FOR FREE YEAR SOLVED
Leap Year
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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);
TIME COMPLEXITY:
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.
