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IMPORTANT: Your isHappy function must not call itself. Subtask III: There are in fact many levels of happiness. The larger the number, the happier we feel about that number. The k-th happy number is the k-th smallest happy number. This means, the 1st happy number is the smallest happy number, which is 1. The 2nd happy number is the second smallest happy number, which is 7. Below is a list of the first few happy numbers: 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, ... Implement a function kThHappy (k: int) -> int that computes and returns the k-th happy num- ber. For example: kThHappy (1) returns 1 kThHappy (3) returns 10 kThHappy (11) returns 49 kThHappy (19) returns 97

IMPORTANT: Your isHappy function must not call itself. Subtask III: There are in fact many levels of happiness. The larger the number, the happier we feel about that number. The k-th happy number is the k-th smallest happy number. This means, the 1st happy number is the smallest happy number, which is 1. The 2nd happy number is the second smallest happy number, which is 7. Below is a list of the first few happy numbers: 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, ... Implement a function kThHappy (k: int) -> int that computes and returns the k-th happy num- ber. For example: kThHappy (1) returns 1 kThHappy (3) returns 10 kThHappy (11) returns 49 kThHappy (19) returns 97

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Make a happy number function

IMPORTANT: Your isHappy function must not call itself. Subtask III: There are in fact many levels of happiness. The larger the number, the happier we feel about that number. The k-th happy number is the k-th smallest happy number. This means, the 1st happy number is the smallest happy number, which is 1. The 2nd happy number is the second smallest happy number, which is 7. Below is a list of the first few happy numbers: 1,7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, ... Implement a function kThHappy (k: int) -> int that computes and returns the k-th happy num- ber. For example: kThHappy (1) returns 1 kThHappy (3) returns 10 • kThHappy (11) returns 49 • kThHappy (19) returns 97
Transcribed Image Text:IMPORTANT: Your isHappy function must not call itself. Subtask III: There are in fact many levels of happiness. The larger the number, the happier we feel about that number. The k-th happy number is the k-th smallest happy number. This means, the 1st happy number is the smallest happy number, which is 1. The 2nd happy number is the second smallest happy number, which is 7. Below is a list of the first few happy numbers: 1,7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, ... Implement a function kThHappy (k: int) -> int that computes and returns the k-th happy num- ber. For example: kThHappy (1) returns 1 kThHappy (3) returns 10 • kThHappy (11) returns 49 • kThHappy (19) returns 97
Happy numbers are a nice mathematical concept. Just as only certain numbers are prime, only cer- tain numbers are happy-under the mathematical definition of happiness. We'll tell you exactly what happiness means. The concept of happy numbers is only defined for whole numbers n> 1. To test whether a number is happy, we can follow a simple step-by-step procedure: (1) Write that number down (2) Stop if that number is either 1 or 4. (3) Cross out the number you have now. Write down instead the sum of the squares of its digits. (4) Repeat Step (2) When you stop, if the number you have is 1, the initial number is happy. If the number you have is 4, the initial number is sad. There are only two possible outcomes, happy or sad. By this definition, 19 is a happy number because 12 + 92 = 82, then 82 + 22 = 68, then 62 + 8² = 100, and then 12 + 02 + 0² = 1. However, 145 is sad because 12 + 42 +52 = 42, 42 +22 = 20, and 22 +02 = 4. Subtask I: First, you'll implement a function sumOfDigitsSquared(n: int) -> int that takes a positive number n and returns the sum the squares of its digits. For example, • sumOfDigitsSquared(7) should return 49 sumOfDigitsSquared(145) should return 42 (i.e., 1**2 + 4**2 + 5**2 = 1 + 16 + 25) • sumOfDigitsSquared(199) should return 163 (i.e., 1**2 + 9**2 + 9**2 = 1 + 81 + 81) Subtask II: Then, you'll write a function isHappy (n: int) -> bool that takes as input a positive number n and tests if n is happy. You may wish to use what you wrote in the previous subtask. isHappy (100) should return True • isHappy (111) should return False • isHappy (1234) should return False isHappy (989) should return True (Did we tell you n must be positive (i.e. at least 1)?)
Transcribed Image Text:Happy numbers are a nice mathematical concept. Just as only certain numbers are prime, only cer- tain numbers are happy-under the mathematical definition of happiness. We'll tell you exactly what happiness means. The concept of happy numbers is only defined for whole numbers n> 1. To test whether a number is happy, we can follow a simple step-by-step procedure: (1) Write that number down (2) Stop if that number is either 1 or 4. (3) Cross out the number you have now. Write down instead the sum of the squares of its digits. (4) Repeat Step (2) When you stop, if the number you have is 1, the initial number is happy. If the number you have is 4, the initial number is sad. There are only two possible outcomes, happy or sad. By this definition, 19 is a happy number because 12 + 92 = 82, then 82 + 22 = 68, then 62 + 8² = 100, and then 12 + 02 + 0² = 1. However, 145 is sad because 12 + 42 +52 = 42, 42 +22 = 20, and 22 +02 = 4. Subtask I: First, you'll implement a function sumOfDigitsSquared(n: int) -> int that takes a positive number n and returns the sum the squares of its digits. For example, • sumOfDigitsSquared(7) should return 49 sumOfDigitsSquared(145) should return 42 (i.e., 1**2 + 4**2 + 5**2 = 1 + 16 + 25) • sumOfDigitsSquared(199) should return 163 (i.e., 1**2 + 9**2 + 9**2 = 1 + 81 + 81) Subtask II: Then, you'll write a function isHappy (n: int) -> bool that takes as input a positive number n and tests if n is happy. You may wish to use what you wrote in the previous subtask. isHappy (100) should return True • isHappy (111) should return False • isHappy (1234) should return False isHappy (989) should return True (Did we tell you n must be positive (i.e. at least 1)?)
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