@@ -5,11 +5,21 @@ require 'eliza1' require 'pat_read' require 'pat_match' -Exp = Struct.new(:lhs, :op, :rhs) - Pattern.match_abbrev(:"?x*", %w(?* ?x)) Pattern.match_abbrev(:"?y*", %w(?* ?y)) +def exp_rhs(exp) + exp[2] +end + +def exp_op(exp) + exp[1] +end + +def exp_lhs(exp) + exp[0] +end + class Rule def self.split(obj) case obj @@ -29,13 +39,13 @@ class Rule ["if ?x* then ?y*", "?x ?y"], ["if ?x* , ?y*", "?x ?y"], ["?x* , and ?y*", "?x ?y"], - ["find ?x* and ?y*", ["to_find_1 == ?x", "to_find_2 == ?y"]], - ["find ?x*", "to_find == ?x"], - ["?x* equals ?y*", "?x == ?y"], - ["?x* same as ?y*", "?x == ?y"], - ["?x* = ?y*", "?x == ?y"], - ["?x* is equal to ?y*", "?x == ?y"], - ["?x* is ?y*", "?x == ?y"], + ["find ?x* and ?y*", ["to_find_1 = ?x", "to_find_2 = ?y"]], + ["find ?x*", "to_find = ?x"], + ["?x* equals ?y*", "?x = ?y"], + ["?x* same as ?y*", "?x = ?y"], + ["?x* = ?y*", "?x = ?y"], + ["?x* is equal to ?y*", "?x = ?y"], + ["?x* is ?y*", "?x = ?y"], ["?x* - ?y*", "?x - ?y"], ["?x* minus ?y*", "?x - ?y"], ["difference between ?x* and ?y*","?x - ?y"], @@ -53,9 +63,9 @@ class Rule ["one half ?x*", "?x / ?y"], ["twice ?x*", "2 * ?x"], ["square ?x*", "?x * ?x"], - ["?x* % less than ?y*", ["?y", "*", [["100 - ?x"], "/", "100"]]], - ["?x* % more than ?y*", ["?y", "*", [["100 + ?x"], "/", "100"]]], - ["?x* % ?y*", ["?x / 100", "*", "?y"]] + ["?x* % less than ?y*", ["?y", "*", [["100.0 - ?x"], "/", "100.0"]]], + ["?x* % more than ?y*", ["?y", "*", [["100.0 + ?x"], "/", "100.0"]]], + ["?x* % ?y*", ["?x / 100.0", "*", "?y"]] ].map{ |s| [Pattern.from_string(s[0]), split(s[1])]} end @@ -115,6 +125,129 @@ module Student def translate_pair(first, second) [first, translate_to_expression(second)] end + + def list_repr(l) + case l + when Array + "(#{l.map{ |x| list_repr(x) }.join(" ")})" + else + l.to_s + end + end + + def print_equations(header, equations) + puts header + equations.each do |eq| + print " " + eq.each do |ee| + print " #{list_repr(ee)}" + end + puts + end + end + + def solve_equations(equations) + print_equations("The equations to be solved are: ", equations) + print_equations("The solution is: ", solve_eq(equations, [])) + end + + def unknown?(exp) + (exp.is_a?(String) && !(Integer(exp) rescue nil) && !(Float(exp) rescue nil)) + end + + def no_unknown(exp) + case + when unknown?(exp) + nil + when !exp.is_a?(Array) || exp.empty? + true + when no_unknown(exp_lhs(exp)) + no_unknown(exp_rhs(exp)) + else + nil + end + end + + def solve_arithmetic(eq) + [exp_lhs(eq), "=", eval(list_repr(exp_rhs(eq)))] + end + + def one_unknown(exp) + case + when unknown?(exp) + exp + when !exp.is_a?(Array) || exp.empty? + nil + when no_unknown(exp_lhs(exp)) + one_unknown(exp_rhs(exp)) + when no_unknown(exp_rhs(exp)) + one_unknown(exp_lhs(exp)) + else + nil + end + end + + def exp?(exp) + exp.is_a?(Array) && exp.length == 3 + end + + def in_exp(x, exp) + x == exp || + (exp?(exp) && (in_exp(x, exp_lhs(exp)) || in_exp(x, exp_rhs(exp)))) + end + + def inverse_op(op) + { + '+' => '-', + '-' => '+', + '*' => '/', + '/' => '*', + '=' => '=' + }[op] + end + + def commutative?(op) + %w(+ * =).include?(op) + end + + def isolate(e, x) + case + when exp_lhs(e) == x + e + when in_exp(x, exp_rhs(e)) + isolate([exp_rhs(e), "=", exp_lhs(e)], x) + when in_exp(x, exp_lhs(exp_lhs(e))) + isolate([exp_lhs(exp_lhs(e)), + "=", + [exp_rhs(e), + inverse_op(exp_op(exp_lhs(e))), + exp_rhs(exp_lhs(e))]],x) + when commutative?(exp_op(exp_lhs(e))) + isolate([exp_rhs(exp_lhs(e)), + "=", + [exp_rhs(e), + inverse_op(exp_op(exp_lhs(e))), + exp_lhs(exp_lhs(e))]],x) + else + isolate([exp_rhs(exp_lhs(e)), + "=", + [exp_lhs(exp_lhs(e)), + exp_op(exp_lhs(e)), + exp_rhs(e)]],x) + end + end + + def solve_eq(equations, known) + equations.some? do |equation| + x = one_unknown(equation) + if x + answer = solve_arithmetic(isolate(equation,x)) + recproc = proc{ |x| x.is_a?(Array) ? x.map(&recproc) : (x==exp_lhs(answer) ? exp_rhs(answer) : x) } + solve_eq((equations-[equation]).map(&recproc), [answer] + known) + end + end || + known + end end end @@ -122,5 +255,8 @@ end if __FILE__ == $0 require 'pp' + Student.solve_equations([[["3", "+", "4"], "=", [["5", "-", ["2", "+", "x"]],"*","7"]], + [[["3", "*", "x"], "+", "y"], "=", "12"]]) + Student.solve(%w(If the number of customers Tom gets is twice the square of 20 % of the number of advertisements he runs , and the number of advertisements is 45 , then what is the number of customers Tom gets ?).map{ |w| w.downcase }) end lib/ch07/student1.rb 9e42381a153d0654dec297b1e10e87bf6dba2c09 Ola Bini ola.bini@gmail.com http://github.com/olabini/paipr/commit/7334d50b3b62924bc7c02effd22be0201658945b 7334d50b3b62924bc7c02effd22be0201658945b 2008-10-19T08:22:00-07:00 2008-10-19T08:22:00-07:00 Rest of student program c5d8772aeaae0c760067f24d4bd2ad83c4280e9b Ola Bini ola.bini@gmail.com