$(10\%)$ The following procedure is a bottom$-$up method for matrix chain order. This procedure assumes that

matrix $A_i$ has dimensions $p_{i-1}{p}_i$ for $i=1,2,$dots,$n.$ Its input is a sequence $p=($:$p_0,p_1,$dots,$p_n$:$),$ where

p$.$ length $=n+1.$ Let $m[i,j]$ be the minimum number of scalar multiplications needed to compute the

matrix $A_i{A}_{i+1}cdots{A}_j.$ The procedure uses an auxiliary table $m[1..n,1..n]$ for storing the $m[i,j]$ costs

and another auxiliary table $s[1..n-1,2..n]$ that records which index of $k$ achieved the optimal cost in

computing $m[i,j].$ Please fill in the empty statements.

$n=p.$ length $-1$

let $m[1..n,1..n]$ and $s[1..n-1,2..n]$ be new tables

For $i=1$ to $n$

$m[i,i]=0$

For $l=2$ to $\frac{n}{\frac{?}{?}}l$ is the chain length

For $i=1$ to $n-l+1$

$j=$

$(a)(3\%)$

$m[i,j]=$

For $k=itoj-1$

$q=$

$(b)(4\%)$

$Ifq$