In the LCS problem, we are given as input two sequences, X = (r1, x2,..., Im) and Y = (y1, Y2,..., Yn) and would like to find a longest subsequence common to both. Towards this end, we define c[i, j]...

Extracted text: In the LCS problem, we are given as input two sequences, X = (r1, x2,..., Im) and Y = (y1, Y2,..., Yn) and would like to find a longest subsequence common to both. Towards this end, we define c[i, j] := length of LCS of X; and Y;, where X; := (r1,2, ..r:) and Y; := (y1, 42,..y;) and obtain the following recurrence. c[i, j] = { cli – 1, j – 1] +1 max(c[i, j – 1], c[i – 1,j]) if i = 0 or j = 0 if i, j > 0 and r; = Yj if i, j > 0 and ri # Yj Analyze the (asymptotic) running time: What is the number of the DP entries/subproblems?