Question: (a) Why is the Principle of Optimality important for dynamic programming method? (b)For the Longest Common Subsequence (LCS) problem with input X=x1x2xm and Y=y1y2yn, we

(a) Why is the Principle of Optimality important for dynamic programming

(a) Why is the Principle of Optimality important for dynamic programming method? (b)For the Longest Common Subsequence (LCS) problem with input X=x1x2xm and Y=y1y2yn, we solved the problem using the dynamic programming method where we defined cij to be the length of a LCS between x1x2xi and y1y2yj. What is the complete recurrence for cij, including the initial condition? For the following X=ABCAD and Y=DADC : fill the following table with the values of cij 's

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