Two character strings may have many common sub-strings. For example, photograph

Question

Two character strings may have many common sub-strings. For example, photograph and tomography have several common sub-strings of length one (i.e., single letters), and common sub-strings ph, to, and ograph (as well as all the sub-strings of ograph). The maximum common sub-string length is 6. Let X = x_1 x_2...x_n and Y = y_1 y_2...y_m be two character strings. The Maximum Common Sub-string (MCS) Problem is to find the maximum common sub-string length for X and Y. Let s[i, j] = the length of the longest common sub-string ending at x_i and y_j, define the functional equation for Give an algorithm to implement this functional equation. What is the time complexity of your algorithm?

Explanation / Answer

Algorithm to find the length of longest common sub string:

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