This is called the 0-1 version of the problem because there are no
fractions.
The thief must take the whole item or leave it behind.

Both the 0-1 Knapsack Problem and the Fractional Knapsack Problem have
optimal substructure.
If we remove item j from the optimal load, the remaining problem must be
optimal for the remaining W - w_{j} pounds for the overall solution to be
optimal.

The greedy solution for the Fractional Knapsack Problem