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4 Inspection of a computer program controlling a weapons system shows 54 if statements (23 with else clauses), 4 switch statements (with 5, 7, 4, and 8 cases ), and 17 for or while loops with parameterized looping boundaries How would you exhaustively test such a program to prove its safety 95 Assume you have just created a program to schedule taxicabs in real time You re sure that your approach is entirely new and much better than anything else available Every taxi company in the world is going to want your software Explain how you would best protect your work patent copyright secret.

The output is:

8b + _

_ (a) _

{22, {22, {AB, {AB, {AB, {AB, 44, 66, 88} 44, 66, 88} CD, EF} CD, EF} XYZ, EF} CD, EF}

INTRODUCTION TO C0MPUTER SCIENCE 1.1 Write an algorithm for your morning routine, from the time the alarm clock rings until you leave the house for work or school. Awake to alarm clock. Get out of bed. Go downstairs to the kitchen. Fix and eat breakfast. Go to my room. Check the temperature and listen to the weather forecast. Get dressed. etc. 1.2 Find or invent an algorithm to calculate the square root of any number. Apply the algorithm to the number 2046, finding its square root to 2 decimal places. Do not use a computer or calculator! First take a guess: in this case 40. Divide the number by the guess: 51.15 Find average of guess and quotient: (51.15 + 40) / 2 = 45.575 Repeat with the new guess (45.575 after the first round). Second round result: 45.23 Third round result: 45.232 (from: http://www.homeschoolmath.net/teaching/square-root-algorithm.php) 1.3 Perl is a computer language that is often used for quick, one-off programming jobs, like converting text in a document from one format to another. ADA is a language used for Department of Defense applications where human life may be at stake. What differences would you imagine to find when you compare Perl with ADA Perl: little type checking of variables lots of default assumptions and short-cuts

t (b)

The array a[] contains four int elements. The array b[] is a duplicate of a[]. Similarly, the array d[] is a duplicate of the array c[], each containing three String elements. In both cases, the duplication is obtained by invoking the clone() method. Since it returns a reference to an Object, it must be cast to the array type being duplicated, int[] or String[]. The last part of the example shows that the cloned array d[] is indeed a separate copy of c[]: Changing c[1] to "XYZ" has no effect upon the value "CD" of d[1].

Fig. 2-17

CHAP. 2]

C +L _

informal code style emphasis on speed of coding ADA: rigorous type checking no default assumptions full declarations required documentation/comments required emphasis on correct and verifiable process

public static void sort(int[] a) { for (int i = 0; i < a.length-1; i++) { int j=i; for (int k = i+1; k < a.length; k++) { if (a[k] < a[j]) { j = k; } } swap(a, i, j); } } public static void sort(int[] a) { sort(a, a.length); } private static void sort(int[] a, int n) { if (n < 2) { return; } int j = 0; for (int k = 1; k < n; k++) { if (a[k] > a[j]) { j = k; } } swap(a, n-1, j); sort(a, n-1); }

T/2 3T/4

The last loop invariant proves correctness So, like the proof for the bubble sort, we need only verify the loop invariants On the first iteration of the main loop (step 1), a[i] is the last element in the array, so the index k of the inner loop runs through every element after a[0] The value of the index j begins at 0 and then changes each time k finds a larger element Since j is always reset to the index of the larger element, a[j] will be the largest element of the array when the inner loop finishes This verifies the first loop invariant On each successive iteration of the outer loop, the index k runs through the remaining unsorted segment of the array, so for the same reason, a[j] will be the largest element of that remaining segment when the inner loop finishes.

5T/4