C++ Practice [GESP2506 Level 2] Counting Right Triangles

GESP Level 2 practice, loops and enumerations, difficulty beginner.

• CCF-GESP C++ Assessment Standards

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Comprehensive Guide – [GESP2506 Level 2] Counting Right Triangles

Problem Requirements

Problem Description

A right triangle has two legs and one hypotenuse. Let the lengths of the two legs be a and b, then the area of the right triangle is a*b/2.

Please calculate how many different right triangles with integer areas can be formed when the lengths of the legs a and b are positive integers not exceeding n. Two right triangles with legs a, b and a′, b′ are considered the same if and only if a=a′, b=b′ or a=b′, b=a′.

Input Format

Input a single line with an integer n, representing the maximum length of the legs.

Output Format

Output a single line with an integer n, representing the maximum length of the legs.

Input and Output Examples

Input #1

3

Output #1

5

Input #2

5

Output #2

9

Data Range

 For all test cases, ensure 1≤n≤1000.

Problem Analysis

Solution Approach

1. Iterate through all possible combinations of legs (a, b) (b>=a to avoid double counting)

2. Check if the area is an integer (i.e., a × b is even)

3. Output the count

Complexity Analysis:

• Time complexity is O(n²)

• Space complexity is O(1)

Example Code

#include <bits/stdc++.h>using namespace std;int main(){    int n, ans = 0;    cin >> n;  // Input maximum leg length n        for (int a = 1; a <= n; a++) {        // Iterate through the first leg a        for (int b = a; b <= n; b++) {    // Iterate through the second leg b (b>=a to avoid double counting)            if (a * b % 2 == 0) {         // Check if the area is an integer                ans++;                    // Count +1            }        }    }        cout << ans << endl;  // Output result    return 0;}

“Comprehensive Guide–” series problems can be evaluated online atInformatics Olympiad Comprehensive Guide (C++ Version).