In order not to get rusty I want to refresh my knowledge of pure ruby by solving some algorithms. I can't solve a larger algorithm without solving a smaller one like the example below.
Have the function missing_digit(str) take the str parameter, which will be a simple mathematical formula with three numbers, a single operator (+, -, *, or /) and an equal sign (=) and return the digit that completes the equation. In one of the numbers in the equation, there will be an x character, and your program should determine what digit is missing. For example, if str is "3x + 12 = 46" then your program should output 4.
Examples
Input: "4 - 2 = x"
Output: 2
Input: "1x0 * 12 = 1200"
Output: 0
I think I found the solution for python but I can't find the corresponding Ruby code anywhere.
Python and Ruby are quite similar, though trying to convert this without some basic TDD would have been difficult. Here is the converted to Ruby file from your python example. I would refactor this code but the simple tests here pass, those given in your linked example.
string_math_x.rb
class StringMathX
def self.calculate(str)
exp = str.split()
first_operand = exp[0]
operator = exp[1]
second_operand = exp[2]
resultant = exp[-1]
# If x is present in resultant
if resultant[/x/]
first_operand = first_operand.to_i
second_operand = second_operand.to_i
if operator == '+'
res = first_operand + second_operand
elsif operator == '-'
res = first_operand - second_operand
elsif operator == '*'
res = first_operand * second_operand
else
res = first_operand / second_operand
end
return res
end
# If x in present in operands
# If x in the first operand
if first_operand == 'x'
x = first_operand.to_i
second_operand = second_operand.to_i
if operator == '+'
res = resultant - second_operand
elsif operator == '-'
res = resultant + second_operand
elsif operator == '*'
res = resultant / second_operand
else
res = resultant / second_operand
end
# If x is in the second operand
else
x = second_operand.to_i
first_operand = first_operand.to_i
if operator == '+'
res = resultant-first_operand
elsif operator == '-'
res = first_operand - second_operand
elsif operator == '*'
res = resultant.to_i / first_operand.to_i
else
res = first_operand.to_i / resultant.to_i
end
end
res = res.to_s
k = 0
for i in [*0..x]
if i == x
result = res[k]
break
else
k += 1
end
end
result.to_i
end
end
./test/test.rb
require 'minitest/autorun'
require_relative '../lib/string_math_x'
class StringMathXTest < Minitest::Test
def test_basic_subtration
input = '4 - 2 = x'
assert(StringMathX.calculate(input) == 2, 'outputs 2')
end
def test_whats_up_returns_doc
input = '1x0 * 12 = 1200'
assert(StringMathX.calculate(input) == 0, 'outputs 0')
end
end
To run this you may need to gem install minitest
Then run ruby test/test.rb
def findx(str)
s = str.sub('=', '==')
i = s.index('x')
pre = s[0,i]
post = s[i+1..-1]
('0'..'9').find { |d| eval(pre+d+post) rescue nil }&.to_i
end
findx("4 - 2 = x") #=> 2
findx("1x0 * 12 = 1200") #=> 0
findx("3**x = 81") #=> 4
findx("1/x == 2.0").nil? #=> true
rescue nil is needed in case division by zero is performed. & is the safe harbor operator. It returns nil, disregarding all that follows, if the part before it returns nil.
Related
I have what I believe is a proper implementation of the miller-rabin algorithm using Lua, and I am trying to get a consistent return for prime numbers. It seems my implementation only works half of the time. Although if I try implementing similar code within python, that code works 100% of the time. Could someone point me in the right direction?
--decompose n-1 as (2^s)*d
local function decompose(negOne)
exponent, remainder = 0, negOne
while (remainder%2) == 0 do
exponent = exponent+1
remainder = remainder/2
end
assert((2^exponent)*remainder == negOne and ((remainder%2) == 1), "Error setting up s and d value")
return exponent, remainder
end
local function isNotWitness(n, possibleWitness, exponent, remainder)
witness = (possibleWitness^remainder)%n
if (witness == 1) or (witness == n-1) then
return false
end
for _=0, exponent do
witness = (witness^2)%n
if witness == (n-1) then
return false
end
end
return true
end
--using miller-rabin primality testing
--n the integer to be tested, k the accuracy of the test
local function isProbablyPrime(n, accuracy)
if n <= 3 then
return n == 2 or n == 3
end
if (n%2) == 0 then
return false
end
exponent, remainder = decompose(n-1)
--checks if it is composite
for i=0, accuracy do
math.randomseed(os.time())
witness = math.random(2, n - 2)
if isNotWitness(n, witness, exponent, remainder) then
return false
end
end
--probably prime
return true
end
if isProbablyPrime(31, 30) then
print("prime")
else
print("nope")
end
Python has arbitrary length integers. Lua doesn't.
The problem is in witness = (possibleWitness^remainder)%n.
Lua is unable to calculate exact result of 29^15 % 31 directly.
There is a workaround working for numbers n < sqrt(2^53):
witness = mulmod(possibleWitness, remainder, n)
where
local function mulmod(a, e, m)
local result = 1
while e > 0 do
if e % 2 == 1 then
result = result * a % m
e = e - 1
end
e = e / 2
a = a * a % m
end
return result
end
Trying to allow a concatenated table to be referenced as such:
local group = table.concat(arguments, ",", 1)
where arguments = {"1,1,1"}
Currently, doing group[2] gives me the comma. How do I avoid that while still allowing for two-digit numbers?
(snippet of what I'm trying to use it for)
for i = 1, #group do
target:SetGroup(i, tonumber(group[i]))
end
Maybe you want something like
local i = 1
for v in string.gmatch(s, "(%w+),*") do
group[i] = v
i = i + 1
end
Revised version in response to comment, avoiding the table altogether:
local i = 1
for v in string.gmatch(s, "(%w+),*") do
target:SetGroup(i, tonumber(v))
i = i + 1
end
split function (you have to add it to code)
split = function(str, delim)
if not delim then
delim = " "
end
-- Eliminate bad cases...
if string.find(str, delim) == nil then
return { str }
end
local result = {}
local pat = "(.-)" .. delim .. "()"
local nb = 0
local lastPos
for part, pos in string.gfind(str, pat) do
nb = nb + 1
result[nb] = part
lastPos = pos
end
-- Handle the last field
result[nb + 1] = string.sub(str, lastPos)
return result
end
so
local arguments = {"1,1,1"};
local group = split(arguments[1], ",");
for i = 1, #group do
target:SetGroup(i, tonumber(group[i]))
end
also note that
local arguments = {"1,1,1"};
local group = split(arguments[1], ",");
local group_count = #group;
for i = 1, group_count do
target:SetGroup(i, tonumber(group[i]))
end
is faster code ;)
I'm currently getting familiar with the LPeg parser module. For this I want to match a version string (e.g. 11.4) against a list.
Such a list is a string with a tight syntax that can also contain ranges. Here is an EBNF-like, but in any case quite simple grammar (I write it down because LPeg code below can be a bit difficult to read):
S = R, { ',', R }
R = N, [ '-', N ]
N = digit+, [ '.', digit+ ]
An example string would be 1-9,10.1-11,12. Here is my enormous code:
local L = require "lpeg"
local LV, LP, LC, LR, floor = L.V, L.P, L.C, L.R, math.floor
local version = "7.25"
local function check(a, op, b)
if op and a+0 <= version and version <= b+0 then
return a..op..b -- range
elseif not op and floor(version) == floor(a+0) then
return a -- single item
end
end
local grammar = LP({ "S",
S = LV"R" * (LP"," * LV"R")^0,
R = LV"V" * (LC(LP"-") * LV"V")^-1 / check,
V = LC(LV"D" * (LP"." * LV"D")^-1),
D = (LR("09")^1),
})
function checkversion(str)
return grammar:match(str)
end
So you would call it like checkversion("1-7,8.1,8.3,9") and if the current version is not matched by the list you should get nil.
Now, the trouble is, if all calls to check return nothing (meaning, if the versions do not match), grammar:match(...) will actually have no captures and so return the current position of the string. But this is exactly what I do not want, I want checkversion to return nil or false if there is no match and something that evaluates to true otherwise, actually just like string:match would do.
If I on the other hand return false or nil from check in case of a non-match, I end up with return values from match like nil, "1", nil, nil which is basically impossible to handle.
Any ideas?
I think you can or + it with a constant capture of nil:
grammar = grammar + lpeg.Cc(nil)
This is the pattern I eventually used:
nil_capturing_pattern * lpeg.Cc(nil)
I incorporated it into the grammar in the S rule (Note that this also includes changed grammar to "correctly" determine version order, since in version numbering "4.7" < "4.11" is true, but not in calculus)
local Minor_mag = log10(Minor);
local function check(a, am, op, b, bm)
if op then
local mag = floor(max(log10(am), log10(bm), Minor_mag, 1))+1;
local a, b, v = a*10^mag+am, b*10^mag+bm, Major*10^mag+Minor;
if a <= v and v <= b then
return a..op..b;
end
elseif a == Major and (am == "0" or am == Minor) then
return a.."."..am;
end
end
local R, V, C, Cc = lpeg.R, lpeg.V, lpeg.C, lpeg.Cc
local g = lpeg.P({ "S",
S = V("R") * ("," * V("R"))^0 * Cc(nil),
R = (V("Vm") + V("VM")) * (C("-") * (V("Vm") + V("VM")))^-1 / check,
VM = V("D") * Cc("0"),
Vm = V("D") * "." * V("D"),
D = C(R("09")^1),
});
Multiple returns from match are not impossible to handle, if you catch them in a way that makes handling them easier. I added a function matched that does that, and added the fallback return of false to your check.
do
local L = require "lpeg"
local LV, LP, LC, LR, floor = L.V, L.P, L.C, L.R, math.floor
local version = 6.25
local function check(a, op, b)
if op and a+0 <= version and version <= b+0 then
return a..op..b -- range
elseif not op and floor(version) == floor(a+0) then
return a -- single item
end
return false
end
local grammar = LP({ "S",
S = LV"R" * (LP"," * LV"R")^0,
R = LV"V" * (LC(LP"-") * LV"V")^-1 / check,
V = LC(LV"D" * (LP"." * LV"D")^-1),
D = (LR("09")^1),
})
local function matched(...)
local n = select('#',...)
if n == 0 then return false end
for i=1,n do
if select(i,...) then return true end
end
return false
end
function checkversion(ver,str)
version = ver
return matched(grammar:match(str))
end
end
I enclosed the whole thing in do ... end so that the local version which is used here as an upvalue to check would have constrained scope, and added a parameter to checversion() to make it clearer to run through few test cases. For example:
cases = { 1, 6.25, 7.25, 8, 8.5, 10 }
for _,v in ipairs(cases) do
print(v, checkversion(v, "1-7,8.1,8.3,9"))
end
When run, I get:
C:\Users\Ross\Documents\tmp\SOQuestions>q18793493.lua
1 true
6.25 true
7.25 false
8 true
8.5 true
10 false
C:\Users\Ross\Documents\tmp\SOQuestions>
Note that either nil or false would work equally well in this case. It just feels saner to have collected a list that can be handled as a normal Lua array-like table without concern for the holes.
I'm writing a grep utility in Lua for our mobile devices running Windows CE 6/7, but I've run into some issues implementing case-insensitive match patterns. The obvious solution of converting everything to uppercase (or lower) does not work so simply due to the character classes.
The only other thing I can think of is converting the literals in the pattern itself to uppercase.
Here's what I have so far:
function toUpperPattern(instr)
-- Check first character
if string.find(instr, "^%l") then
instr = string.upper(string.sub(instr, 1, 1)) .. string.sub(instr, 2)
end
-- Check the rest of the pattern
while 1 do
local a, b, str = string.find(instr, "[^%%](%l+)")
if not a then break end
if str then
instr = string.sub(instr, 1, a) .. string.upper(string.sub(instr, a+1, b)) .. string.sub(instr, b + 1)
end
end
return instr
end
I hate to admit how long it took to get even that far, and I can still see right away there are going to be problems with things like escaped percent signs '%%'
I figured this must be a fairly common issue, but I can't seem to find much on the topic.
Are there any easier (or at least complete) ways to do this? I'm starting to go crazy here...
Hoping you Lua gurus out there can enlighten me!
Try something like this:
function case_insensitive_pattern(pattern)
-- find an optional '%' (group 1) followed by any character (group 2)
local p = pattern:gsub("(%%?)(.)", function(percent, letter)
if percent ~= "" or not letter:match("%a") then
-- if the '%' matched, or `letter` is not a letter, return "as is"
return percent .. letter
else
-- else, return a case-insensitive character class of the matched letter
return string.format("[%s%s]", letter:lower(), letter:upper())
end
end)
return p
end
print(case_insensitive_pattern("xyz = %d+ or %% end"))
which prints:
[xX][yY][zZ] = %d+ [oO][rR] %% [eE][nN][dD]
Lua 5.1, LPeg v0.12
do
local p = re.compile([[
pattern <- ( {b} / {escaped} / brackets / other)+
b <- "%b" . .
escaped <- "%" .
brackets <- { "[" ([^]%]+ / escaped)* "]" }
other <- [^[%]+ -> cases
]], {
cases = function(str) return (str:gsub('%a',function(a) return '['..a:lower()..a:upper()..']' end)) end
})
local pb = re.compile([[
pattern <- ( {b} / {escaped} / brackets / other)+
b <- "%b" . .
escaped <- "%" .
brackets <- {: {"["} ({escaped} / bcases)* {"]"} :}
bcases <- [^]%]+ -> bcases
other <- [^[%]+ -> cases
]], {
cases = function(str) return (str:gsub('%a',function(a) return '['..a:lower()..a:upper()..']' end)) end
, bcases = function(str) return (str:gsub('%a',function(a) return a:lower()..a:upper() end)) end
})
function iPattern(pattern,brackets)
('sanity check'):find(pattern)
return table.concat({re.match(pattern, brackets and pb or p)})
end
end
local test = '[ab%c%]d%%]+ o%%r %bnm'
print(iPattern(test)) -- [ab%c%]d%%]+ [oO]%%[rR] %bnm
print(iPattern(test,true)) -- [aAbB%c%]dD%%]+ [oO]%%[rR] %bnm
print(('qwe [%D]% O%r n---m asd'):match(iPattern(test, true))) -- %D]% O%r n---m
Pure Lua version:
It is necessary to analyze all the characters in the string to convert it into a correct pattern because Lua patterns do not have alternations like in regexps (abc|something).
function iPattern(pattern, brackets)
('sanity check'):find(pattern)
local tmp = {}
local i=1
while i <= #pattern do -- 'for' don't let change counter
local char = pattern:sub(i,i) -- current char
if char == '%' then
tmp[#tmp+1] = char -- add to tmp table
i=i+1 -- next char position
char = pattern:sub(i,i)
tmp[#tmp+1] = char
if char == 'b' then -- '%bxy' - add next 2 chars
tmp[#tmp+1] = pattern:sub(i+1,i+2)
i=i+2
end
elseif char=='[' then -- brackets
tmp[#tmp+1] = char
i = i+1
while i <= #pattern do
char = pattern:sub(i,i)
if char == '%' then -- no '%bxy' inside brackets
tmp[#tmp+1] = char
tmp[#tmp+1] = pattern:sub(i+1,i+1)
i = i+1
elseif char:match("%a") then -- letter
tmp[#tmp+1] = not brackets and char or char:lower()..char:upper()
else -- something else
tmp[#tmp+1] = char
end
if char==']' then break end -- close bracket
i = i+1
end
elseif char:match("%a") then -- letter
tmp[#tmp+1] = '['..char:lower()..char:upper()..']'
else
tmp[#tmp+1] = char -- something else
end
i=i+1
end
return table.concat(tmp)
end
local test = '[ab%c%]d%%]+ o%%r %bnm'
print(iPattern(test)) -- [ab%c%]d%%]+ [oO]%%[rR] %bnm
print(iPattern(test,true)) -- [aAbB%c%]dD%%]+ [oO]%%[rR] %bnm
print(('qwe [%D]% O%r n---m asd'):match(iPattern(test, true))) -- %D]% O%r n---m
I am working on a client's site, and I'm writing an amortization schedule calculator in in ruby on rails. For longer loan term calculations, it doesn't seem to be breaking when the balance reaches 0
Here is my code:
def calculate_amortization_results
p = params[:price].to_i
i = params[:rate].to_d
l = params[:term].to_i
j = i/(12*100)
n = l * 12
m = p * (j / (1 - (1 + j) ** (-1 * n)))
#loanAmount = p
#rateAmount = i
#monthlyAmount = m
#amort = []
#interestAmount = 0
while p > 0
line = Hash.new
h = p*j
c = m-h
p = p-c
line["interest"] = h
line["principal"] = c
if p <= 0
line["balance"] = 0
else
line["balance"] = p
end
line["payment"] = h+c
#amort.push(line)
#interestAmount += h
end
end
And here is the view:
- #amort.each_with_index do |a, i|
%li
.m
= i+1
.i
= number_to_currency(a["interest"], :unit => "$")
.p
= number_to_currency(a["principal"], :unit => "$")
.pp
= number_to_currency(a["payment"], :unit => "$")
.b
= number_to_currency(a["balance"], :unit => "$")
What I am seeing is, in place of $0.00 in the final payment balance, it shows "-$-inf", iterates one more loop, then displays $0.00, but shows "-$-inf" for interest. It should loop until p gets to 0, then stop and set the balance as 0, but it isn't. Any idea what I've done wrong?
The calculator is here. It seems to work fine for shorter terms, like 5 years, but longer terms cause the above error.
Edit:
Changing the while loop to n.times do
and then changing the balance view to
= number_to_currency(a["balance"], :unit => "$", :negative_format => "$0.00")
Is a workaround, but i'd like to know why the while loop wouldn't work correctly
in Ruby the default for numerical values is Fixnum ... e.g.:
> 15 / 4
=> 3
You will see weird rounding errors if you try to use Fixnum values and divide them.
To make sure that you use Floats, at least one of the numbers in the calculation needs to be a Float
> 15.0 / 4
=> 3.75
> 15 / 4.0
=> 3.75
You do two comparisons against 0 , which should be OK if you make sure that p is a Float.
As the other answer suggests, you should use "decimal" type in your database to represent currency.
Please try if this will work:
def calculate_amortization_results
p = params[:price].to_f # instead of to_i
i = params[:rate].to_f # <-- what is to_d ? use to_f
l = params[:term].to_i
j = i/(12*100.0) # instead of 100
n = l * 12
m = p * (j / (1 - (1 + j) ** (-1 * n))) # division by zero if i==0 ==> j==0
#loanAmount = p
#rateAmount = i
#monthlyAmount = m
#amort = []
#interestAmount = 0.0 # instead of 0
while p > 0
line = Hash.new
h = p*j
c = m-h
p = p-c
line["interest"] = h
line["principal"] = c
if p <= 0
line["balance"] = 0
else
line["balance"] = p
end
line["payment"] = h+c
#amort.push(line)
#interestAmount += h
end
end
If you see "inf" in your output, you are doing a division by zero somewhere.. better check the logic of your calculation, and guard against division by zero.
according to Wikipedia the formula is:
http://en.wikipedia.org/wiki/Amortization_calculator
to improve rounding errors, it's probably better to re-structure the formula like this:
m = (p * j) / (1 - (1 + j) ** (-1 * n) # these are two divisions! x**-1 == 1/x
which is equal to:
m = (p * j) + (p * j) / ((1 + j) ** n) - 1.0)
which is equal to: (use this one)
q = p * j # this is much larger than 1 , so fewer rounding errors when dividing it by something
m = q + q / ((1 + j) ** n) - 1.0) # only one division
I think it has something to do with the floating point operations precision. It has already been discussed here: Ruby number precision with simple arithmetic and it would be better to use decimal format for financial purposes.
The answer could be computing the numbers in the loop, but with precomputed number of iterations and from the scratch.