CSCA67H3 Lecture 1: Permutation and Combination

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salmonhare362

24 Dec 2015

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Adapted from: bretscher, csca67 week 1 lecture notes, Consider a pizza commercial that advertises: 2 pizzas, up to 5 toppings on each, 11 toppings to choose from. # of combinations of up to 5 toppings = # of combinations of no toppings + # of combinations of 1 topping + . # of combinations of 4 toppings + # of combinations of 5 toppings: there is only 1 way to combine no toppings. # of combinations of no toppings = 1: there are 11 choices of toppings, meaning that there are 11 ways to combine a single topping. # of combinations of 1 topping = 11: there are 11 di erent ways to choose a single topping. This means that there are 11 10 ways to choose 2 toppings. However, some of the combinations of 2 toppings are equivalent, since the order in which the toppings are selected does not matter. (cid:124) (cid:123)(cid:122)

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16. The following method takes two integer arrays and a target integer as input. It is supposed to return true if there is an element from the first array and an element from the second array whose sum is the target integer. For instance, given arrays a=[1,4,3] and b=[2,6,3] and target 7, the method should return true because a[1]+b[2] = 4+3 = 7. However, if the target is 8, it should return false, as no element in array a, added with an element of array b results in 8. What should be the body of this method? public static boolean foo (int[] a, int[] b, int target) // What should go here? (A) for (int i = 0; i < a.length + b.length; i++) if(a[i] + b[i] == target) return true; else return false; (B) for (int i = 0; i

(c) Consider the following class: public class Student Grades private int ( grades; 1/loads values into grades from a file public void initializeFromFile(String filename) ....! //gets the total number of grades entered public int get NumRecords () (....) public class WebCT 1 public static void main(String[] args) Student Grades grades = new Student Grades(); grades.initializeFromFile("records. L.sv"); System.out.println("There are " + grades.length file.") " grades in that The goal of the program is to load the files and then print the total number of grades in the file. However, when you try to compile the above classes, you get the following error: WebCT.java:5: cannot find symbol symbol : variable length location: class Student Grades System.out.println("There are " + grades.length + " grades in that file." Explain why the crror occurs and write the code to fix it (while maintaining the intended functionality).

I. [10 marks For each row in the table below, determine what would happen if you opened DrScheme and tried to evaluate the given code. If there is an error, brielly explain what is wrong (be more specific than saying "invalid Scheme expression"). If there is no error, give the value produced by DrScheme. The first two rows have been completed for you as examples. Answer Scheme Code (+ 12) (+ 1 2)) (7 + 12) Error. There is an extra) (+ 4 (* 1 (+ 4 2))) ( 1 ((reraircer 27 9) (sqr 5))) (/ 10 (-3 (-14))) (= 'apple 'banana) (and (< 3 4) 19 10)) (- 12 (string-length. "iya")) (reso rest (rest (rest (cors'a (cons 3 (cons 5 empty))))))) (cond [(> 3 8) "happy! [(-34) 'sad) [(even? 9) 'oops] ) (posn-X (first (rest (coris (make-posn 3 4) (cons (make-posr. 56) empty)))))

CSCA67H3 Lecture 1: Permutation and Combination

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