## coin-change

### Description

Coin change problem solver with finite number of coins, using a greedy algorithm.

### Author

siiky

### Repository

https://git.sr.ht/~siiky/coin-change

### Requirements

The following eggs are required for using this egg:

The following eggs are required for testing this egg:

### API

*[procedure]*

`(coin-change target denominations) --> (values solution memo)`

`target`- The value that the solution must add up to.
`denominations`- The list of available denominations, and respective counts (i.e., upper closed limit).

Returns two values: the solution (or `#f`), and the memoization table.

Solves the coin change problem, taking into account a given finite limit of coins of each denomination, using a "dumb" greedy algorithm. This doesn't necessarily result in the minimum number of coins for non-canonical sets of denominations, but is in practice not far from it, and is simple to implement. Uses a couple of simple checks to fail early in certain scenarios, and a memoization table, from target to denomination to solution (this works because of the greedy nature). The recursive level will be at most the number of denominations.

Mathematically speaking, given target `T`, denominations `di`, and counts `ci`, it computes the coefficients `si` of the following linear equation, such that `0 <= si <= ci`: `T = (sum (* si di))`

(coin-change 765 '((50 . 123) (10 . 456) (5 . 789))) ;=> ((50 . 15) (10 . 1) (5 . 1)) ; ((5 (5)) (15 (10) (5 . 1)) (765 (50) (10 . 1) (5 . 1)))

This is **NOT** the solutions counting algorithm!

*[procedure]*

`(coin-change/unlimited target denominations) --> (values solution memo)`

`target`- The value that the solution must add up to.
`denominations`- The list of available denominations.

Convenience wrapper around `coin-change` that, given a list of denominations, computes the maximum number of coins of each denomination.

### License

This is free and unencumbered software released into the public domain. Anyone is free to copy, modify, publish, use, compile, sell, or distribute this software, either in source code form or as a compiled binary, for any purpose, commercial or non-commercial, and by any means. In jurisdictions that recognize copyright laws, the author or authors of this software dedicate any and all copyright interest in the software to the public domain. We make this dedication for the benefit of the public at large and to the detriment of our heirs and successors. We intend this dedication to be an overt act of relinquishment in perpetuity of all present and future rights to this software under copyright law. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. For more information, please refer to <http://unlicense.org>

### Version History

#### 1.0.0 (2023/11/18)

- Initial implementation

#### 1.0.1 (2023/11/18)

- Fix tests report formatting

#### 1.0.2 (2023/11/18)

- Add
`coin-change/unlimited`