Consider the following java-like code for a recursive sorting algorithm: // sorts the items from l[i] through l[j] void threewaysort(int[ ] l, int i, int j) { if (l[i] > l[j]) swap (i, j); if ((j - i + 1) > 2) { t = (j - i + 1)/3; threewaysort(l, i, j-t); threewaysort(l, i+t, j); threewaysort(l, i, j-t); } } (a) prove that this algorithm is correct, that is, that the call threewaysort(l, 0, l. length-1) actually has the side effect of making l sorted. (b) let f(n) be the running time of threewaysort(l, i,j) when j − i + 1 = n. write a recurrence for f(n). (c) solve your recurrence to determine the worst-case running time of threewaysort on lists of size n. how does it compare to other sorting algorithms you know?

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Jason, samantha, ravi, sheila, and ankit are preparing for an upcoming marathon. each day of the week, they run a certain number of miles and write them into a notebook. at the end of the week, they would like to know the number of miles run each day, the total miles for the week, and average miles run each day. write a program to them analyze their data. your program must contain parallel arrays: an array to store the names of the runners and a two-dimensional array of five rows and seven columns to store the number of miles run by each runner each day. furthermore, your program must contain at least the following functions: a function to read and store the runners’ names and the numbers of miles run each day; a function to find the total miles run by each runner and the average number of miles run each day; and a function to output the results. (you may assume that the input data is stored in a file and each line of data is in the following form: runnername milesday1 milesday2 milesday3 milesday4 milesday5 milesday6 milesday7.)

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