We say that a string w is a 'braid' of strings u and v if w can be written as the catenation of strings w = x_1*y_1*x_2*y_2 · · · x_n*y_n, where x_i , y_i are (possibly empty) strings such that u = x_1 · · · x_k and v = y_1 · · · y_k. For example, the string drnonfamatiicction is a braid of the strings 'dramatic' and 'nonfiction'.   Given strings u, v, w with lengths m, n, m + n respectively, give an algorithm in pseudocode that determines whether w is a braid of u and v. Give proofs of correctness and running time for your algorithm.

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