C++ Practice Problem – Automorphic Numbers

Time Limit: 2s Memory Limit: 192MB

Problem Description

An automorphic number is a number whose square ends with the number itself.

For example:

25^2=625

76^2=5776

9376^2=87909376

Find all automorphic numbers less than or equal to 200000.

Input Format

No input

Output Format

All automorphic numbers less than or equal to 200000 (including 0, numbers separated by two spaces, no trailing space)

Sample Input

No input

Sample Output

0 1 5 6 25 76 376 625 9376 90625 109376

Code

#include <iostream>#include <vector>#include <cmath>using namespace std;
// Function: Check if a number is automorphic
bool isAutomorphic(long long n) {    if (n == 0 || n == 1) return true;
    long long square = n * n;    long long temp = n;    long long divisor = 1;
    // Calculate the number of digits in n to determine the number of digits to compare
    while (temp > 0) {        divisor *= 10;        temp /= 10;    }
    // Compare if the last digits of the square equal the original number
    return (square % divisor) == n;}
int main() {    vector<long long> results;
    // Check all numbers from 0 to 200000
    for (long long i = 0; i <= 200000; i++) {        if (isAutomorphic(i)) {            results.push_back(i);        }    }
    // Output results, numbers separated by two spaces
    for (int i = 0; i < results.size(); i++) {        if (i > 0) {            cout << "  ";        }        cout << results[i];    }
    return 0;}

Output Result

Problem Analysis

An automorphic number is a number whose square ends with the number itself. For example:

• 5² = 25, the last digit is 5

• 25² = 625, the last digits are 25

• 76² = 5776, the last digits are 76

We need to find all automorphic numbers less than or equal to 200000.

Methodology

1. Check for Automorphic Numbers: For a number n, calculate n², then check if the last digits of n² equal n.

2. Get the Number of Digits: Based on the number of digits in n, take the corresponding last digits of n² for comparison.

3. Iterate Through All Numbers: Iterate from 0 to 200000, checking each number to see if it is automorphic.

Code Explanation

1. Automorphic Number Check Function: <span>isAutomorphic</span> function:

• Calculate the square of n

• Calculate the number of digits in n to determine the number of digits to compare

• Check if the last digits of the square equal the original number n

Main Function:

• Create a vector to store results

• Iterate through all numbers from 0 to 200000, checking if they are automorphic

• Output results in the specified format (numbers separated by two spaces)

C++ Basic Tutorial Collection

C++ Basic Resources

1. C++ Output

2. C++ Variables

3. C++ Input

4. C++ Expressions

5. IF Statements

6. IF Applications

7. WHILE Loops

8. FOR Loops

9. Arrays

10. One-Dimensional Arrays

11. Two-Dimensional Arrays

12. C++ Functions

13. C++ File Operations – Writing Files

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