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Unformatted text preview: 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....
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This note was uploaded on 02/04/2010 for the course COMPUTER S cs300 taught by Professor Unkown during the Spring '08 term at Korea Advanced Institute of Science and Technology.
- Spring '08