Data commit

Task/Fibonacci-sequence/Python/fibonacci-sequence-1.py

@@ -0,0 +1,10 @@
+from math import *
+
+def analytic_fibonacci(n):
+  sqrt_5 = sqrt(5);
+  p = (1 + sqrt_5) / 2;
+  q = 1/p;
+  return int( (p**n + q**n) / sqrt_5 + 0.5 )
+
+for i in range(1,31):
+  print analytic_fibonacci(i),

Task/Fibonacci-sequence/Python/fibonacci-sequence-10.py

@@ -0,0 +1,7 @@
+def fib(n, c={0:1, 1:1}):
+    if n not in c:
+        x = n // 2
+        c[n] = fib(x-1) * fib(n-x-1) + fib(x) * fib(n - x)
+    return c[n]
+
+fib(10000000)  # calculating it takes a few seconds, printing it takes eons

Task/Fibonacci-sequence/Python/fibonacci-sequence-11.py

@@ -0,0 +1,8 @@
+F = {0: 0, 1: 1, 2: 1}
+def fib(n):
+    if n in F:
+        return F[n]
+    f1 = fib(n // 2 + 1)
+    f2 = fib((n - 1) // 2)
+    F[n] = (f1 * f1 + f2 * f2 if n & 1 else f1 * f1 - f2 * f2)
+    return F[n]

Task/Fibonacci-sequence/Python/fibonacci-sequence-12.py

@@ -0,0 +1,10 @@
+def fib():
+    """Yield fib[n+1] + fib[n]"""
+    yield 1  # have to start somewhere
+    lhs, rhs = fib(), fib()
+    yield next(lhs) # move lhs one iteration ahead
+    while True:
+        yield next(lhs)+next(rhs)
+
+f=fib()
+print [next(f) for _ in range(9)]

Task/Fibonacci-sequence/Python/fibonacci-sequence-13.py

@@ -0,0 +1,11 @@
+from itertools import islice
+
+def fib():
+    yield 0
+    yield 1
+    a, b = fib(), fib()
+    next(b)
+    while True:
+        yield next(a)+next(b)
+
+print(tuple(islice(fib(), 10)))

Task/Fibonacci-sequence/Python/fibonacci-sequence-14.py

@@ -0,0 +1,31 @@
+'''Fibonacci accumulation'''
+
+from itertools import accumulate, chain
+from operator import add
+
+
+# fibs :: Integer :: [Integer]
+def fibs(n):
+    '''An accumulation of the first n integers in
+       the Fibonacci series. The accumulator is a
+       pair of the two preceding numbers.
+    '''
+    def go(ab, _):
+        return ab[1], add(*ab)
+
+    return [xy[1] for xy in accumulate(
+        chain(
+            [(0, 1)],
+            range(1, n)
+        ),
+        go
+    )]
+
+
+# MAIN ---
+if __name__ == '__main__':
+    print(
+        'First twenty: ' + repr(
+            fibs(20)
+        )
+    )

Task/Fibonacci-sequence/Python/fibonacci-sequence-15.py

@@ -0,0 +1,21 @@
+'''Nth Fibonacci term (by folding)'''
+
+from functools import reduce
+from operator import add
+
+
+# nthFib :: Integer -> Integer
+def nthFib(n):
+    '''Nth integer in the Fibonacci series.'''
+    def go(ab, _):
+        return ab[1], add(*ab)
+    return reduce(go, range(1, n), (0, 1))[1]
+
+
+# MAIN ---
+if __name__ == '__main__':
+    print(
+        '1000th term: ' + repr(
+            nthFib(1000)
+        )
+    )

Task/Fibonacci-sequence/Python/fibonacci-sequence-16.py

@@ -0,0 +1,3 @@
+def fib(n):
+    from functools import reduce
+    return reduce(lambda x, y: (x[1], x[0] + x[1]), range(n), (0, 1))[0]

Task/Fibonacci-sequence/Python/fibonacci-sequence-17.py

@@ -0,0 +1,6 @@
+fibseq = [1,1,]
+fiblength = 21
+for x in range(1,fiblength-1):
+	xcount = fibseq[x-1] + fibseq[x]
+	fibseq.append(xcount)
+print(xcount)

Task/Fibonacci-sequence/Python/fibonacci-sequence-18.py

@@ -0,0 +1,7 @@
+fi1=fi2=fi3=1 # FIB Russia rextester.com/FEEJ49204
+for da in range(1, 88): # Danilin
+    print("."*(20-len(str(fi3))), end=' ')
+    print(fi3)
+    fi3 = fi2+fi1
+    fi1 = fi2
+    fi2 = fi3

Task/Fibonacci-sequence/Python/fibonacci-sequence-2.py

@@ -0,0 +1,8 @@
+def fibIter(n):
+    if n < 2:
+        return n
+    fibPrev = 1
+    fib = 1
+    for _ in range(2, n):
+        fibPrev, fib = fib, fib + fibPrev
+    return fib

Task/Fibonacci-sequence/Python/fibonacci-sequence-3.py

@@ -0,0 +1,5 @@
+def fib(n,x=[0,1]):
+   for i in range(abs(n)-1): x=[x[1],sum(x)]
+   return x[1]*pow(-1,abs(n)-1) if n<0 else x[1] if n else 0
+
+for i in range(-30,31): print fib(i),

Task/Fibonacci-sequence/Python/fibonacci-sequence-4.py

@@ -0,0 +1,5 @@
+def fibRec(n):
+    if n < 2:
+        return n
+    else:
+        return fibRec(n-1) + fibRec(n-2)

Task/Fibonacci-sequence/Python/fibonacci-sequence-5.py

@@ -0,0 +1,11 @@
+def fibMemo():
+    pad = {0:0, 1:1}
+    def func(n):
+        if n not in pad:
+            pad[n] = func(n-1) + func(n-2)
+        return pad[n]
+    return func
+
+fm = fibMemo()
+for i in range(1,31):
+    print fm(i),

Task/Fibonacci-sequence/Python/fibonacci-sequence-6.py

@@ -0,0 +1,7 @@
+def fibFastRec(n):
+    def fib(prvprv, prv, c):
+        if c < 1:
+            return prvprv
+        else:
+            return fib(prv, prvprv + prv, c - 1)
+    return fib(0, 1, n)

Task/Fibonacci-sequence/Python/fibonacci-sequence-7.py

@@ -0,0 +1,5 @@
+def fibGen(n):
+    a, b = 0, 1
+    while n>0:
+        yield a
+        a, b, n = b, a+b, n-1

Task/Fibonacci-sequence/Python/fibonacci-sequence-8.py

@@ -0,0 +1,3 @@
+>>> [i for i in fibGen(11)]
+
+[0,1,1,2,3,5,8,13,21,34,55]

Task/Fibonacci-sequence/Python/fibonacci-sequence-9.py

@@ -0,0 +1,30 @@
+def prevPowTwo(n):
+    'Gets the power of two that is less than or equal to the given input'
+    if ((n & -n) == n):
+        return n
+    else:
+        n -= 1
+        n |= n >> 1
+        n |= n >> 2
+        n |= n >> 4
+        n |= n >> 8
+        n |= n >> 16
+        n += 1
+        return (n/2)
+
+def crazyFib(n):
+    'Crazy fast fibonacci number calculation'
+    powTwo = prevPowTwo(n)
+
+    q = r = i = 1
+    s = 0
+
+    while(i < powTwo):
+        i *= 2
+        q, r, s = q*q + r*r, r * (q + s), (r*r + s*s)
+
+    while(i < n):
+        i += 1
+        q, r, s = q+r, q, r
+
+    return q