branch: externals/org-mathsheet
commit 1cd7959d035fff1dc262f44e7ae0932c7642c57d
Author: Ian Martins <ia...@jhu.edu>
Commit: Ian Martins <ia...@jhu.edu>
Can generate sheet based on templates
---
mathsheet.org | 202 ++++++++++++++++++++++++++++++++++------------------------
1 file changed, 119 insertions(+), 83 deletions(-)
diff --git a/mathsheet.org b/mathsheet.org
index e3a13d57ae..2f08aec235 100644
--- a/mathsheet.org
+++ b/mathsheet.org
@@ -4,7 +4,7 @@ the goal is to generate a math practice sheet.
similar to https://www.math-aids.com
* script
** vars
--#+property: header-args+ :var student="Noble" problem-count=24
+#+property: header-args+ :var student="Noble" problem-count=26
** problem sets
*** add and subtract
@@ -14,9 +14,9 @@ similar to https://www.math-aids.com
|--------+-------+-------------------------------+------------------------|
| 3 | 1 | [1..10] + [0..10] | simple |
| 2 | 2 | [1..10] + [8..15] | second number bigger |
+| 1 | 2 | [a=3..10] - [0..$a] | subtraction |
| 1 | 3 | [1..10] + [1..7] + [1..5] | three numbers |
-| 1 | 4 | [a=3..10] - [0..$a] | subtraction |
-| 1 | 4 | [a=1..10] + [0..10] - [1..$a] | three with subtraction |
+| 1 | 4 | [a=1..10] + [0..10] - [0..$a] | three with subtraction |
| 0 | 0 | [$a*[1..5]] / [a=1..10] | division |
** problem generation
@@ -159,23 +159,6 @@ reduces.
(lambda (x) (funcall x)))))
#+end_src
-#+begin_example
- simple range
- [10..11]
-
- complex range
- [-10..[10..20]]
-
- complex with assignment
- [a=1..[2..8]]
-
- complex with inner assignment
- [-10..[b=10..20]]
-
- simple with variable
- [0..[$a..$b]]
-#+end_example
-
*** replace field
replace a field with the value returned from processing it.
@@ -234,7 +217,7 @@ processes all fields in a problem.
;; find fields, assignments, dependencies
(setq fields (ianxm/scan-problem))
- (message "fields %s" fields)
+ ;;(message "fields %s" fields)
;; order fields according to dependencies
(dolist (node fields)
@@ -247,93 +230,146 @@ test with this
#+begin_src elisp :noweb yes
<<full>>
- (ianxm/fill-problem "[1..12] + [1..10]")
+ ;;(ianxm/fill-problem "[1..12] + [1..10]")
;;(ianxm/fill-problem "[1..[2..[10..100]]]")
;;(ianxm/fill-problem "[$a*[1..10]] / [a=1..10]")
;;(ianxm/fill-problem "[$a]/(3+[a=1..5])")
+ (ianxm/fill-problem "[-10..[10..20]]")
#+end_src
#+RESULTS:
-: 11 + 8
+: -7
+
+other examples
+#+begin_example
+ simple range
+ [10..11]
+
+ complex range
+ [-10..[10..20]]
+
+ complex with assignment
+ [a=1..[2..8]]
+
+ complex with inner assignment
+ [-10..[b=10..20]]
+
+ simple with variable
+ [0..[$a..$b]]
+#+end_example
*** full script
tangles everything needed to convert a template to a problem
#+name: full
#+begin_src elisp :noweb yes :tangle mathsheet.el
-<<var-list>>
+ <<var-list>>
-<<scan-problem>>
+ <<scan-problem>>
-<<reduce-field>>
+ <<reduce-field>>
-<<catalog-fields>>
+ <<catalog-fields>>
-<<replace-field>>
+ <<replace-field>>
-<<dfs-visit>>
+ <<dfs-visit>>
-<<fill-problem>>
-#+end_src
-** generate problem set from template
+ <<fill-problem>>
-#+name: problem-set
-#+begin_src elisp :noweb yes :var template=first-set
- (let (prob ret)
- (dotimes (index problem-count ret)
- (setq prob
- <<one-problem>>)
- (setq ret (push (list (car prob) (cdr prob)) ret ))))
+ <<generate-problems>>
+#+end_src
+** generate problem set from templates
+
+1. load table
+2. determine how many of each
+ 1. sort by weight, low to high
+ 2. for each row
+ 1. calculate number, round with min 1, but 0->0
+ 3. for last entry (highest weight) just take however many are left.
+ 4. produce '(order template nil) for each problem
+ 5. convert to '(order problem answer)
+3. sort
+4. loop through list, replacing entry with '(problem . solution)
+
+#+name: generate-problems
+#+begin_src elisp :results table :var templates=firstset
+ (defun ianxm/generate-problems ()
+ (let (total-weight problems)
+ ;; sort by weight (low to high)
+ (setq templates (sort templates (lambda (a b) (< (car a) (car b))))
+ ;; calc total weight
+ total-weight (float
+ (seq-reduce (lambda (total item) (+ total (car
item)))
+ templates
+ 0)))
+ ;; calculate number for each row
+ (dotimes (ii (length templates) problems)
+ (let* (problem answer
+ (item (nth ii templates))
+ (weight (car item))
+ (needed (cond
+ ((= weight 0)
+ 0)
+ ((= ii (1- (length templates)))
+ (- problem-count (length problems)))
+ (t
+ (max (round (* (/ weight total-weight)
problem-count) ) 1)))))
+ ;; add problems to list
+ (dotimes (jj needed)
+ (let* ((problem (ianxm/fill-problem (nth 2 item)))
+ (answer (calc-eval problem))
+ (order (nth 1 item)))
+ (setq problems (push (list order problem answer) problems))))))
+
+ ;; shuffle
+ (dotimes (ii (- (length problems) 1))
+ (let ((jj (+ (random (- (length problems) ii)) ii)))
+ (psetf (elt problems ii) (elt problems jj)
+ (elt problems jj) (elt problems ii))))
+
+ ;; sort by order
+ (sort problems (lambda (a b) (< (car a) (car b))))
+
+ ;; remove the "order" column and return
+ (mapcar (lambda (x) (seq-drop x 1)) problems)))
#+end_src
+test with this
-#+name: one-problem
-#+begin_src elisp :var template=first-set
- (let (vars probs prob weight order answ)
- ;; parse input
- (dolist (line (split-string template "\n"))
- (pcase (read (concat "(" line ")"))
- (`(var ,name in [,min ,max])
- ;; assign vars
- (push (cons name (+ (random (- max min -1)) min)) vars))
- ((and
- (pred (lambda (x) (eq 'problem (car x))))
- `(problem weight ,weight order ,order ,prob))
- ;; save problems
- (push (cons prob weight)
- probs))))
- ;; choose problem given weights
- (let ((tot (reduce
- (lambda (tot prob) (+ tot (cdr prob)))
- probs
- :initial-value 0))
- indx chosen-prob)
- (setq indx (random tot)
- chosen-prob (reduce
- (lambda (rem prob)
- (cond
- ((not (numberp rem)) rem)
- ((> rem 0) (setq rem (- rem (cdr prob))) (if (>
rem 0) rem (car prob)))
- (t (car prob))))
- probs
- :initial-value indx))
- ;; do replacements
- (dolist (var vars)
- (setq chosen-prob (replace-regexp-in-string
- (symbol-name (car var))
- (number-to-string (cdr var))
- chosen-prob)))
- ;; calculate answer
- (setq answ (calc-eval chosen-prob))
-
- (cons chosen-prob answ)))
-#+end_src
+#+name: problem-set
+#+begin_src elisp :results table :noweb yes :var templates=firstset
+ <<full>>
-#+RESULTS: one-problem
-: (7 + 8 . 15)
+ (ianxm/generate-problems)
+#+end_src
-*** TODO dedup
+#+RESULTS: problem-set
+| 9 + 9 | 18 |
+| 1 + 4 | 5 |
+| 8 + 2 | 10 |
+| 3 + 7 | 10 |
+| 6 + 4 | 10 |
+| 1 + 1 | 2 |
+| 7 + 4 | 11 |
+| 5 + 5 | 10 |
+| 4 + 1 | 5 |
+| 9 + 13 | 22 |
+| 2 + 14 | 16 |
+| 4 + 10 | 14 |
+| 9 + 11 | 20 |
+| 4 + 12 | 16 |
+| 3 + 12 | 15 |
+| 3 + 4 + 3 | 10 |
+| 2 + 6 + 1 | 9 |
+| 7 + 5 + 1 | 13 |
+| 8 - 7 | 1 |
+| 8 + 1 - 3 | 6 |
+| 4 - 0 | 4 |
+| 6 + 3 - 3 | 6 |
+| 3 - 0 | 3 |
+| 8 + 7 - 5 | 10 |
** lay out problems and answers
this generates a problem set.
