Example $2$:

A typical knapsack problem has the following inputs:

$$ Number of items: N

$$ Capacity of Knapsack: K

$$ Weights of the items: w$0,$ w$1,$ w$2,...,$ wn$-1$

$$ Values of the items: v$0,$ v$1,$ v$2,...,$ vn$-1$

Let$$s assume that the output of an algorithm solving this problem is:

$$ Total value V of the items in the knapsack

$$ Total weight W of the items in the knapsack

$$ An array of size N consisting of $0$s and $1$s corresponding to each item, $0$ if the item is not

picked and $1$ if it is picked.