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Author: Mukesh751

Nth-Fibonacci-Number-Generator/Nth_Fibonnaci_Generator.py

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+'''
+This algorithm calculates the Nth Fibonacci Nummber in log(N) time complexity
+The key idea behind this algorimth is to use matrix exponentiation technique (matrix multiplication + binary exponentiation)
+This algorithm uses the fact that the Fibonacci Numbers can be converted to a 2D matrix of 2x2 size, [[1, 1][1, 0]], and the Fibonacci 
+Number which is to be calculated with the help of matrix multiplication will be nothing but cell, (0,0) of (Matrix)^n ,i.e, our resultant 
+matrix. 
+'''
+def fib(n):
+ 
+    F = [[1, 1],
+         [1, 0]]
+    if (n == 0):
+        return 0
+    power(F, n - 1)
+ 
+    return F[0][0]
+ 
+'''
+Matrix multiplication is calculated using Strassen Algorithm which calculates the product of Two Matrices in o(N^3) time complexity.
+Since, the size of matrix here is fixed, i.e, 2x2, so, the Time Complexity will be O(1). 
+'''
+def multiply(F, M):
+ 
+    x = (F[0][0] * M[0][0] +
+         F[0][1] * M[1][0])
+    y = (F[0][0] * M[0][1] +
+         F[0][1] * M[1][1])
+    z = (F[1][0] * M[0][0] +
+         F[1][1] * M[1][0])
+    w = (F[1][0] * M[0][1] +
+         F[1][1] * M[1][1])
+ 
+    F[0][0] = x
+    F[0][1] = y
+    F[1][0] = z
+    F[1][1] = w
+ 
+'''
+Power function uses Binary Exponentiation Technique to calculate the value of x^n in O(logN) time instead of O(N) time.
+'''
+def power(F, n):
+ 
+    if(n == 0 or n == 1):
+        return
+    M = [[1, 1],
+         [1, 0]]
+ 
+    power(F, n // 2)
+    multiply(F, F)
+ 
+    if (n % 2 != 0):
+        multiply(F, M)
+ 
+ 
+# Driver Code
+if __name__ == "__main__":
+    n = 5  
+    print(fib(n))
+
+'''
+I hope you have a fun time reading this algorithm. 
+Problems for practice: 
+https://practice.geeksforgeeks.org/problems/generalised-fibonacci-numbers1820/1
+https://practice.geeksforgeeks.org/problems/nth-fibonacci-number1335/1
+https://practice.geeksforgeeks.org/problems/37f36b318a7d99c81f17f0a54fc46b5ce06bbe8c/0
+'''

Nth-Fibonacci-Number-Generator/README.md

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+# Nth Fibonacci Number Generator
+
+This script calculates Nth Fibonacci Nunber.
+Version of Python used : Python 3.10.7
+
+## Setup instructions
+
+Click on the script and run the program.
+
+## Output
+
+![Screenshot (146)](https://github.com/Mukesh751/Amazing-Python-Scripts/assets/91366697/72b62e84-62de-4b6f-a37a-21844b685157)
+
+
+## Author(s)
+
+Mukesh751
+