(4 points) A strand of DNA is represented as a string over the alphabet -{a, c, g,t). You are given a DNA text T E and a DNA pattern P E ", n-m. Explain how to compute the Hamming distance between the pattern and every offset of the text, i.e., you want to compute the array where, for equal length strings X, Y, HamDist(X, Y) is the number of positions where they differ: Give an O(n log n) algorithm to compute the array A. Just for fun: show how to speed up the algorithm to run in O(n log m) time Hint: convolutions (4 points) A strand of DNA is represented as a string over the alphabet -{a, c, g,t). You are given a DNA text T E and a DNA pattern P E ", n-m. Explain how to compute the Hamming distance between the pattern and every offset of the text, i.e., you want to compute the array where, for equal length strings X, Y, HamDist(X, Y) is the number of positions where they differ: Give an O(n log n) algorithm to compute the array A. Just for fun: show how to speed up the algorithm to run in O(n log m) time Hint: convolutions