# mknapsack¶

Solving knapsack problems with Python using algorithms by Martello and Toth:

Single 0-1 knapsack problem: MT1, MT2, MT1R (real numbers)

Bounded knapsack problem: MTB2

Unbounded knapsack problem: MTU1, MTU2

Multiple 0-1 knapsack problem: MTM, MTHM

Change-making problem: MTC2

Bounded change-making problem: MTCB

Generalized assignment problem: MTG, MTHG

Bin packing problem: MTP

Subset sum problem: MTSL

Documentation is available here.

## Installation¶

`pip install mknapsack`

## Example usage¶

### Single 0-1 Knapsack Problem¶

```
from mknapsack import solve_single_knapsack
# Given ten items with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]
# ...and a knapsack with the following capacity:
capacity = 190
# Assign items into the knapsack while maximizing profits
res = solve_single_knapsack(profits, weights, capacity)
```

If your inputs are real numbers, you may set parameter `method='mt1r'`

.

### Bounded Knapsack Problem¶

```
from mknapsack import solve_bounded_knapsack
# Given ten item types with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]
# ...and the number of items available for each item type:
n_items = [1, 2, 3, 2, 2, 1, 2, 2, 1, 4]
# ...and a knapsack with the following capacity:
capacity = 190
# Assign items into the knapsack while maximizing profits
res = solve_bounded_knapsack(profits, weights, capacity, n_items)
```

### Unbounded Knapsack Problem¶

```
from mknapsack import solve_unbounded_knapsack
# Given ten item types with the following profits and weights:
profits = [16, 72, 35, 89, 36, 94, 75, 74, 100, 80]
weights = [30, 18, 9, 23, 20, 59, 61, 70, 75, 76]
# ...and a knapsack with the following capacity:
capacity = 190
# Assign items repeatedly into the knapsack while maximizing profits
res = solve_unbounded_knapsack(profits, weights, capacity, n_items)
```

### Multiple 0-1 Knapsack Problem¶

```
from mknapsack import solve_multiple_knapsack
# Given ten items with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]
# ...and two knapsacks with the following capacities:
capacities = [90, 100]
# Assign items into the knapsacks while maximizing profits
res = solve_multiple_knapsack(profits, weights, capacities)
```

### Change-Making Problem¶

```
from mknapsack import solve_change_making
# Given ten item types with the following weights:
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]
# ...and a knapsack with the following capacity:
capacity = 190
# Fill the knapsack while minimizing the number of items
res = solve_change_making(weights, capacity)
```

### Bounded Change-Making Problem¶

```
from mknapsack import solve_bounded_change_making
# Given ten item types with the following weights:
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]
# ...and the number of items available for each item type:
n_items = [1, 2, 3, 2, 1, 1, 1, 2, 1, 2]
# ...and a knapsack with the following capacity:
capacity = 190
# Fill the knapsack while minimizing the number of items
res = solve_bounded_change_making(weights, n_items, capacity)
```

### Generalized Assignment Problem¶

```
from mknapsack import solve_generalized_assignment
# Given seven item types with the following knapsack dependent profits:
profits = [[6, 9, 4, 2, 10, 3, 6],
[4, 8, 9, 1, 7, 5, 4]]
# ...and the following knapsack dependent weights:
weights = [[4, 1, 2, 1, 4, 3, 8],
[9, 9, 8, 1, 3, 8, 7]]
# ...and two knapsacks with the following capacities:
capacities = [11, 22]
# Assign items into the knapsacks while maximizing profits
res = solve_generalized_assignment(profits, weights, capacities)
```

### Bin Packing Problem¶

```
from mknapsack import solve_bin_packing
# Given six items with the following weights:
weights = [4, 1, 8, 1, 4, 2]
# ...and bins with the following capacity:
capacity = 10
# Assign items into bins while minimizing the number of bins required
res = solve_bin_packing(weights, capacity)
```

### Subset Sum Problem¶

```
from mknapsack import solve_subset_sum
# Given six items with the following weights:
weights = [4, 1, 8, 1, 4, 2]
# ...and a knapsack with the following capacity:
capacity = 10
# Choose items to fill the knapsack to the fullest
res = solve_subset_sum(weights, capacity)
```

## References¶

Knapsack problems: algorithms and computer implementations by S. Martello and P. Toth, 1990

Original Fortran77 source code by S. Martello and P. Toth

Jesse Myrberg (jesse.myrberg@gmail.com)