## bin+lib subset_sum

Solves subset sum problem and returns a set of decomposed integers. It also can match corresponding numbers from two vectors and be used for Account reconciliation.

### 44 releases

 0.22.3 Oct 24, 2023 Jun 8, 2023 May 9, 2022 Mar 31, 2022

#163 in Algorithms

1.5MB
1.5K SLoC

# Subset Sum(dpss)

This is a Rust implementation that calculates subset sum problem using dynamic programming. It solves subset sum problem and returns a set of decomposed integers. It also can match corresponding numbers from two vectors and be used for Account reconciliation.

Any feedback is welcome!

There are four ways to use this program.

And it has two methods.

• `find_subset`
• It finds a subset from an array.
• `Sequence Matcher`
• It finds subset sum relationships with two arrays. Solving multiple subset sub problem.

`dpss` is short for `dynamic programming subset sum`.

Name URL
github https://github.com/europeanplaice/subset_sum
crates.io https://crates.io/crates/subset_sum
docs.rs https://docs.rs/subset_sum/latest/dpss/
pypi https://pypi.org/project/dpss/
Website https://europeanplaice.github.io/subset_sum/

## Usage

### Subset sum

First, you need to prepare a text file containing a set of integers like this

``````1
2
-3
4
5
``````

and save it at any place.

Second, call `subset_sum` with the path of the text file and the target sum.

#### Example

Call `subset_sum.exe num_set.txt 3 3`
The executable's name `subset_sum.exe` would be different from your choice. Change this example along with your environment. The second argument is the target sum. The third argument is the maximum length of the combination.

In this example, the output is
`[[2, 1], [4, -3, 2], [5, -3, 1]]`

### Sequence Matcher

`arr1.txt`

``````1980
2980
3500
4000
1050
``````

`arr2.txt`

``````1950
2900
30
80
3300
200
3980
1050
20
``````

Call `subset_sum.exe arr1.txt arr2.txt 100 100 10 false false`

Synopsis:

``````[executable] [keys text file path] [targets text file path] [max key length] [max target length] [the maximum number of answers] [boolean to use all keys] [boolean to use all targets]
``````
• `max_key_length` is used to restrict the number of values in keys chosen.
• If `max_key_length` is 3, an answer's length is at most 3, such as `[1980 + 2980 + 3500], [1050]`
• `max_target_length` is the same as `max_key_length` for targets.
• `the maximum number of answers` specifies the maximum number of patterns.
• If `use_all_keys` is true, an answer must contain all the elements of the keys.
• If `use_all_targets` is true, an answer must contain all the elements of the targets.
• When both `use_all_keys` and `use_all_targets` are true, the sum of the keys and the targets must be the same.

In this example, the output is

``````pattern 1  => [(Sum(1050) -> keys:[1050] == targets:[1050])],
keys remainder    : 1980, 2980, 3500, 4000
targets remainder : 20, 30, 80, 200, 1950, 2900, 3300, 3980

pattern 2  => [(Sum(1050) -> keys:[1050] == targets:[1050])
(Sum(12460) -> keys:[1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 3  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[30 + 1050 + 1950])],
keys remainder    : 2980, 3500, 4000
targets remainder : 20, 80, 200, 2900, 3300, 3980

pattern 4  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[30 + 1050 + 1950])
(Sum(10480) -> keys:[2980 + 3500 + 4000] == targets:[20 + 80 + 200 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 5  => [(Sum(13510) -> keys:[1050 + 1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1050 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 6  => [(Sum(1980) -> keys:[1980] == targets:[30 + 1950])],
keys remainder    : 1050, 2980, 3500, 4000
targets remainder : 20, 80, 200, 1050, 2900, 3300, 3980

pattern 7  => [(Sum(2980) -> keys:[2980] == targets:[80 + 2900])],
keys remainder    : 1050, 1980, 3500, 4000
targets remainder : 20, 30, 200, 1050, 1950, 3300, 3980

pattern 8  => [(Sum(2980) -> keys:[2980] == targets:[80 + 2900])
(Sum(10530) -> keys:[1050 + 1980 + 3500 + 4000] == targets:[20 + 30 + 200 + 1050 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 9  => [(Sum(3500) -> keys:[3500] == targets:[200 + 3300])],
keys remainder    : 1050, 1980, 2980, 4000
targets remainder : 20, 30, 80, 1050, 1950, 2900, 3980

pattern 10 => [(Sum(3500) -> keys:[3500] == targets:[200 + 3300])
(Sum(10010) -> keys:[1050 + 1980 + 2980 + 4000] == targets:[20 + 30 + 80 + 1050 + 1950 + 2900 + 3980])],
keys remainder    :
targets remainder :
``````

## Use in Python

### installation

``````pip install dpss
``````

### Usage

#### `find_subset`

``````import inspect
import dpss
help(dpss.find_subset)
``````
``````>>> find_subset(arr, value, max_length, /)
>>>     Finds subsets sum of a target value. It can accept negative values.
>>>     # Arguments
>>>     * `arr` - An array.
>>>     * `value` - The value to the sum of the subset comes.
>>>     * `max_length` - The maximum length of combinations of the answer.
``````
``````print(dpss.find_subset([1, -2, 3, 4, 5], 2, 3))
``````
``````>>> [[4, -2], [3, -2, 1]]
``````

#### `sequence_matcher`

``````help(dpss.sequence_matcher)
``````
``````>>> sequence_matcher(keys, targets, max_key_length, max_target_length /)
>>>     Finds the integers from two vectors that sum to the same value.
>>>     This method assumes that the two vectors have Many-to-Many relationships.
>>>     Each integer of the `keys` vector corresponds to the multiple integers of the `targets` vector.
>>>     With this method, we can find some combinations of the integers.
>>>
>>>     To avoid combinatorial explosion, some parameters need to be set.
>>>     `max_key_length` is used to restrict the number of values in keys chosen.
>>>     If `max_key_length` is 3, an answer's length is at most 3, such as `[1980 + 2980 + 3500], [1050]`
>>>     `max_target_length` is the same as `max_key_length` for targets.
>>>     `n_candidates` specifies the maximum number of patterns.
>>>     If `use_all_keys` is true, an answer must contain all the elements of the keys.
>>>     If `use_all_targets` is true, an answer must contain all the elements of the targets.
>>>     When both `use_all_keys` and `use_all_targets` are true, the sum of the keys and the targets must be the same.
>>>
>>>     # Arguments
>>>     * `keys` - An array.
>>>     * `targets` - An array.
>>>     * `max_key_length` - An integer.
>>>     * `max_target_length` - An integer.
>>>     * `n_candidates` - An integer.
>>>     * `use_all_keys` - Boolean.
>>>     * `use_all_targets` - Boolean.
``````
``````a = dpss.sequence_matcher(
[1980, 2980, 3500, 4000, 1050],
[1950, 2900, 30, 80, 3300, 200, 3980, 1050, 20], 10, 10, 10, True, True)
print(dpss.sequence_matcher_formatter(a))
``````
``````pattern 1  => [(Sum(1050) -> keys:[1050] == targets:[1050])
(Sum(12460) -> keys:[1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 2  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[20 + 30 + 80 + 2900])
(Sum(10480) -> keys:[2980 + 3500 + 4000] == targets:[200 + 1050 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 3  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[30 + 1050 + 1950])
(Sum(10480) -> keys:[2980 + 3500 + 4000] == targets:[20 + 80 + 200 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 4  => [(Sum(13510) -> keys:[1050 + 1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1050 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 5  => [(Sum(4030) -> keys:[1050 + 2980] == targets:[80 + 1050 + 2900])
(Sum(9480) -> keys:[1980 + 3500 + 4000] == targets:[20 + 30 + 200 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 6  => [(Sum(1980) -> keys:[1980] == targets:[30 + 1950])
(Sum(11530) -> keys:[1050 + 2980 + 3500 + 4000] == targets:[20 + 80 + 200 + 1050 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 7  => [(Sum(2980) -> keys:[2980] == targets:[80 + 2900])
(Sum(10530) -> keys:[1050 + 1980 + 3500 + 4000] == targets:[20 + 30 + 200 + 1050 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 8  => [(Sum(3500) -> keys:[3500] == targets:[200 + 3300])
(Sum(10010) -> keys:[1050 + 1980 + 2980 + 4000] == targets:[20 + 30 + 80 + 1050 + 1950 + 2900 + 3980])],
keys remainder    :
targets remainder :

pattern 9  => [(Sum(4000) -> keys:[4000] == targets:[20 + 30 + 1050 + 2900])
(Sum(9510) -> keys:[1050 + 1980 + 2980 + 3500] == targets:[80 + 200 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 10 => [(Sum(4000) -> keys:[4000] == targets:[20 + 3980])
(Sum(9510) -> keys:[1050 + 1980 + 2980 + 3500] == targets:[30 + 80 + 200 + 1050 + 1950 + 2900 + 3300])],
keys remainder    :
targets remainder :
``````

## Use in Rust

`Cargo.toml`

``````[dependencies]
dpss = { version = "(version)", package = "subset_sum" }
``````

### Find subset

`main.rs`

``````use dpss::dp::find_subset;

fn main() {
let result = find_subset(vec![1, 2, 3, 4, 5], 6, 3);
println!("{:?}", result);
}
``````

Output

``````[[3, 2, 1], [4, 2], [5, 1]]
``````

### Sequence Matcher

`main.rs`

``````use dpss::dp::sequence_matcher;
use dpss::dp::sequence_matcher_formatter;

fn main() {
let result = sequence_matcher(&mut vec![1980, 2980, 3500, 4000, 1050], &mut vec![1950, 2900, 30, 80, 3300, 200, 3980, 1050, 20], 10, 10, 10, true, true);
println!("{}", sequence_matcher_formatter(result));
}
``````

Output

``````pattern 1  => [(Sum(1050) -> keys:[1050] == targets:[1050])
(Sum(12460) -> keys:[1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 2  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[20 + 30 + 80 + 2900])
(Sum(10480) -> keys:[2980 + 3500 + 4000] == targets:[200 + 1050 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 3  => [(Sum(3030) -> keys:[1050 + 1980] == targets:[30 + 1050 + 1950])
(Sum(10480) -> keys:[2980 + 3500 + 4000] == targets:[20 + 80 + 200 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 4  => [(Sum(13510) -> keys:[1050 + 1980 + 2980 + 3500 + 4000] == targets:[20 + 30 + 80 + 200 + 1050 + 1950 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 5  => [(Sum(4030) -> keys:[1050 + 2980] == targets:[80 + 1050 + 2900])
(Sum(9480) -> keys:[1980 + 3500 + 4000] == targets:[20 + 30 + 200 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 6  => [(Sum(1980) -> keys:[1980] == targets:[30 + 1950])
(Sum(11530) -> keys:[1050 + 2980 + 3500 + 4000] == targets:[20 + 80 + 200 + 1050 + 2900 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 7  => [(Sum(2980) -> keys:[2980] == targets:[80 + 2900])
(Sum(10530) -> keys:[1050 + 1980 + 3500 + 4000] == targets:[20 + 30 + 200 + 1050 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 8  => [(Sum(3500) -> keys:[3500] == targets:[200 + 3300])
(Sum(10010) -> keys:[1050 + 1980 + 2980 + 4000] == targets:[20 + 30 + 80 + 1050 + 1950 + 2900 + 3980])],
keys remainder    :
targets remainder :

pattern 9  => [(Sum(4000) -> keys:[4000] == targets:[20 + 30 + 1050 + 2900])
(Sum(9510) -> keys:[1050 + 1980 + 2980 + 3500] == targets:[80 + 200 + 1950 + 3300 + 3980])],
keys remainder    :
targets remainder :

pattern 10 => [(Sum(4000) -> keys:[4000] == targets:[20 + 3980])
(Sum(9510) -> keys:[1050 + 1980 + 2980 + 3500] == targets:[30 + 80 + 200 + 1050 + 1950 + 2900 + 3300])],
keys remainder    :
targets remainder :
``````

~2.6–9.5MB
~82K SLoC