A number is called happy if it leads to 1 after a sequence of steps wherein each step number is replaced by the sum of squares of its digit that is if we start with a Happy Number and keep replacing it with digits square sum, we reach 1. In this article, we will check if the given number is a Happy Number
Examples
Input: n = 19
Output: True
19 is Happy Number,1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1
As we reached to 1, 19 is a Happy Number.Input: n = 20
Output: False
Python Program to Check if Given Number is Happy Number
Below are the example of Python program to check if the given number is Happy Number.
- Using Set() Method
- Using No Extra Space
- Using Extra Space.
Check if Given Number is Happy Number Using Set Method
In this example, below code defines two functions: numSquareSum calculates the sum of squares of digits of a number, and isHappyNumber checks if a number is a Happy Number, using a set to detect cycles. The example usage demonstrates checking if the number 20 is a Happy Number, which returns False.
# Function to return the sum of squares of digits of n
def numSquareSum(n):
squareSum = 0
while (n != 0):
squareSum += (n % 10) * (n % 10)
n = n // 10
return squareSum
# Function to return true if n is a Happy Number
def isHappyNumber(n):
st = set()
while (1):
n = numSquareSum(n)
if (n == 1):
return True
if n in st:
return False
st.add(n)
# Example usage:
print(isHappyNumber(20))
Output
False
Time Complexity: O(n*log(n)).
Auxiliary Space: O(n) since we are using set.
Check if Given Number is Happy Number Using No Extra Space
In this example, we have a method named numSquareSum which calculates the sum of the squares of the digits of a given number. The isHappynumber method determines whether a number is a "happy number" or not. It employs two pointers, slow and fast, to iterate through the sum of squares until they either meet or reach 1, indicating a happy number.
# Utility method to return
# sum of square of digit of n
def numSquareSum(n):
squareSum = 0;
while(n):
squareSum += (n % 10) * (n % 10);
n = int(n / 10);
return squareSum;
# method return true if
# n is Happy number
def isHappynumber(n):
# initialize slow
# and fast by n
slow = n;
fast = n;
while(True):
# move slow number
# by one iteration
slow = numSquareSum(slow);
# move fast number
# by two iteration
fast = numSquareSum(numSquareSum(fast));
if(slow != fast):
continue;
else:
break;
# if both number meet at 1,
# then return true
return (slow == 1);
# Driver Code
n = 13;
if (isHappynumber(n)):
print(n , "is a Happy number");
else:
print(n , "is not a Happy number");
Output
13 is a Happy number
Time Complexity: O(n*log(n)).
Auxiliary Space: O(1).
Check if Given Number is Happy Number Using Extra Space.
In this example, below code defines a method isHappynumber to check if a given number is a "happy number". It first checks if the number is 1 or 7, which are happy numbers, and returns True. Otherwise, it iterates through the sum of squares of digits until it either reaches 1 or 7, or enters a cycle. If it reaches 1 or 7, it returns True; otherwise, it returns False.
# Method - returns true if the input is
# a happy number else returns false
def isHappynumber(n):
if n == 1 or n == 7:
return True
Sum, x = n, n
# This loop executes till the sum
# of square of digits obtained is
# not a single digit number
while Sum > 9:
Sum = 0
# This loop finds the sum of
# square of digits
while x > 0:
d = x % 10
Sum += d * d
x = int(x / 10)
if Sum == 1:
return True
x = Sum
if Sum == 7:
return True
return False
n = 13
if isHappynumber(n):
print(n, "is a Happy number")
else:
print(n, "is not a Happy number")
Output
13 is a Happy number
Time Complexity: O(n*log(n)).
Auxiliary Space: O(1).