Q:

# Program to print all happy numbers between 1 and 100

belongs to collection: Number Programs

### Explanation

In this program, we need to display all happy numbers between 1 and 100.

Happy number

The happy number can be defined as a number which will yield 1 when it is replaced by the sum of the square of its digits repeatedly. If this process results in an endless cycle of numbers containing 4, then the number is called an unhappy number.

For example, 32 is a happy number as the process yields 1 as follows

### Formula

```32 + 22 = 13
12 + 32 = 10
12 + 02 = 1
```

Some of the other examples of happy numbers are 7, 28, 100, 320 and so on.

Unhappy number will result into a cycle of 4, 16, 37, 58, 89, 145, 42, 20, 4, ...

To find whether a given number is happy or not, calculate the square of each digit present in number and add it to a variable sum. If resulting sum is equal to 1 then, given number is a happy number. If the sum is equal to 4 then, the number is an unhappy number. Else, replace the number with the sum of the square of digits.

### Algorithm

1. isHappyNumber() determines whether a given number is happy or not.
1. If the number is greater than 0, calculate remainder rem by dividing the number with 10.
2. Calculate square of rem and add it to a variable sum.
3. Divide number by 10.
4. Repeat the steps from a to c till the sum of the square of all digits present in number has been calculated.
5. Finally, return the sum.
2. To display all happy numbers between 1 and 100,
1. Start a loop from 1 to 100, then make a call to isHappyNumber() method for each value from 1 to 100 and store the return value into a variable result.
2. If the result is neither equal to 1 nor 4 then, make a call to isHappyNumber().
3. Otherwise, if the result is equal to 1, it implies that the number is happy and display it.

Input:

range(1, 101)

Output:

`List of happy numbers between 1 and 100: 1 7 10 13 19 23 28 31 32 44 49 68 70 79 82`

### Python

``````#isHappyNumber() will determine whether a number is happy or not
def isHappyNumber(num):
rem = sum = 0;

#Calculates the sum of squares of digits
while(num > 0):
rem = num%10;
sum = sum + (rem*rem);
num = num//10;
return sum;

#Displays all happy numbers between 1 and 100
print("List of happy numbers between 1 and 100: ");
for i in range(1, 101):
result = i;

#Happy number always ends with 1 and
#unhappy number ends in a cycle of repeating numbers which contains 4
while(result != 1 and result != 4):
result = isHappyNumber(result);

if(result == 1):
print(i),
print(" "),  ``````

Output:

``` List of happy numbers between 1 and 100:
1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100
```

### C

``````#include <stdio.h>

//isHappyNumber() will determine whether a number is happy or not
int isHappyNumber(int num){
int rem = 0, sum = 0;

//Calculates the sum of squares of digits
while(num > 0){
rem = num%10;
sum = sum + (rem*rem);
num = num/10;
}
return sum;
}

int main()
{
//Displays all happy numbers between 1 and 100
printf("List of happy numbers between 1 and 100: \n");
for(int i = 1; i <= 100; i++){
int result = i;

//Happy number always ends with 1 and
//unhappy number ends in a cycle of repeating numbers which contains 4
while(result != 1 && result != 4){
result = isHappyNumber(result);
}

if(result == 1)
printf("%d ", i);
}

return 0;
}  ``````

Output:

```List of happy numbers between 1 and 100:
1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100
```

### JAVA

``````public class HappyNumbers
{
//isHappyNumber() will determine whether a number is happy or not
public static int isHappyNumber(int num){
int rem = 0, sum = 0;

//Calculates the sum of squares of digits
while(num > 0){
rem = num%10;
sum = sum + (rem*rem);
num = num/10;
}
return sum;
}

public static void main(String[] args) {

//Displays all happy numbers between 1 and 100
System.out.println("List of happy numbers between 1 and 100: ");
for(int i = 1; i <= 100; i++){
int result = i;

//Happy number always ends with 1 and
//unhappy number ends in a cycle of repeating numbers which contains 4
while(result != 1 && result != 4){
result = isHappyNumber(result);
}

if(result == 1)
System.out.print(i + " ");
}
}
}  ``````

Output:

```List of happy numbers between 1 and 100:
1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100
```

### C#

``````using System;

public class HappyNumbers
{
//isHappyNumber() will determine whether a number is happy or not
public static int isHappyNumber(int num){
int rem = 0, sum = 0;

//Calculates the sum of squares of digits
while(num > 0){
rem = num%10;
sum = sum + (rem*rem);
num = num/10;
}
return sum;
}

public static void Main()
{
//Displays all happy numbers between 1 and 100
Console.WriteLine("List of happy numbers between 1 and 100: ");
for(int i = 1; i <= 100; i++){
int result = i;

//Happy number always ends with 1 and
//unhappy number ends in a cycle of repeating numbers which contains 4
while(result != 1 && result != 4){
result = isHappyNumber(result);
}

if(result == 1)
Console.Write(i + " ");
}
}
}  ``````

Output:

```List of happy numbers between 1 and 100:
1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100
```

### PHP

``````<!DOCTYPE html>
<html>
<body>
<?php
//isHappyNumber() will determine whether a number is happy or not
function isHappyNumber(\$num){
\$rem = \$sum = 0;

//Calculates the sum of squares of digits
while(\$num > 0){
\$rem = \$num%10;
\$sum = \$sum + (\$rem*\$rem);
\$num = intval(\$num/10);
}
return \$sum;
}

//Displays all happy numbers between 1 and 100
print("List of happy numbers between 1 and 100: <br>");
for(\$i = 1; \$i <= 100; \$i++){
\$result = \$i;

//Happy number always ends with 1 and
//unhappy number ends in a cycle of repeating numbers which contains 4
while(\$result != 1 && \$result != 4){
\$result = isHappyNumber(\$result);
}
if(\$result == 1)
print(\$i . " ");
}
?>
</body>
</html>  ``````

Output:

```List of happy numbers between 1 and 100:
1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100```