HW2 - Fall Semester 2008 CS300 Algorithms Homework#2(due...

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Fall Semester 2008 CS300 Algorithms Homework #2 (due 10/10) 1. We can recursively define the number of combinations of m things out of n , denoted ( n m ) , for n 1 and 0 m n , by ( n m ) = 1 if m = 0 or m = n ( n m ) = ( n - 1 m ) + ( n - 1 m - 1 ) if 0 < m < n (a) Give a recursive function to compute ( n m ) . (b) What is its worst-case running time as a function of n ? (c) Give a dynamic programming algorithm to compute ( n m ) . Hint 1 The algorithm constructs a table generally known as Pascal’s triangle. (d) What is the running time of your answer to (c) as a function of n ? 2. Suppose you are consulting for a company that manufactures PC equipment and ships it to distributors all over the country. For each of the next n weeks, they have a projected supply s i of equipment (measured in pounds), which has to be shipped by an air freight carrier. Each week’s supply can be carried by one of two air freight companies, A or B. Company A charges a fixed rate r per pound (so it costs r × s i to ship a week’s supply s i ).
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