I've read somewhere that a variable should be entered into the code if it is reused. But when I write my code for logic transparency, I sometimes create intermediate variables (with names reflecting what they contain) which are used only once.
How incorrect is this concept?
PS:
I want to do it right.
It is important to note that most of the time clarity takes precedence over re-usability or brevity. This is one of the basic principles of clean code. Most modern compilers optimize code anyway so creating new variables need not be a concern at all.
It is perfectly fine to create a new variable if it would add clarity to your code. Make sure to give it a meaningful name. Consider the following function:
public static boolean isLeapYear(final int yyyy) {
if ((yyyy % 4) != 0) {
return false;
}
else if ((yyyy % 400) == 0) {
return true;
}
else if ((yyyy % 100) == 0) {
return false;
}
else {
return true;
}
}
Even though the boolean expressions are used only once, they may confuse the reader of the code. We can rewrite it as follows
public static boolean isLeapYear(int year) {
boolean fourth = year % 4 == 0;
boolean hundredth = year % 100 == 0;
boolean fourHundredth = year % 400 == 0;
return fourth && (!hundredth || fourHundredth);
}
These boolean variables add much more clarity to the code.
This example is from the Clean Code book by Robert C. Martin.
I have a tree of structs which I'd like to test using testing/quick, but constraining it to within my invariants.
This example code works:
var rnd = rand.New(rand.NewSource(time.Now().UnixNano()))
type X struct {
HasChildren bool
Children []*X
}
func TestSomething(t *testing.T) {
x, _ := quick.Value(reflect.TypeOf(X{}), rnd)
_ = x
// test some stuff here
}
But we hold HasChildren = true whenever len(Children) > 0 as an invariant, so it'd be better to ensure that whatever quick.Value() generates respects that (rather than finding "bugs" that don't actually exist).
I figured I could define a Generate function which uses quick.Value() to populate all the variable members:
func (X) Generate(rand *rand.Rand, size int) reflect.Value {
x := X{}
throwaway, _ := quick.Value(reflect.TypeOf([]*X{}), rand)
x.Children = throwaway.Interface().([]*X)
if len(x.Children) > 0 {
x.HasChildren = true
} else {
x.HasChildren = false
}
return reflect.ValueOf(x)
}
But this is panicking:
panic: value method main.X.Generate called using nil *X pointer [recovered]
And when I change Children from []*X to []X, it dies with a stack overflow.
The documentation is very thin on examples, and I'm finding almost nothing in web searches either.
How can this be done?
Looking at the testing/quick source code it seems that you can't create recursive custom generators and at the same time reuse the quick library facilities to generate the array part of the struct, because the size parameter, that is designed to limit the number of recursive calls, cannot be passed back into quick.Value(...)
https://golang.org/src/testing/quick/quick.go (see around line 50)
in your case this lead to an infinite tree that quickly "explodes" with 1..50 leafs at each level (that's the reason for the stack overflow).
If the function quick.sizedValue() had been public we could have used it to accomplish your task, but unfortunately this is not the case.
BTW since HasChildren is an invariant, can't you simply make it a struct method?
type X struct {
Children []*X
}
func (me *X) HasChildren() bool {
return len(me.Children) > 0
}
func main() {
.... generate X ....
if x.HasChildren() {
.....
}
}
How does one write custom accessor methods in Perl6?
If I have this class:
class Wizard {
has Int $.mana is rw;
}
I can do this:
my Wizard $gandalf .= new;
$gandalf.mana = 150;
Let's say I want to add a little check to a setter in my Perl6 class without giving up the $gandalf.mana = 150; notation (in other words, I don't want to write this: $gandalf.setMana(150);). The program should die, if it tries to set a negative mana. How do I do this? The Perl6 documentation just mentions it is possible to write custom accessors, but does not say how.
With more recent versions of Rakudo there is a subset named UInt that restricts it to positive values.
class Wizard {
has UInt $.mana is rw;
}
So that you're not stuck in a lurch if you need to something like this; here is how that is defined:
( you can leave off the my, but I wanted to show you the actual line from the Rakudo source )
my subset UInt of Int where * >= 0;
You could also do this:
class Wizard {
has Int $.mana is rw where * >= 0;
}
I would like to point out that the * >= 0 in the where constraint is just a short way to create a Callable.
You could have any of the following as a where constraint:
... where &subroutine # a subroutine that returns a true value for positive values
... where { $_ >= 0 }
... where -> $a { $a >= 0 }
... where { $^a >= 0 }
... where $_ >= 0 # statements also work ( ｢$_｣ is set to the value it's testing )
( If you wanted it to just not be zero you could also use ... where &prefix:<?> which is probably better spelled as ... where ?* or ... where * !== 0 )
If you feel like being annoying to people using your code you could also do this.
class Wizard {
has UInt $.mana is rw where Bool.pick; # accepts changes randomly
}
If you want to make sure the value "makes sense" when looking at all of the values in the class in aggregate, you will have to go to a lot more work.
( It may require a lot more knowledge of the implementation as well )
class Wizard {
has Int $.mana; # use . instead of ! for better `.perl` representation
# overwrite the method the attribute declaration added
method mana () is rw {
Proxy.new(
FETCH => -> $ { $!mana },
STORE => -> $, Int $new {
die 'invalid mana' unless $new >= 0; # placeholder for a better error
$!mana = $new
}
)
}
}
You can get the same accessor interface that saying $.mana provides by declaring a method is rw. Then you can wrap a proxy around the underlying attribute like so:
#!/usr/bin/env perl6
use v6;
use Test;
plan 2;
class Wizard {
has Int $!mana;
method mana() is rw {
return Proxy.new:
FETCH => sub ($) { return $!mana },
STORE => sub ($, $mana) {
die "It's over 9000!" if ($mana // 0) > 9000;
$!mana = $mana;
}
}
}
my Wizard $gandalf .= new;
$gandalf.mana = 150;
ok $gandalf.mana == 150, 'Updating mana works';
throws_like sub {
$gandalf.mana = 9001;
}, X::AdHoc, 'Too much mana is too much';
Proxy is basically a way to intercept read and write calls to storage and do something other than the default behavior. As their capitalization suggests, FETCH and STORE are called automatically by Perl to resolve expressions like $gandalf.mana = $gandalf.mana + 5.
There's a fuller discussion, including whether you should even attempt this, at PerlMonks. I would recommend against the above -- and public rw attributes in general. It's more a display of what it is possible to express in the language than a useful tool.
Take a look at this C++ code:
#include <iostream>
using namespace std;
class B{
public:
int& f() {
int local_n = 447;
return local_n ;
} // local_n gets out of scope here
};
int main()
{
B b;
int n = b.f(); // and now n = 447
}
I don't understand why n = 447 at the end of main, because I tried to return a reference to a local_n, when it should be NULL;
Returning a reference to a local variable invokes undefined behavior - meaning you might get lucky and it might work... sometimes... or it might format your hard drive or summon nasal demons. In this case, the compiler generated code that managed to copy the old value off the stack before it got overwritten with something else. Oh, and references do not have a corresponding NULL value...
Edit - here's an example where returning a reference is a bad thing. In your example above, since you copy the value out of the reference immediately before calling anything else, it's quite possible (but far from guaranteed) that it might work most of the time. However, if you bind another reference to the returned reference, things won't look so good:
extern void call_some_other_functions();
extern void lucky();
extern void oops();
int& foo()
{ int bar = 0;
return bar;
}
main()
{ int& x = foo();
x = 5;
call_some_other_functions();
if (x == 5)
lucky();
else
oops();
}
I'm writing a function to find triangle numbers and the natural way to write it is recursively:
function triangle (x)
if x == 0 then return 0 end
return x+triangle(x-1)
end
But attempting to calculate the first 100,000 triangle numbers fails with a stack overflow after a while. This is an ideal function to memoize, but I want a solution that will memoize any function I pass to it.
Mathematica has a particularly slick way to do memoization, relying on the fact that hashes and function calls use the same syntax:
triangle[0] = 0;
triangle[x_] := triangle[x] = x + triangle[x-1]
That's it. It works because the rules for pattern-matching function calls are such that it always uses a more specific definition before a more general definition.
Of course, as has been pointed out, this example has a closed-form solution: triangle[x_] := x*(x+1)/2. Fibonacci numbers are the classic example of how adding memoization gives a drastic speedup:
fib[0] = 1;
fib[1] = 1;
fib[n_] := fib[n] = fib[n-1] + fib[n-2]
Although that too has a closed-form equivalent, albeit messier: http://mathworld.wolfram.com/FibonacciNumber.html
I disagree with the person who suggested this was inappropriate for memoization because you could "just use a loop". The point of memoization is that any repeat function calls are O(1) time. That's a lot better than O(n). In fact, you could even concoct a scenario where the memoized implementation has better performance than the closed-form implementation!
You're also asking the wrong question for your original problem ;)
This is a better way for that case:
triangle(n) = n * (n - 1) / 2
Furthermore, supposing the formula didn't have such a neat solution, memoisation would still be a poor approach here. You'd be better off just writing a simple loop in this case. See this answer for a fuller discussion.
I bet something like this should work with variable argument lists in Lua:
local function varg_tostring(...)
local s = select(1, ...)
for n = 2, select('#', ...) do
s = s..","..select(n,...)
end
return s
end
local function memoize(f)
local cache = {}
return function (...)
local al = varg_tostring(...)
if cache[al] then
return cache[al]
else
local y = f(...)
cache[al] = y
return y
end
end
end
You could probably also do something clever with a metatables with __tostring so that the argument list could just be converted with a tostring(). Oh the possibilities.
In C# 3.0 - for recursive functions, you can do something like:
public static class Helpers
{
public static Func<A, R> Memoize<A, R>(this Func<A, Func<A,R>, R> f)
{
var map = new Dictionary<A, R>();
Func<A, R> self = null;
self = (a) =>
{
R value;
if (map.TryGetValue(a, out value))
return value;
value = f(a, self);
map.Add(a, value);
return value;
};
return self;
}
}
Then you can create a memoized Fibonacci function like this:
var memoized_fib = Helpers.Memoize<int, int>((n,fib) => n > 1 ? fib(n - 1) + fib(n - 2) : n);
Console.WriteLine(memoized_fib(40));
In Scala (untested):
def memoize[A, B](f: (A)=>B) = {
var cache = Map[A, B]()
{ x: A =>
if (cache contains x) cache(x) else {
val back = f(x)
cache += (x -> back)
back
}
}
}
Note that this only works for functions of arity 1, but with currying you could make it work. The more subtle problem is that memoize(f) != memoize(f) for any function f. One very sneaky way to fix this would be something like the following:
val correctMem = memoize(memoize _)
I don't think that this will compile, but it does illustrate the idea.
Update: Commenters have pointed out that memoization is a good way to optimize recursion. Admittedly, I hadn't considered this before, since I generally work in a language (C#) where generalized memoization isn't so trivial to build. Take the post below with that grain of salt in mind.
I think Luke likely has the most appropriate solution to this problem, but memoization is not generally the solution to any issue of stack overflow.
Stack overflow usually is caused by recursion going deeper than the platform can handle. Languages sometimes support "tail recursion", which re-uses the context of the current call, rather than creating a new context for the recursive call. But a lot of mainstream languages/platforms don't support this. C# has no inherent support for tail-recursion, for example. The 64-bit version of the .NET JITter can apply it as an optimization at the IL level, which is all but useless if you need to support 32-bit platforms.
If your language doesn't support tail recursion, your best option for avoiding stack overflows is either to convert to an explicit loop (much less elegant, but sometimes necessary), or find a non-iterative algorithm such as Luke provided for this problem.
function memoize (f)
local cache = {}
return function (x)
if cache[x] then
return cache[x]
else
local y = f(x)
cache[x] = y
return y
end
end
end
triangle = memoize(triangle);
Note that to avoid a stack overflow, triangle would still need to be seeded.
Here's something that works without converting the arguments to strings.
The only caveat is that it can't handle a nil argument. But the accepted solution can't distinguish the value nil from the string "nil", so that's probably OK.
local function m(f)
local t = { }
local function mf(x, ...) -- memoized f
assert(x ~= nil, 'nil passed to memoized function')
if select('#', ...) > 0 then
t[x] = t[x] or m(function(...) return f(x, ...) end)
return t[x](...)
else
t[x] = t[x] or f(x)
assert(t[x] ~= nil, 'memoized function returns nil')
return t[x]
end
end
return mf
end
I've been inspired by this question to implement (yet another) flexible memoize function in Lua.
https://github.com/kikito/memoize.lua
Main advantages:
Accepts a variable number of arguments
Doesn't use tostring; instead, it organizes the cache in a tree structure, using the parameters to traverse it.
Works just fine with functions that return multiple values.
Pasting the code here as reference:
local globalCache = {}
local function getFromCache(cache, args)
local node = cache
for i=1, #args do
if not node.children then return {} end
node = node.children[args[i]]
if not node then return {} end
end
return node.results
end
local function insertInCache(cache, args, results)
local arg
local node = cache
for i=1, #args do
arg = args[i]
node.children = node.children or {}
node.children[arg] = node.children[arg] or {}
node = node.children[arg]
end
node.results = results
end
-- public function
local function memoize(f)
globalCache[f] = { results = {} }
return function (...)
local results = getFromCache( globalCache[f], {...} )
if #results == 0 then
results = { f(...) }
insertInCache(globalCache[f], {...}, results)
end
return unpack(results)
end
end
return memoize
Here is a generic C# 3.0 implementation, if it could help :
public static class Memoization
{
public static Func<T, TResult> Memoize<T, TResult>(this Func<T, TResult> function)
{
var cache = new Dictionary<T, TResult>();
var nullCache = default(TResult);
var isNullCacheSet = false;
return parameter =>
{
TResult value;
if (parameter == null && isNullCacheSet)
{
return nullCache;
}
if (parameter == null)
{
nullCache = function(parameter);
isNullCacheSet = true;
return nullCache;
}
if (cache.TryGetValue(parameter, out value))
{
return value;
}
value = function(parameter);
cache.Add(parameter, value);
return value;
};
}
}
(Quoted from a french blog article)
In the vein of posting memoization in different languages, i'd like to respond to #onebyone.livejournal.com with a non-language-changing C++ example.
First, a memoizer for single arg functions:
template <class Result, class Arg, class ResultStore = std::map<Arg, Result> >
class memoizer1{
public:
template <class F>
const Result& operator()(F f, const Arg& a){
typename ResultStore::const_iterator it = memo_.find(a);
if(it == memo_.end()) {
it = memo_.insert(make_pair(a, f(a))).first;
}
return it->second;
}
private:
ResultStore memo_;
};
Just create an instance of the memoizer, feed it your function and argument. Just make sure not to share the same memo between two different functions (but you can share it between different implementations of the same function).
Next, a driver functon, and an implementation. only the driver function need be public
int fib(int); // driver
int fib_(int); // implementation
Implemented:
int fib_(int n){
++total_ops;
if(n == 0 || n == 1)
return 1;
else
return fib(n-1) + fib(n-2);
}
And the driver, to memoize
int fib(int n) {
static memoizer1<int,int> memo;
return memo(fib_, n);
}
Permalink showing output on codepad.org. Number of calls is measured to verify correctness. (insert unit test here...)
This only memoizes one input functions. Generalizing for multiple args or varying arguments left as an exercise for the reader.
In Perl generic memoization is easy to get. The Memoize module is part of the perl core and is highly reliable, flexible, and easy-to-use.
The example from it's manpage:
# This is the documentation for Memoize 1.01
use Memoize;
memoize('slow_function');
slow_function(arguments); # Is faster than it was before
You can add, remove, and customize memoization of functions at run time! You can provide callbacks for custom memento computation.
Memoize.pm even has facilities for making the memento cache persistent, so it does not need to be re-filled on each invocation of your program!
Here's the documentation: http://perldoc.perl.org/5.8.8/Memoize.html
Extending the idea, it's also possible to memoize functions with two input parameters:
function memoize2 (f)
local cache = {}
return function (x, y)
if cache[x..','..y] then
return cache[x..','..y]
else
local z = f(x,y)
cache[x..','..y] = z
return z
end
end
end
Notice that parameter order matters in the caching algorithm, so if parameter order doesn't matter in the functions to be memoized the odds of getting a cache hit would be increased by sorting the parameters before checking the cache.
But it's important to note that some functions can't be profitably memoized. I wrote memoize2 to see if the recursive Euclidean algorithm for finding the greatest common divisor could be sped up.
function gcd (a, b)
if b == 0 then return a end
return gcd(b, a%b)
end
As it turns out, gcd doesn't respond well to memoization. The calculation it does is far less expensive than the caching algorithm. Ever for large numbers, it terminates fairly quickly. After a while, the cache grows very large. This algorithm is probably as fast as it can be.
Recursion isn't necessary. The nth triangle number is n(n-1)/2, so...
public int triangle(final int n){
return n * (n - 1) / 2;
}
Please don't recurse this. Either use the x*(x+1)/2 formula or simply iterate the values and memoize as you go.
int[] memo = new int[n+1];
int sum = 0;
for(int i = 0; i <= n; ++i)
{
sum+=i;
memo[i] = sum;
}
return memo[n];