Merge pull request #599 from CO18326/patch-1

fastfibonacci.py

Author: probot-auto-merge[bot]

Python/fastfibonacci.py

@@ -1,11 +1,45 @@
-def fastfibonacci(i): 
-    if i<0: 
-        print("Incorrect input, enter number >= 0") 
-    elif i==0: 
-        return 0 
-    elif i==1: 
-        return 1
-    else: 
-        return fastfibonacci(i-1)+fastfibonacci(i-2) 
-  
-print(fastfibonacci(2)) 
+# the method relies on the fact that if we multiply matrix [[1,1],[1,0]] with it self n times we get nth fibonacci number at (0,0)
+#place
+# Fibonacci Series : 0,1,1,2............
+
+# function that returns nth with 0 based indexing 
+
+def fastfibonacci(n): 
+	
+	f = [[1, 1], 
+		[1, 0]] 
+	if (n == 0): 
+		return 0
+	power(f, n - 1) 
+		
+	return f[0][0] 
+	
+def multiply(f, g): 
+	
+	a = (f[0][0] * g[0][0] + f[0][1] * g[1][0]) 
+	s = (f[0][0] * g[0][1] + f[0][1] * g[1][1]) 
+	d = (f[1][0] * g[0][0] + f[1][1] * g[1][0]) 
+	h = (f[1][0] * g[0][1] + f[1][1] * g[1][1]) 
+	
+	f[0][0] = a 
+	f[0][1] = s 
+	f[1][0] = d 
+	f[1][1] = h 
+		
+ 
+def power(f, n): 
+
+	if( n == 0 or n == 1): 
+		return; 
+	g = [[1, 1], 
+		[1, 0]]; 
+		
+	power(f, n // 2) 
+	multiply(f, f) 
+		
+	if (n % 2 != 0): 
+		multiply(f, g) 
+	
+
+ 
+