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Examples: Input: 122 Output: 1 Explanation: Four good numbers of length 2 exist - 11, 12, 21, and 22. Of those four, only 11 is superb because its digits sum up to 2. Input: 58 997690 Output: 21735480 Input: 782 Output: */

Examples: Input: 122 Output: 1 Explanation: Four good numbers of length 2 exist - 11, 12, 21, and 22. Of those four, only 11 is superb because its digits sum up to 2. Input: 58 997690 Output: 21735480 Input: 782 Output: */

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Examples: Input: 122 Output: 1 Explanation: Four good numbers of length 2 exist - 11, 12, 21, and 22. Of those four, only 11 is superb because its digits sum up to 2. Input: 58 997690 Output: 21735480 Input: 782 Output: * /
Transcribed Image Text:Examples: Input: 122 Output: 1 Explanation: Four good numbers of length 2 exist - 11, 12, 21, and 22. Of those four, only 11 is superb because its digits sum up to 2. Input: 58 997690 Output: 21735480 Input: 782 Output: * /
Holy Numbers /* Winnica loves numbers. She considers the digits a and b to be holy, and thus considers a number good if it only contains digits a and b. Winnica considers a good number to be superb if the sum of its digits is a good number. Help Winnica determine how many superb numbers exist of length n. In order to prevent overflow when calculating your answer, print your answer modulo 1000000007. Why 1000000007? Consider the sequence 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... modulo 8 = 2, 4, 6, 0, 2, 4, 6, 0, 2, 4 ... repeating values. %3D Now consider 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,... modulo 7 (prime) = 3, 6, 2, 5, 1, 4, 0, 3, 6, 2,...no repeats in first 7 terms. The best number to prevent modulo repeats, or overlaps, is a prime number greater than the number of terms. When concerned with integer overflow, the best choice is the largest prime <= the largest integer which can be stored in 32 bits, which is 2^31 - 1 (the 32nd bit is used for sign). As it turns out, 2^31 - 1 = 2,147,483,647 =1111111 2.147483647 x 10^9 is itself prime. 111111111111111111111 base 2 = %3D 1,000,000,007 = 10^9 + 7, the first 10-digit prime number, is however easier to write and for our purposes will do the job. The true number theorist will pursue the reason why prime numbers are so useful in modular arithetic more deeply. See, e.g. https://theoryofprogramming.wordpress.com/2014/12/24/modular-arithmetic- properties/ Incidentally, 1000000007 is not only a naughty prime, meaning all except the end digits = 0, but also an extremely naughty prime, meaning the number of zeros = the sum of the end digits. It is also an emirp (prime spelled backwards), meaning it gives you a different prime when its digits are reversed. %3D Input: The first line contains three integers a, b, and n (1< a<b< 9,1sn< 10^6). Output: Print the answer modulo 1000000007 (10^9 + 7).
Transcribed Image Text:Holy Numbers /* Winnica loves numbers. She considers the digits a and b to be holy, and thus considers a number good if it only contains digits a and b. Winnica considers a good number to be superb if the sum of its digits is a good number. Help Winnica determine how many superb numbers exist of length n. In order to prevent overflow when calculating your answer, print your answer modulo 1000000007. Why 1000000007? Consider the sequence 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... modulo 8 = 2, 4, 6, 0, 2, 4, 6, 0, 2, 4 ... repeating values. %3D Now consider 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,... modulo 7 (prime) = 3, 6, 2, 5, 1, 4, 0, 3, 6, 2,...no repeats in first 7 terms. The best number to prevent modulo repeats, or overlaps, is a prime number greater than the number of terms. When concerned with integer overflow, the best choice is the largest prime <= the largest integer which can be stored in 32 bits, which is 2^31 - 1 (the 32nd bit is used for sign). As it turns out, 2^31 - 1 = 2,147,483,647 =1111111 2.147483647 x 10^9 is itself prime. 111111111111111111111 base 2 = %3D 1,000,000,007 = 10^9 + 7, the first 10-digit prime number, is however easier to write and for our purposes will do the job. The true number theorist will pursue the reason why prime numbers are so useful in modular arithetic more deeply. See, e.g. https://theoryofprogramming.wordpress.com/2014/12/24/modular-arithmetic- properties/ Incidentally, 1000000007 is not only a naughty prime, meaning all except the end digits = 0, but also an extremely naughty prime, meaning the number of zeros = the sum of the end digits. It is also an emirp (prime spelled backwards), meaning it gives you a different prime when its digits are reversed. %3D Input: The first line contains three integers a, b, and n (1< a<b< 9,1sn< 10^6). Output: Print the answer modulo 1000000007 (10^9 + 7).
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