Leap Year in C++

Problem Description
For an input year N, find whether the year is a leap or not.

Input format
First line contains an integer - N.

Output format
Print "true" if it is a leap year otherwise "false".

Sample Input 1
1600

Sample Output 1
true

Explanation
Year 1600 is a leap year

Sample Input 2
1800

Sample Output 2
false

Explanation
Year 1800 is not a leap year

Constraints
1 <= N <= 9999

Solution

To determine if a given year \( N \) is a leap year, we need to follow the rules of the Gregorian calendar:

1. A year is a leap year if it is divisible by 4.

2. However, if the year is divisible by 100, it is not a leap year unless:

3. The year is also divisible by 400, in which case it is a leap year.

Based on these rules, we can implement a C++ program that reads a year \( N \) and determines if it is a leap year.

### C++ Code

#include <iostream>

using namespace std;

int main() {

    int N;

    cin >> N;

    

    bool isLeapYear = false;

    

    if (N % 4 == 0) {

        if (N % 100 == 0) {

            if (N % 400 == 0) {

                isLeapYear = true;

            } else {

                isLeapYear = false;

            }

        } else {

            isLeapYear = true;

        }

    } else {

        isLeapYear = false;

    }

    

    if (isLeapYear) {

        cout << "true" << endl;

    } else {

        cout << "false" << endl;

    }

    

    return 0;

}

### Explanation

1. **Input Handling**: The program reads an integer \( N \) from the standard input.

2. **Leap Year Check**:

   - First, it checks if \( N \) is divisible by 4.

   - If \( N \) is divisible by 4, it then checks if \( N \) is divisible by 100.

   - If \( N \) is divisible by 100, it further checks if \( N \) is divisible by 400.

   - Based on these checks, the program sets the `isLeapYear` flag to `true` or `false`.

3. **Output**: The program prints "true" if `isLeapYear` is `true`, otherwise it prints "false".

### Sample Runs

#### Sample Input 1

1600

#### Sample Output 1

true

#### Explanation

Year 1600 is divisible by 400, so it is a leap year.

#### Sample Input 2

1800

#### Sample Output 2

false

#### Explanation

Year 1800 is divisible by 100 but not by 400, so it is not a leap year.

This program efficiently determines whether a given year is a leap year based on the rules of the Gregorian calendar.