Suppose the trustee for the estate of famous photographer, Ansel Adams, was interested in finding examples of people posting Ansel Adams photographs on their personal websites without including attributions to him. Suppose further that some of these people have tried to conceal their possible copyright infringement by cropping the image down to be a smaller size. Thus, given a candidate image, P, taken from someone’s personal website, and his own photograph, T, Mr. Adams is interested in determining whether it is possible to create the image P by cropping the image T. Assuming that P and T are square images, this problem can be easily modeled as a two-dimensional version of the pattern matching problem. In two-dimensional pattern matching, a pattern, P, is given as an m × m array of characters, and the text, T, is given as an n × n array of characters, and we are interested in finding a location, (i, j), such that P is a submatrix of T when shifted to the location, (i, j). That is, 

P[k,l] = T[i + k, j + l], 

for k = 0,...,m − 1 and l = 0,...,m − 1. In the context of the problem of interest for the trustee of the estate of Ansel Adams, each pixel in an image could be viewed as a character (corresponding, for example, to an 8-bit intensity value in a black-and-white image). Describe an efficient algorithm for solving this two-dimensional pattern matching problem. What are the worst-case and expected-case running times for your algorithm?