CAN YOU HELP ME WITH THESE $2$ PROBLEMS:

Exercises

$10\mathrm{.}1-1$

Consider an $mn$ matrix in row$-$major order, where both $m$ and $n$ are powers of $2$

and rows and columns are indexed from $0.$ We can represent a row index $i$ in binary

by the $lgm$ bits $($:$i_{lgm-1},i_{lgm-2},$dots,$i_0$:$)$ and a column index $j$ in binary by the $lgn$

bits $($:$j_{lgn-1},j_{lgn-2},$dots,$j_0$:$).$ Suppose that this matrix is a $22$ block matrix, where

each block has $\frac{m}{2}$ rows and $\frac{n}{2}$ columns, and it is to be represented by a single

array with $0-$origin indexing. Show how to construct the binary representation of

the $(lgm+lgn)-$bit index into the single array from the binary representations of

i and $j.$

$10\mathrm{.}1-2$

Using Figure $10\mathrm{.}2$ as a model, illustrate the result of each operation in the sequence

Push$(S,4),$Push$(S,1),$Push$(S,3),$Pop$(S),$Push$(S,8),$ and Pop$(S)$ on an

initially empty stack $S$ stored in array $S[1$:$6]$