Fibonacci sequence in Ruby (recursion)

问题:

I'm trying to implement the following function, but it keeps giving me the stack level too deep (SystemStackError) error.

Any ideas what the problem might be ?

def fibonacci( n )
    [ n ] if ( 0..1 ).include? n
    ( fibonacci( n - 1 ) + fibonacci( n - 2 ) ) if n > 1
end

puts fibonacci( 5 )

回答1:

Try this

def fibonacci( n )
  return  n  if ( 0..1 ).include? n
  ( fibonacci( n - 1 ) + fibonacci( n - 2 ) )
end
puts fibonacci( 5 )
# => 5

check this post too Fibonacci One-Liner

and more .. https://web.archive.org/web/20120427224512/http://en.literateprograms.org/Fibonacci_numbers_(Ruby)

You have now been bombarded with many solutions :)

regarding problem in ur solution

you should return n if its 0 or 1

and add last two numbers not last and next

New Modified version

def fibonacci( n )
    return  n  if n <= 1 
    fibonacci( n - 1 ) + fibonacci( n - 2 )
end 
puts fibonacci( 10 )
# => 55

One liner

def fibonacci(n)
   n <= 1 ? n :  fibonacci( n - 1 ) + fibonacci( n - 2 ) 
end
puts fibonacci( 10 )
# => 55

回答2:

Here is something I came up with, I find this more straight forward.

def fib(n)
  n.times.each_with_object([0,1]) { |num, obj| obj << obj[-2] + obj[-1] }
end
fib(10)

回答3:

This is not the way you calculate fibonacci, you are creating huge recursive tree which will fail for relatively small ns. I suggest you do something like this:

def fib_r(a, b, n)
  n == 0 ? a : fib_r(b, a + b, n - 1)
end

def fib(n)
  fib_r(0, 1, n)
end

p (0..100).map{ |n| fib(n) }

回答4:

Linear

module Fib
  def self.compute(index)
    first = 0
    second = 1
    index.times do
      third = first + second
      first = second
      second = third
    end
    first
  end
end

Recursive with caching

module Fib
  @@mem = {}
  def self.compute(index)
    if index <= 1
      return index
    else
      @@mem[index] ||= compute(index-1) + compute(index-2)
    end
  end
end

neither of these solutions will crash your system if you call Fib.compute(256)

回答5:

PHI = 1.6180339887498959
TAU = 0.5004471413430931

def fibonacci(n)
  (PHI**n + TAU).to_i
end

You don't need recursion.

回答6:

This approach is fast and makes use of memoization:

fib = Hash.new {|hash, key| hash[key] = key < 2 ? key : hash[key-1] + hash[key-2] }

fib[123] # => 22698374052006863956975682

In case you're wondering about how this hash initialization works read here:

https://ruby-doc.org/core/Hash.html#method-c-new

回答7:

Recursion's very slow, here's a faster way

a = []; a[0] = 1; a[1] = 1
i = 1
while i < 1000000
    a[i+1] = (a[i] + a[i-1])%1000000007
    i += 1
end

puts a[n]    

It's O(1), however you could use matrix exponentiation, here's one of mine's implementation, but it's in java => http://pastebin.com/DgbekCJM, but matrix exp.'s O(8logn) .Here's a much faster algorithm, called fast doubling. Here's a java implementation of fast doubling.

class FD {

    static int mod = 1000000007;

    static long fastDoubling(int n) {
        if(n <= 2) return 1;
        int k = n/2;
        long a = fastDoubling(k+1);
        long b = fastDoubling(k);
        if(n%2 == 1) return (a*a + b*b)%mod;
        else return (b*(2*a - b))%mod;
}

Yet, using karatsuba multiplication, both matrix exp. and fast doubling becomes much faster, yet fast doubling beats matrix exp. by a constant factor, well i didn't want to be very thorough here. But i recently did a lot of research on fibonacci numbers and i want my research to be of use to anyone willing to learn, ;).

回答8:

This may help you.

def fib_upto(max)
  i1, i2 = 1, 1
  while i1 <= max
    yield i1
    i1, i2 = i2, i1+i2
  end
end

fib_upto(5) {|f| print f, " "}

回答9:

i think this is pretty easy:

def fibo(n) a=0 b=1 for i in 0..n c=a+b print "#{c} " a=b b=c end

end

回答10:

Try this oneliner

def fib (n)
    n == 0 || n == 1 ? n : fib(n-2) + fib(n-1)
end
print fib(16)

Output: 987

回答11:

fastest and smallest in lines solution:

fiby = ->(n, prev, i, count, selfy) {
  i < count ? (selfy.call n + prev, n, i + 1, count, selfy) : (puts n)
}
fiby.call 0, 1, 0, 1000, fiby

functional selfie pattern :)

回答12:

We can perform list fibo series using below algorithm

def fibo(n)
  n <= 2 ? 1 : fibo(n-1) + fibo(n-2)
end

We can generate series like below

p (1..10).map{|x| fibo(x)}

below is the output of this

=> [1, 1, 2, 3, 5, 8, 13, 21, 34, 55] 

回答13:

If you want to write the fastest functonal algorithem for fib, it will not be recursive. This is one of the few times were the functional way to write a solution is slower. Because the stack repeats its self if you use somethingn like

fibonacci( n - 1 ) + fibonacci( n - 2 ) 

eventually n-1 and n-2 will create the same number thus repeats will be made in the calculation. The fastest way to to this is iteratvily

def fib(num)
# first 5 in the sequence 0,1,1,2,3
fib1 = 1 #3
fib2 = 2 #4
i = 5 #start at 5 or 4 depending on wheather you want to include 0 as the first number
while i <= num
    temp = fib2
    fib2 = fib2 + fib1
    fib1 = temp
    i += 1
end
p fib2
end
fib(500)

回答14:

Another approach of calculating fibonacci numbers taking the advantage of memoization:

$FIB_ARRAY = [0,1]
def fib(n)
  return n if $FIB_ARRAY.include? n
  ($FIB_ARRAY[n-1] ||= fib(n-1)) + ($FIB_ARRAY[n-2] ||= fib(n-2))
end

This ensures that each fibonacci number is being calculated only once reducing the number of calls to fib method greatly.

回答15:

a = [1, 1]
while(a.length < max) do a << a.last(2).inject(:+) end

This will populate a with the series. (You will have to consider the case when max < 2)

If only the nth element is required, You could use Hash.new

fib = Hash.new {|hsh, i| hsh[i] = fib[i-2] + fib[i-1]}.update(0 => 0, 1 => 1)

fib[10]
# => 55 

回答16:

Here is a more concise solution that builds a lookup table:

fibonacci = Hash.new do |hash, key|
  if key <= 1
    hash[key] = key
  else
    hash[key] = hash[key - 1] + hash[key - 2]
  end
end

fibonacci[10]
# => 55 
fibonacci
# => {1=>1, 0=>0, 2=>1, 3=>2, 4=>3, 5=>5, 6=>8, 7=>13, 8=>21, 9=>34, 10=>55}

回答17:

Someone asked me something similar today but he wanted to get an array with fibonacci sequence for a given number. For instance,

fibo(5)  => [0, 1, 1, 2, 3, 5]
fibo(8)  => [0, 1, 1, 2, 3, 5, 8]
fibo(13) => [0, 1, 1, 2, 3, 5, 8, 13]
# And so on...

Here's my solution. It's not using recursion tho. Just one more solution if you're looking for something similar :P

def fibo(n)
  seed = [0, 1]
  n.zero? ? [0] : seed.each{|i| i + seed[-1] > n ? seed : seed.push(i + seed[-1])}
end

回答18:

Here is one in Scala:

object Fib {
  def fib(n: Int) {
    var a = 1: Int
    var b = 0: Int
    var i = 0: Int
    var f = 0: Int
    while(i < n) {
      println(s"f(${i+1}) -> $f")
      f = a+b
      a = b
      b = f
      i += 1
    }
  }

  def main(args: Array[String]) {
    fib(10)
  }
}

回答19:

I think this is the best answer, which was a response from another SO post asking a similar question.

The accepted answer from PriteshJ here uses naive fibonacci recursion, which is fine, but becomes extremely slow once you get past the 40th or so element. It's much faster if you cache / memoize the previous values and passing them along as you recursively iterate.

回答20:

It's been a while, but you can write a fairly elegant and simple one line function:

def fib(n)
  n > 1 ? fib(n-1) + fib(n-2) : n
end

回答21:

This is the snippet that I used to solve a programming challenge at URI Online Judge, hope it helps.

def fib(n)
  if n == 1
    puts 0
  else
    fib = [0,1]
    (n-2).times do
      fib << fib[-1] + fib[-2]
    end
    puts fib.join(' ')
  end
end

fib(45)

An it outputs

# => 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269 2178309 3524578 5702887 9227465 14930352 24157817 39088169 63245986 102334155 165580141 267914296 433494437 701408733

回答22:

Joining the Fibonacci train:

Regular:

def fib(num)
  return num if (num < 2) else fib(num-1) + fib(num-2)
end

With caching:

module Fib
  @fibs = [0,1]
  def self.calc(num)
    return num if (num < 2) else @fibs[num] ||= self.calc(num-1) + self.calc(num-2)
  end
end