Merge pull request #339 from Prakash5bisht/version2

nth fibonacci term using matrix.

Author: amritansh22

fibonacciNumberUsingMatrix.cpp

@@ -0,0 +1,68 @@
+// Program to find the nth fibonacci term
+
+// what is fibonacci series?
+// A series is said to be fibonacci if every nth term is the sum of (n-1)th and (n-2)th term. 0 1 1 2 3 5 8,..... is the fibonacci series
+
+/*
+According to this method, to get the nth fibonacci number, we need to multiply matrix [[1,1],[1,0]] to 
+itself (n-1) times. Then, the [0,0]th element of this resultant matrix will be the required nth fibonacci number
+*/
+
+#include <cstdio>
+#include<stdlib.h>
+#include<iomanip>
+#include<iostream>
+using namespace std;
+
+void multiply(int Fib[2][2], int mat[2][2])
+{
+
+    int topleft = Fib[0][0] * mat[0][0] + Fib[0][1] * mat[1][0];
+    int topRight = Fib[0][0] * mat[0][1] + Fib[0][1] * mat[1][1];
+    int bottomLeft = Fib[1][0] * mat[0][0] + Fib[1][1] * mat[1][0];
+    int bottomRight = Fib[1][0] * mat[0][1] + Fib[1][1] * mat[1][1];
+    
+    Fib[0][0] = topleft;
+    Fib[0][1] = topRight;
+    Fib[1][0] = bottomLeft;
+    Fib[1][1] = bottomRight;
+}
+
+void power(int Fib[2][2], int n)
+{
+
+	if(n == 0 || n == 1)
+       return;
+    int mat[2][2] = {{1, 1}, {1, 0}};
+    
+    power(Fib, n / 2);
+    multiply(Fib, Fib);
+    
+    if (n % 2 != 0)
+        multiply(Fib, mat);
+}
+
+
+int fibonacci(int n)
+{
+    int Fib[2][2] = {{1, 1}, {1, 0}};
+    if (n == 0)
+        return 0;
+    power(Fib, n - 1);
+
+    return Fib[0][0];
+}
+
+
+int main()
+{
+	system("cls");
+    int n;
+    cout<<"Enter the nth fibonaci you want to know:  ";
+    cin>>n;
+    cout << fibonacci(n)<<endl;
+    fflush(stdin);
+    getchar();
+    return 0;
+}
+