From 274df27f641a0df9b26ac0537119b149fa0ba7d1 Mon Sep 17 00:00:00 2001 From: Masaya Tojo Date: Thu, 22 Aug 2024 03:34:40 +0900 Subject: Initial commit --- LICENSE | 202 ++++++++++++++++++++++++++++++++++++++++ README.md | 68 ++++++++++++++ integer-partition/accel-asc.scm | 62 ++++++++++++ 3 files changed, 332 insertions(+) create mode 100644 LICENSE create mode 100644 README.md create mode 100644 integer-partition/accel-asc.scm diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..d645695 --- /dev/null +++ b/LICENSE @@ -0,0 +1,202 @@ + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/README.md b/README.md new file mode 100644 index 0000000..c01ed66 --- /dev/null +++ b/README.md @@ -0,0 +1,68 @@ +# AccelAsc for R7RS + +This library provides an implementation of the algorithm called `accel_asc` by Jerome Kelleher, which generates integer partitions in R7RS. +For more details, please refer to [Jerome Keller's website](https://jeromekelleher.net/category/combinatorics.html). + +## Requirements + +- `(scheme generator)` of R7RS-large or `(srfi 158)` + +## Usage + +### Library `(integer-partition accel-asc)` + +#### `(accel-asc n) → ` + +Returns a generator that produces a list of integers representing integer partitions for the given value of integer `n`. + +## Examples + +```scheme +(import (scheme base) + (srfi 158) + (integer-partition accel-asc)) + +(generator-for-each (lambda (lst) (display lst) (newline)) + (accel-asc 8)) +``` + +Output: + +``` +(1 1 1 1 1 1 1 1) +(1 1 1 1 1 1 2) +(1 1 1 1 1 3) +(1 1 1 1 2 2) +(1 1 1 1 4) +(1 1 1 2 3) +(1 1 1 5) +(1 1 2 2 2) +(1 1 2 4) +(1 1 3 3) +(1 1 6) +(1 2 2 3) +(1 2 5) +(1 3 4) +(1 7) +(2 2 2 2) +(2 2 4) +(2 3 3) +(2 6) +(3 5) +(4 4) +(8) +``` + +## License + +This library is released under the Apache License Version 2.0. +See the LICENSE file for more details. + +## References + +- Kelleher, J. (2006). *Encoding partitions as ascending compositions* [Doctoral dissertation, University College Cork]. [https://jeromekelleher.net/downloads/k06.pdf](https://jeromekelleher.net/downloads/k06.pdf) +- Kelleher, J. (2014, May 26). *Generating Integer Partitions*. [https://jeromekelleher.net/generating-integer-partitions.html](https://jeromekelleher.net/generating-integer-partitions.html) + +## Copyright + +Copyright (c) 2024 Masaya Tojo diff --git a/integer-partition/accel-asc.scm b/integer-partition/accel-asc.scm new file mode 100644 index 0000000..6b44e4d --- /dev/null +++ b/integer-partition/accel-asc.scm @@ -0,0 +1,62 @@ +;;; Copyright 2024 Masaya Tojo +;;; +;;; Licensed under the Apache License, Version 2.0 (the "License"); +;;; you may not use this file except in compliance with the License. +;;; You may obtain a copy of the License at +;;; +;;; http://www.apache.org/licenses/LICENSE-2.0 +;;; +;;; Unless required by applicable law or agreed to in writing, software +;;; distributed under the License is distributed on an "AS IS" BASIS, +;;; WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +;;; See the License for the specific language governing permissions and +;;; limitations under the License. + +(define-library (integer-partition accel-asc) + (export accel-asc) + (import (scheme base)) + (cond-expand + ((library (scheme generator)) + (import (only (scheme generator) make-coroutine-generator))) + ((library (srfi 158)) + (import (only (srfi 158) make-coroutine-generator)))) + (begin + (define-syntax while + (syntax-rules () + ((_ condition body body* ...) + (let loop () + (if condition + (begin + body + body* ... + (loop)) + (if #f #f))))))) + (begin + (define (accel-asc n) + (accel-asc* n vector->list)) + + (define (accel-asc* n convert) + (make-coroutine-generator + (lambda (yield) + (let ((a (make-vector (+ n 1) 0)) + (k 1) + (x 0) + (y (- n 1))) + (while (not (= k 0)) + (set! x (+ (vector-ref a (- k 1)) 1)) + (set! k (- k 1)) + (while (<= (* 2 x) y) + (vector-set! a k x) + (set! y (- y x)) + (set! k (+ k 1))) + (let ((l (+ k 1))) + (while (<= x y) + (vector-set! a k x) + (vector-set! a l y) + (yield (convert a 0 (+ k 2))) + (set! x (+ x 1)) + (set! y (- y 1))) + (vector-set! a k (+ x y)) + (set! y (+ x y -1)) + (yield (convert a 0 (+ k 1))))))))) + )) -- cgit v1.2.3