Suggest, the Top-Down Approach to solve the given problem. proof your answer with proper/valid reason.

Let Pm =< p1, p2, ..., pm > and Qn =< q1, q2, ..., qn > be two sequences and the LCS of P and Q is given by R, where R =< r1, r2, ..., rk >.

1. If pm = qn, then rk = pm = qn and Rk1 is an LCS of Pm1 and Qn1

2. If pm 6 qn, then rk 6 pm implies that R is an LCS of Pm1 and Q

3. If pm 6 qn, then rk 6 qn implies that R is an LCS of Pm and Qn1