2 n n n k0 mn nm k k n towards a dynamic programming

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Unformatted text preview: tches – (#mismatches) μ – (#indels) σ •  Objective: find the best scoring alignment Number of pairwise alignments •  For two sequences of length n: ￿ 2n n ￿ (2n)! 22 n = ≈√ 2 (n!) πn •  Derived using Stirling’s approximation: n! ≈ √ 2π n ￿ n ￿n k=0 ￿￿ ￿ ￿ ￿ mn n+m = k k n Towards a dynamic programming algorithm for pairwise alignment •  •  •  •  •  The Change Problem The Manhattan Tourist Problem The Longest Common Subsequence Problem Edit Distance Sequence Alignment e 2 A greedy algorithm for Change The Change Problem Goal: Convert some amount of money M into g iven denominations, using the fewest possible number of coins Input: An amount of money M, and an array of d denominations c = (c1, c2, …, cd), in decreasing order of value (c1 > c2 > … > cd) Output: A list of d integers i1, i2, …, id s.t. c1i1 + c2i2 + … + cdid = M and i1 + i2 + … + id is minimal •  Use the maximal number of the largest denomination •  Fails: example - change 40 when we have denominatio...
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This note was uploaded on 02/10/2014 for the course CS 548 taught by Professor Asaben-hur during the Spring '12 term at Colorado State.

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