Chapter 8, Problem 14SE

To determine

(a)

To show:

$M\left(j,w\right)=M\left(j-1,w\right)$ if, $w_j>w$

To determine

(b)

To show:

$M\left(j,w\right)=\max \left(M\left(j-1,w\right),w_j+M\left(j-1,w-w_j\right)\right)$ if $w_j\le w$

To determine

(c)

Construct a dynamic programming algorithm for determining the maximum total

weight of items so that this total weight does not exceed W

To determine

(d)

To show:

How we can use the value of $M\left(j,w\right)$ computed by the algorithm in part (c) to find a

subset of items with maximum total weight not exceeding W?