# CREATE OWN LIBRARY

## Leap Year

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### Description

A year is taken as input to check whether it is a leap year or not. The conditions for a year to be a leap year are stated below:

# The year is divisible by 4 but not divisible by 100.

# For the century years, the years should be divisible by 4 as well as 400 to be a leap year.

# If the year is not divisible by 4 then it is not a leap year.

# For the century years, if it is divisible by 4 and 100 but not by 400 then that year will not be a leap year.

For example,

# If we consider the year 2000, it is divisible by 4 as well as 400; therefore, this year is a leap year.

# If we consider the year 1900, it is divisible by 4 as well as by 100. But, the year is not divisible by 400. Therefore, the year 1900 is not a leap year.

# If the year is 2016, it is not a century year, but it is divisible by 4. So, 2016 is a leap year.

# If the year is 2015, it is not divisible by 4, so, it is not a leap year.

### Algorithm

INPUT: A year

OUTPUT: Whether the year is a leap year or not.

PROCESS:

Step 1: [taking the input]

Read y [the year to check for leap year]

Step 2: [Checking for leap year]

If y Mod 4 = 0 then

If y Mod 100 = 0 then

If y Mod 400 = 0 then

Print "y is a Leap Year"

Else

Print "y is not a Leap Year"

[End of ‘if’]

Else

Print "y is a Leap Year"

[End of ‘if’]

Else

Print "y is not a Leap Year"

[End of ‘if’]

Step 3: Stop.

### Code

TIME COMPLEXITY:

if(y % 4 == 0) ----------------------------------- O(1)

{

//if the year is divisible by 400

//then it is a leap year else not

if( y % 100 == 0) --------------------------- O(1)

{

if ( y % 400 == 0) --------------- O(1)

printf("%d is a Leap Year", y);

else ------------------------------- O(1)

printf("%d is not a Leap Year", y);

}

//if the year is not divisible by 100 but divisible by 4

//then it is a leap year

else ----------------------------------------- O(1)

printf("%d is a Leap Year", y );

}

//if the year is not divisible by 4

//then it is not a leap year

else -------------------------------------------- O(1)

printf("%d is not a Leap Year", y);

The time complexity of this program is O(1) as it needs a constant time to execute.

SPACE COMPLEXITY:

The space complexity of this program is O(1) as it requires same number of memory spaces to execute for any given input.

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