hw2sol.doc

Run some test inputs on both algorithms and compare

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Implement Sequential Search and Binary Search in your favorite programming language. Run some test inputs on both algorithms and compare the running times. NOT SHOWN 9. Implement Selection Sort, Insertion Sort, Bubble Sort and Merge Sort in your favorite programming language. Compare running time on an in order array and a reversed array. What does this show about the best and worst case inputs for these algorithms? NOT SHOWN 10. Please solve exercises 1.4.2 #1 and 1.4.2 #2 in the textbook. (a) The following functions are ordered from fastest growing to slowest growing: n!, 2^n, 2^(n-1), (3/2)^n, n- n^2+5n^3, n^3+ log n, n^3, n^2, n log n, n, sqrt(n), (log n)^2, log n, log log n, 6 (b) Please show which function is faster growing between the following two functions: a.(n^2-n)/2 and 6n (n^2-n)/2 b. n+2sqrt(n) and n^2 n^2 c. n+nlog(n) and n*sqrt(n) n*sqrt(n)

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d. n^2 + 3n + 4 and n^3 n^3 e. n log(n) and n*sqrt(n)/2 n*sqrt(n)/2 f. n + log(n) and sqrt(n) n + log(n) g. 2log(n)^2 and log n +1 2log(n)^2 h. 4nlog(n) + n and (n^2-n)/2 (n^2-n)/2 11. Order the following function from slowest growing to fastest growing: n^3, lg n, 2^n, n, n^2, n lg n lg n, n, n lg n, n^2, n^3, 2^n 12. Use the product rule for derivates [(fg)' = f'g + fg'] to prove by mathematical induction that for every integer n >= 1, the derivative of is .

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