Suppose you have solved a dynamic programming algorithm and come up with the following two variable recurrence:

OPT$(i,j)=$max$\{A(i)+$OPT$(i-1,j-1),$OPT$(i-1,j)\}$

for $i=0,1,$dots,$n$ and $j=0,1,$dots,$m,$ with base cases OPT$(0,j)=0$ and OPT$(i,0)=0.$ In this recurrence, A is some array representing the input to the problem. In all of

the code snippets, A will be a global variable.

Each of the following pseudocode snippets represents an attempt at a polynomial time algorithm for efficiently and correctly computing the value OPT$($n$,$m$).$ For

each pseudocode snippet, answer "true" if it correctly computes OPT$($i$,$j$)$ in polynomial time and "false" if it fails to do so$.$Let OPT $($i$,0)=0$ and OPT $(0,$j$)=0$ for all i$,$j For i $=1,2,,.,$ n:FindOPT$\_$b$($n$,$m$)$:ElseIf $($m $=0)$: Return $0$ Return max$\{$ A$($n$)+$ FindOPT$\_$b$($n$-1,$m$-1),$ FindOPT$\_$b$($n$-1,$m$)\}$

FindOPT$\_$c$()$:For i $=1,2,\backslash$ldots$,$ n:Return OPT$($ n$,$m$)$

FindOPT$\_$d$()$:For j $=1,2,\backslash$ldots$,$ m: Let OPT$($i$,$j$)=\backslash$operatorname$\{$max$\}\{$A$($i$)+$OPT$($i$-1,$j$-1),$ OPT$($i$-1,$j$)\}$

Mainly confused on the last one. Thank you!