucket Sort com Kruskal mostra o avanço analítico: o limite rígido de peso permitiu um super salto de performance de O(E log E) para O(E).

| Time Limit | Memory Limit | Time Complexity | Space Complexity |
| :--- | :--- | :--- | :--- |
| -s | -MB | O(E) | - |

## Stats
| Metric | Count |
| :--- | :--- |
| Test Scenarios | 22 |
| Solutions | 1 |

## Statements
| ID | Status | Level | Natural Languages | Skills |
| :--- | :--- | :--- | :--- | :--- |
| `a-design` | ✅ | A | pt | mst, kruskal |

## Test Scenarios
| Name | Description | Count | Type | Level | Skills | DB Sync |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| **Carga N Alta (1M Arestas)** | Grafo gigante exigindo DSU rápido e ordenação não-exponencial. | 3 | Performance | A | bucket-sort | - |
| **Fuzzing** | Grafos gerados aleatoriamente garantindo conexões únicas. | 15 | TDD | B | kruskal | - |
| **Caso Extremo** | Grafos mínimos, w=1, v=2, n=1. | 3 | TDD | C | mst | - |
| **Exemplo** | Base. | 1 | TDD | D | basic-io | - |

## Solutions
- **Kruskal + Bucket Sort** (`a-otima-basica`)
  - Languages: `cpp, py, java`

## Components
- ✅ Statements
- ✅ Solutions
- ✅ Test Cases

Actions

Workflow do Problema

Local Workspace

Pasta criada no disco
Metadados

Informações básicas preenchidas
Validação

Soluções passam nos testes
4

Sincronização

Enviado para DB e GitLab

Components

Statements ✅
Solutions 1 ✅
Test Cases 22 ✅

Database Info

DB ID 2683

Name Design de Projetos

Time Limit 1.0s

Mem Limit 250 MB

Version 0.8

Difficulty Level O

Test Cases 0

🚀 Quick Prompts

Structure Scaffolding

Generate metadata & folder structure

ID: 1.1

Context & Description

Draft description & editorial

ID: 1.2

Statements List

⚠️

Warning: The defaultStatement defined in metadata (a-design) was not found in the file system.

ID	Level	Natural Languages	Skills	Status	Action
a-design	A	a c d	mst, kruskal	⚠️

Statement Details

Select a statement above to view details.

Actions

Statistics

1 Total Statements

By Type (ID)

a-design 1

By Level

Level A 1

🚀 Quick Prompts

Statement Analysis

Analyze ambiguity & clarity

ID: 2.1

WOK Statement Generation

Rewrite in WOK Universe theme

ID: 2.2

Statement Expansion

Expand to 4 difficulty levels

ID: 2.3

Testcase Scenarios Sync

YAML Source vs Database

Slug	Level	Name	Type	Skills	Status	Actions
`a-performance`	A	Carga N Alta (1M Arestas) Grafo gigante exigindo DSU rápido e ordenação...	PERFORMANCE	bucket-sort 1pts	Not in DB	Details
`b-fuzzing`	B	Fuzzing Grafos gerados aleatoriamente garantindo...	TDD	kruskal 1pts	Not in DB	Details
`c-edge`	C	Caso Extremo Grafos mínimos, w=1, v=2, n=1.	TDD	mst 1pts	Not in DB	Details
`d-sample`	D	Exemplo Base.	TDD	basic-io 1pts	Not in DB	Details

Local Test Cases (Disk)

Scenario: a-performance 3 cases

Name	Files (Input / Output)	Actions
design-01 📄 📷	Input `design-01.in` 96387199be591df828fbd85797cf9b0a Output `design-01.out` dd2b2c641195af0f2e28976e08330ba6	🔍 Details
design-02 📄 📷	Input `design-02.in` d50f732ac7c4dbb0d8aae34e34537abd Output `design-02.out` 85a8c2d5c5d44998966486646e3f24ea	🔍 Details
design-03 📄 📷	Input `design-03.in` b9abfdf6e2d6e629a2d468f564563f00 Output `design-03.out` 9a11e6d97cfc0a6af64421ab647d7445	🔍 Details

Scenario: b-fuzzing 15 cases

Name	Files (Input / Output)	Actions
design-01 📄 📷	Input `design-01.in` bbe5d5707dbc73f230f1afc18311ebb7 Output `design-01.out` e08c79cb8594018ba93cec19dcad0088	🔍 Details
design-02 📄 📷	Input `design-02.in` 4579d0ed61a25fd835d63746e769b196 Output `design-02.out` 19dd8afdf3881f9492bec1016626efc4	🔍 Details
design-03 📄 📷	Input `design-03.in` 14a357dcdd5812d7bd229ee3e3755fa0 Output `design-03.out` 59646076def656e8229512cd8da1b373	🔍 Details
design-04 📄 📷	Input `design-04.in` bc9f0f2a49d5737ec5847b9895a09f79 Output `design-04.out` a1f0a4fa65ff5d68851ba3d09c0475b1	🔍 Details
design-05 📄 📷	Input `design-05.in` f426eb39be4075a3944f67422a4017e7 Output `design-05.out` 2ec2bb5ec8339a32dfbed6f5b77e9836	🔍 Details
design-06 📄 📷	Input `design-06.in` 93dc10a37c65260c3be60a46e3cad9c2 Output `design-06.out` 86f2567f479bb17e6c52d64bd3912402	🔍 Details
design-07 📄 📷	Input `design-07.in` 9348ad282f54eb893076bf118c67f656 Output `design-07.out` d39a5c3a9a62706716c13b1ce9e4e46a	🔍 Details
design-08 📄 📷	Input `design-08.in` 7e2ab5181597817c4af20091e6ed0368 Output `design-08.out` 08e095b3259c4a5333844363d7f458f0	🔍 Details
design-09 📄 📷	Input `design-09.in` f7a9253ba816eb66451f50f58cf9d5f6 Output `design-09.out` c8d97fe192e0490d3876b9ba7a1ab189	🔍 Details
design-10 📄 📷	Input `design-10.in` b1726d987fe8571f177efbdee198a8d4 Output `design-10.out` df50628b556c96172ed697cd75bd4e56	🔍 Details
design-11 📄 📷	Input `design-11.in` 71c54006eb37210a4f8642045609d3b3 Output `design-11.out` 2a393c41164d3133067f30ad54d1b144	🔍 Details
design-12 📄 📷	Input `design-12.in` a3dbd33ebc0a9179180a5f94bfd79e4d Output `design-12.out` 26baca528d53303f669e00b50ce414c9	🔍 Details
design-13 📄 📷	Input `design-13.in` 27cb95f2f1ed5d97ba1f345e6f958775 Output `design-13.out` c76e04a72f9eeec9606071c3d600535f	🔍 Details
design-14 📄 📷	Input `design-14.in` 75df05299fe1b8fc813659c6fc9f7811 Output `design-14.out` eb01788fdb98c8a6e660d1545aad4720	🔍 Details
design-15 📄 📷	Input `design-15.in` bd00d8a92284812759bfdb463ed91a8d Output `design-15.out` ab50001cf6c9db62d5500867721bca96	🔍 Details

Scenario: c-edge 3 cases

Name	Files (Input / Output)	Actions
design-01 📄 📷	Input `design-01.in` 146cf45cb1c216fa9016cdf663e665c4 Output `design-01.out` 3d0765eaf5596f0b0ee30175909bf9e4	🔍 Details
design-02 📄 📷	Input `design-02.in` 16b8a10bd4ef2632a558d4edb23d0ee2 Output `design-02.out` 462d8bc7d4078e4e382acba61e7c77f8	🔍 Details
design-03 📄 📷	Input `design-03.in` f460a3a1e591784656a7a056cc7e6414 Output `design-03.out` 8e7a2693440ac1f85d5cb9db3d86f82a	🔍 Details

Scenario: d-sample 1 cases

Name	Files (Input / Output)	Status	Actions
design-01 📄 📷	Input `design-01.in` e51a869811b1e25bb9532a03a21d17a9 Output `design-01.out` f5818137a37113aebc94ce4394a72375		🔍 Details

📊 Sync Statistics

Total (Disk) 22

Total (Database) 0

✓ Synchronized 0

⚠ Desynchronized 22

Duplicates (MD5)

Duplicates in (MD5) 0

Desync = (DB missing on Disk) + (Disk missing on DB)

Actions

Kruskal + Bucket Sort

ID: a-otima-basica

Usa array de listas w=1..200 para dispensar o Sort O(E log E).

Implementations

Solutions Check Report

## Solutions Check Report (Detalhado / Debug)
**Generated**: 2026-06-02T16:16:19.102781
**Solution**: `solutions/a-otima-basica/design.py`

### Compilation
✅ No compilation needed

### Resultados

<table class="results-table"><thead><tr><th>Test Case</th><th>Result</th><th>Time (s)</th></tr></thead><tbody>
<tr class="scenario-row"><td colspan="3"><strong>a-performance - Performance</strong></td></tr>
<tr id="row-a-performance-design-01-in"><td>design-01.in</td><td>✅ PASS</td><td>0.872</td></tr>
<tr id="row-a-performance-design-02-in"><td>design-02.in</td><td>✅ PASS</td><td>0.867</td></tr>
<tr id="row-a-performance-design-03-in"><td>design-03.in</td><td>✅ PASS</td><td>0.872</td></tr>
<tr class="scenario-row"><td colspan="3"><strong>b-fuzzing - TDD</strong></td></tr>
<tr id="row-b-fuzzing-design-01-in"><td>design-01.in</td><td>✅ PASS</td><td>0.014</td></tr>
<tr id="row-b-fuzzing-design-02-in"><td>design-02.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-03-in"><td>design-03.in</td><td>✅ PASS</td><td>0.015</td></tr>
<tr id="row-b-fuzzing-design-04-in"><td>design-04.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-05-in"><td>design-05.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-06-in"><td>design-06.in</td><td>✅ PASS</td><td>0.014</td></tr>
<tr id="row-b-fuzzing-design-07-in"><td>design-07.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-08-in"><td>design-08.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-09-in"><td>design-09.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-10-in"><td>design-10.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-11-in"><td>design-11.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-12-in"><td>design-12.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-13-in"><td>design-13.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-14-in"><td>design-14.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-b-fuzzing-design-15-in"><td>design-15.in</td><td>✅ PASS</td><td>0.014</td></tr>
<tr class="scenario-row"><td colspan="3"><strong>c-edge - TDD</strong></td></tr>
<tr id="row-c-edge-design-01-in"><td>design-01.in</td><td>✅ PASS</td><td>0.012</td></tr>
<tr id="row-c-edge-design-02-in"><td>design-02.in</td><td>✅ PASS</td><td>0.013</td></tr>
<tr id="row-c-edge-design-03-in"><td>design-03.in</td><td>✅ PASS</td><td>0.014</td></tr>
<tr class="scenario-row"><td colspan="3"><strong>d-sample - TDD</strong></td></tr>
<tr id="row-d-sample-design-01-in"><td>design-01.in</td><td>✅ PASS</td><td>0.013</td></tr>
</tbody></table>

✅ Verification

Validate your solutions against test cases using the metadata rules.

🚀 Quick Prompts

Solution Generation

Create Optimal/Sub-optimal code

ID: 3.1

📄 Enunciados

A 1

Idiomas: pt

💡 Soluções

cpp: 1 py: 1 java: 1

✅ 0 ❌ 0

🧪 Casos de Teste

4 Scen.

Total no Disco 22

Total no Banco 0

Sincronização 0.0%

Metadata (form)

Version

Name

Slug

ID Beecrowd

Difficulty

Time Complexity

Space Complexity

Time Limit (s)

Memory Limit (MB)

Origin

Author (Problem)

Author (Editorial)

Default Statement

Topics

Skills

Description

Editorial

Success message

metadata.yaml

# yaml-language-server: $schema=https://api.mundodocodigo.com.br/api/public/json/wok-problem.json --- version: "0.5" id: 2683 name: "Design de Projetos" slug: "design-de-projetos" timelimit: 2.0 memlimit: 200 difficultyLevelId: B author: "Emílio Wuerges" origin: "Beecrowd" description: 'Encontre e otimize duas Árvores Geradoras em um só grafo (MST e MaxST) utilizando o Algoritmo de Kruskal e Bucket Sort.' editorial: | Este é o problema clássico de se descobrir a Minimum Spanning Tree (MST) e a Maximum Spanning Tree (MaxST) num grafo para orçamentos. A sacada aqui não é só Kruskal. Como temos 1 MILHÃO de arestas, o QSort do Kruskal custaria O(E log E), que ainda passaria porque 2 segundos é alto, mas pode ser apertado em linguagens mais lentas. Porém, os pesos w <= 200!! Então basta usar Counting Sort/Bucket Sort de O(E), juntando os vetores nas 200 gavetas e depois varrendo do menor pro maior (para MST) ou do maior pro menor (para MaxST), junto ao seu bom e velho Union-Find. successmsg: 'Dominar MST usando Bucket Sort com Kruskal mostra o avanço analítico: o limite rígido de peso permitiu um super salto de performance de O(E log E) para O(E).' timeComplexity: O(E) skills: - mst - kruskal - bucket-sort statements: - id: a-design testScenarioLevel: A thematicSkills: - skill: mst points: 2 - skill: kruskal points: 1 testScenarios: - id: a-performance name: Carga N Alta (1M Arestas) description: "Grafo gigante exigindo DSU rápido e ordenação não-exponencial." helpTip: "Seu sort tradicional está demorando muito? Use a tática do 'Array de Baldes' já que W é apenas até 200." level: A testType: PERFORMANCE skills: - skill: bucket-sort points: 1 - id: b-fuzzing name: Fuzzing description: "Grafos gerados aleatoriamente garantindo conexões únicas." helpTip: "Você zerou o Union-Find DSU antes de rodar a segunda checagem do MST?" level: B testType: TDD skills: - skill: kruskal points: 1 - id: c-edge name: Caso Extremo description: "Grafos mínimos, w=1, v=2, n=1." helpTip: "Funcionando em 1 aresta e retornando ela como max e min?" level: C testType: TDD skills: - skill: mst points: 1 - id: d-sample name: Exemplo description: "Base." helpTip: "Passe o Exemplo." level: D testType: TDD skills: - skill: basic-io points: 1 solutions: - id: a-otima-basica name: Kruskal + Bucket Sort description: Usa array de listas w=1..200 para dispensar o Sort O(E log E). level: A implementations: - language: cpp paradigm: Imperative main: design.cpp filenames: - design.cpp - language: py paradigm: Imperative main: design.py filenames: - design.py - language: java paradigm: OO main: Design filenames: - Design.java authorSlugProblem: Unknown defaultStatement: a-design

2683-design-de-projetos

README.md Preview

Actions

Workflow do Problema

Local Workspace

Metadados

Validação

Sincronização

Components

Database Info

🚀 Quick Prompts

Statements List

Statement Details

Actions

Statistics

By Type (ID)

By Level

🚀 Quick Prompts

📊 Sync Statistics

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Test Case Details

Testcase Scenarios Sync

Local Test Cases (Disk)

Scenario: a-performance 3 cases

Scenario: b-fuzzing 15 cases

Scenario: c-edge 3 cases

Scenario: d-sample 1 cases

📊 Sync Statistics

Actions

Kruskal + Bucket Sort

Implementations

Solutions Check Report

✅ Verification

🚀 Quick Prompts

📄 Enunciados

💡 Soluções

🧪 Casos de Teste

Metadata (form)

Git Status

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🛠️ Validation Tools

✅ Synced with API

✅ Synced with Database

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📋 Processo de Criação

Select a Prompt

📤 API Synchronization

📄 Recreating README.md...

💻 Git Action Output

Running Verification...

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📄 Sync Statements to DB

🚀 Batch Auto-Link Process

⬇️ Repo Sync Output

📝 Update Manifest Output

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