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249 Winter 2014 Recursion
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| // -------------------------------------------------------------------------------------------------------- | |
| // Recursion249.java | |
| // Written by: Maxwell Mowbray | |
| // For COMP 249 Section PP - Tutorial PB - Winter 2014. | |
| // These are the questions from the COMP 249 final which dealt with recursion | |
| // -------------------------------------------------------------------------------------------------------- | |
| public class Recursion249 | |
| { | |
| public static int count = 0; | |
| public static void main(String[] args) | |
| { | |
| //magic(6); | |
| //System.out.println(count); | |
| System.out.println(exp(3,10)); | |
| } | |
| // Question 1: Analyse this recursive method and predict its output when main() has only: | |
| /*public static void main(String[] args) | |
| { | |
| magic(6); | |
| System.out.println(count); | |
| }*/ | |
| public static int magic(int n) | |
| { | |
| count++; | |
| int ret = 0; | |
| if (n < 3) | |
| ret = n; | |
| else | |
| ret = magic(n-2) + n + magic(n-3); | |
| System.out.println(ret); | |
| return ret; | |
| } | |
| /* | |
| Question 2: e^x can be approximated with a Taylor series. | |
| e^x = 1 + x/1! + x^2/2! + x^3/3! + ... + x^n/n! | |
| where x is any integer and n is a sufficiently large integer (larger integer -> closer approximation of e^x) | |
| In simple terms, you can calculate e^7 by computing 1 + 7/1! + 7^2/2! + 7^3/3! + ... | |
| First, write two recursive functions that will help. The first is the factorial function (factorial(n)) that | |
| recursively computes n!. Then, a recursive function that computes x^n. This function is pow (x,n). | |
| */ | |
| public static double factorial(int n) //go to a maximum of ten for n for an int or the number will be too large for an int | |
| { | |
| if (n == 0) | |
| return 1; | |
| else | |
| return (n * factorial(n-1)); | |
| } | |
| public static double pow (int x, int n) //x^4 = x * x^3. x^3 = x * x^2. and so on... | |
| { | |
| if (n == 0) | |
| return 1; | |
| else | |
| return (x * pow(x, n - 1)); | |
| } | |
| //To get the series computer, put both functions together recursively | |
| public static double exp (int x, int n) | |
| { | |
| if (n == 0) | |
| return 1; | |
| else | |
| return ((pow(x,n)) / factorial(n) + exp(x, n - 1)); | |
| } | |
| } |
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