Detailed Explanation and Practice Questions for C++ GESP Level 5: Master These and You’re Set

1. Detailed Explanation of Core Topics for C++ GESP Level 5

According to the official GESP syllabus and analysis of past exam questions, the Level 5 exam mainly covers the following knowledge points:

1. Elementary Number Theory

• Core Content: Prime number determination (Sieve of Eratosthenes, linear sieve), greatest common divisor (Euclidean algorithm), congruences and modular arithmetic, prime factorization (unique factorization theorem).

• Typical Applications: Prime table generation, GCD/LCM calculations, modular arithmetic optimization problems.

• Example Questions: Recursive implementation for prime number determination, code completion for prime factorization.

2. High-Precision Arithmetic

• Core Content: Array simulation for large number addition, subtraction, multiplication, and division (handling carries and borrows), leading zero handling.

• Typical Applications: Large integer multiplication, high-precision division optimization.

• Example Questions: Implementation of carry logic for high-precision multiplication, boundary condition handling for large number addition.

3. Advanced Data Structures

• Core Content: Operations (insert, delete, search, modify) on singly linked lists, doubly linked lists, and circular linked lists, dynamic memory management, pointer operations.

• Typical Applications: Reversing linked lists, designing virtual head nodes, memory leak detection.

• Example Questions: Deleting nodes in a doubly linked list, traversing a circular linked list.

4. Divide and Conquer & Recursion

• Core Content: Merge sort (divide and conquer strategy), quicksort, recursive design (termination conditions, stack overflow prevention).

• Typical Applications: Counting inversions in an array, optimizing divide and conquer merges.

• Example Questions: Non-recursive implementation of merge sort, recursive maximum value calculation.

5. Greedy Algorithms

• Core Content: Optimal substructure design (e.g., activity selection problem), relationship between local and global optima.

• Typical Applications: Minimum coin combination, task scheduling optimization.

• Example Questions: Optimizing returns with greedy strategies, interval scheduling problems.

6. Complexity Analysis

• Core Content: Big O notation, polynomial and logarithmic complexity estimation (e.g., quicksort O(n log n)).

• Typical Applications: Comparing algorithm time/space efficiency.

Recommended 50 Questions of the Same Difficulty and Knowledge Points for GESP Level 5

Based on the GESP Level 5 syllabus (elementary number theory, high-precision arithmetic, linked list operations, divide and conquer, greedy algorithms, etc.) and the official recommended question list, the following are 50 categorized questions, with difficulty aligned to the GESP Level 5 exam (approximately corresponding to Luogu’s popularization+/improvement- difficulty):

1. Elementary Number Theory (10 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P3383	[Template] Linear Sieve for Primes	Sieve of Eratosthenes/Euler Sieve	Popularization-
P1029	Greatest Common Divisor and Least Common Multiple	Euclidean Algorithm	Popularization
P1835	Prime Density	Interval Sieve Method	Popularization+
P1069	Cell Division	Prime Factorization	Popularization+
P1072	Congruence Equation (Extended Euclidean)	Modular Arithmetic and Congruences	Improvement-
P4549	Pell’s Theorem	Application of Number Theory Theorems	Popularization+
P1572	Sum of Factors	Properties of Divisors	Popularization
P3912	Prime Statistics	Sieve Optimization	Popularization
P5535	Congruence Equation	Modular Arithmetic and Equation Solving	Improvement-
P2527	Prime Distance	Sieve Application	Improvement-

2. High-Precision Arithmetic (8 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P1601	A+B Problem (High Precision)	High-Precision Addition	Entry
P2142	Large Integer Subtraction	High-Precision Subtraction	Entry
P1303	A*B Problem (High Precision)	High-Precision Multiplication	Popularization-
P1480	High-Precision Division	High-Precision Division	Popularization
P1009	Sum of Factorials	High-Precision Mixed Multiplication and Addition	Popularization
P1255	Counting Stairs	High-Precision Fibonacci	Popularization-
P1591	Factorial Digit Statistics	Application of High-Precision Multiplication	Popularization
P1249	Maximum Product	Combination of High Precision and Number Theory	Improvement-

3. Linked Lists and Data Structures (7 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P1160	Queue Arrangement	Doubly Linked List Operations	Popularization
P1996	Josephus Problem	Circular Linked List Simulation	Popularization-
P2058	Harbor	Combination of Linked List and Queue	Popularization+
P4387	Validate Stack Sequence	Stack and Linked List Operations	Popularization
P1449	Evaluate Postfix Expression	Application of Linked List and Stack	Popularization
P2816	Polynomial Output	Linked List Traversal and Conditional Judgement	Popularization
P1540	Machine Translation	Queue Simulation	Popularization

4. Divide and Conquer & Recursion (8 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P1908	Inversion Pairs	Merge Sort Divide and Conquer	Popularization+
P1177	[Template] Quick Sort	Quick Sort Divide and Conquer	Popularization-
P1226	Fast Power	Recursive and Divide and Conquer Optimization	Popularization
P1257	Closest Pair of Points	Divide and Conquer Strategy	Improvement-
P1115	Maximum Subarray Sum	Divide and Conquer and Dynamic Programming	Popularization
P1309	Swiss Round	Application of Merge Sort	Popularization+
P1010	Power	Recursive Decomposition	Popularization
P5468	Quick Sort (Non-Recursive)	Non-Recursive Implementation of Divide and Conquer	Improvement-

5. Greedy Algorithms (7 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P1223	Queueing for Water	Classic Greedy Problem	Popularization-
P1090	Merging Fruits	Priority Queue Greedy	Popularization
P1803	Messy yyy	Interval Scheduling Greedy	Popularization
P5019	Road Paving	Greedy Strategy Design	Popularization
P2240	Fractional Knapsack Problem	Greedy and Sorting	Popularization
P1080	King’s Game	Greedy and High Precision Combination	Improvement-
P4995	Jump Jump!	Greedy and Mathematics Combination	Popularization+

6. Complexity and Algorithm Analysis (10 Questions)

Question Number	Question Name	Knowledge Point	Difficulty
P2678	Jumping Stones	Binary Search Answers and Complexity Optimization	Popularization+
P1182	Segmented Sequence II	Binary Search Application	Popularization+
P2440	Wood Processing	Binary Search Answers and Boundary Handling	Popularization
P3853	Setting Road Signs	Binary Search Answers and Greedy Combination	Popularization
P1024	Solving Cubic Equations	Binary Method and Precision Control	Popularization
P1316	Lost Bottle Caps	Binary Search Answers and Maximum Minimum	Popularization
P3743	kotori’s Device	Binary Search Answers and Resource Allocation	Improvement-
P2920	Time Management	Greedy and Binary Search Combination	Popularization
P4344	Matrix Cutting	Divide and Conquer Complexity Analysis	Improvement-
P4059	Finding Dad	Dynamic Programming and Complexity Optimization	Improvement-

Complete Question List and Practice Suggestions

1. Question List Address: Official GESP Level 5 Recommended Question List: https://www.luogu.com.cn/training/555#problems
2. Specialized Breakthrough: It is recommended to practice categorized by knowledge points, such as prioritizing basic questions in high-precision arithmetic (P1601/P1303) and linked list operations (P1160/P1996).
3. Mock Exam: Select 5-8 questions from different knowledge points (e.g., P3383+P1908+P1223), with a time limit of 90 minutes to simulate exam conditions.