- The thief wants to steal n items
- The ith item weighs
*w*_{i}and has value*v*_{i} - Take the most valuable load, limit of W pounds
- 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
does not work here.

**Example:**

Item | Value | Weight | Val/Weight |

1 | 60 | 10 | 6 |

2 | 100 | 20 | 5 |

3 | 120 | 30 | 4 |

W = 50

The greedy solution would select 1, leaving 40 pounds.

At this point if we pick items 1 and 2 the total value is 160.

If we pick items 1 and 3 the total value is 180.

The optimal solution is to pick items 2 and 3. The total value of this solution is 220.