Analysis of GESP C++ Level 1 Exam Questions – Pyramid (luogu-B4410)

GESP C++ Level 1 exam questions from September 2025, basic statement exercises, difficulty ★☆☆☆☆.

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luogu-B4410 [GESP202509 Level 1] Pyramid

Problem Requirements

Problem Description

The pyramid is built with layers of stones. From the bottom to the top, each layer requires stones. How many stones are needed in total to build the pyramid?

Input Format

One line, a positive integer , representing the number of layers of the pyramid.

Output Format

One line, a positive integer, representing the total number of stones required to build the pyramid.

Input/Output Example #1

Input #1
2
Output #1
5

Input/Output Example #2

Input #2
5
Output #2
55

Notes/Tips

For all test cases, it is guaranteed that .

Problem Analysis

The number of stones required for each layer of the pyramid from bottom to top is .The total number of stones is to be calculated.

Since , either direct accumulation or using a formula can be applied, with a time complexity of or , and space .

Conventional Approach: Accumulation Method

Using a loop to accumulate the stones layer by layer, the code is straightforward and suitable for beginners. The example code implements this method.

Elementary Math Expert Approach: Formula Method

Directly applying the square sum formula , calculates the answer in one step, which is the most efficient. (Everyone can try it themselves)

Example Code

#include <iostream>

int main() {
    int n;              // Number of layers of the pyramid
    std::cin >> n;      // Read the number of layers n from user input

    int count = 0;      // Initialize total stone count to 0

    // Loop from layer n to layer 1, calculating the number of stones for each layer i*i and accumulating to count
    for (int i = n; i > 0; i--) {
        count += i * i; // Number of stones for each layer is i×i
    }

    std::cout << count << std::endl; // Output the total number of stones required
    return 0;
}

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