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Happy Number
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A number is said to be a happy number if the number reaches 1 after a number of steps and in each step, the sum of the squares of the digits are calculated and the number is replaced with the sum and again the same step is repeated till it reaches 1.
For example, let us consider the number 82.
82+22=64+4=68
62+82=36+64=100
12+02+02=1
Therefore, it is a happy number.
Algorithm
INPUT: A number
OUTPUT: Whether the number is a happy number or not
PROCESS:
Step 1: [Taking the input]
Read n [the number to be checked]
Step 2: [Checking for Happy Number]
Set sum<-0
[Checking for happy number]
While sum≠1 and sum≠4 repeat
Set sum<-0
While n>0 repeat
Set r<-n mod 10
Set sum<-sum+(r×r)
Set n<-n/10
[End of ‘while’ loop]
Set n<-sum
[End of ‘while’ loop]
[Printing the result]
If sum=1
Print "The number is a Happy Number"
Else
Print "The number is not a Happy Number"
[End of ‘if-else’]
Step 3: Stop.
Code
Time Complexity:
while (sum!=1 && sum!=4)
{ sum=0;
while(n>0)
{
r=n%10;
sum+=(r*r);
n=n/10;
}
n=sum; }
The time complexity of this program is O(m*) where ‘m’ is the number of elements before reaching 1 of which the sum of the square of the digits are to be calculated and ‘n’ is each number that is checked.
Space Complexity:
The space complexity of this program is O(1) as it requires a constant number of memory spaces for any given input.
