Fibonacci using matrix chain exponentiation

Languages/C++/fibmat.cpp

@@ -0,0 +1,70 @@
+// Fibonacci Series using Optimized Method 
+#include <bits/stdc++.h> 
+#define int long long
+#define mod 1000000007
+using namespace std; 
+
+void multiply(int F[2][2], int M[2][2]); 
+void power(int F[2][2], int n); 
+
+// Function that returns nth Fibonacci number 
+int fib(int n) 
+{ 
+    int F[2][2] = {{1, 1}, {1, 0}}; 
+    if (n == 0) 
+        return 0; 
+    power(F, n ); 
+
+    return F[0][0]%mod; 
+} 
+
+void power(int F[2][2], int n) 
+{ 
+    if(n == 0 || n == 1) 
+    return; 
+    int M[2][2] = {{1, 1}, {1, 0}}; 
+
+    power(F, n / 2); 
+    multiply(F, F); 
+
+    if (n % 2 != 0) 
+        multiply(F, M); 
+} 
+
+void multiply(int F[2][2], int M[2][2]) 
+{ 
+    int x = (F[0][0] * M[0][0] + F[0][1] * M[1][0])% mod; 
+    int y = (F[0][0] * M[0][1] + F[0][1] * M[1][1])% mod; 
+    int z = (F[1][0] * M[0][0] + F[1][1] * M[1][0])% mod; 
+    int w = (F[1][0] * M[0][1] + F[1][1] * M[1][1])% mod; 
+
+    F[0][0] = x; 
+    F[0][1] = y; 
+    F[1][0] = z; 
+    F[1][1] = w; 
+} 
+
+// Driver code 
+int32_t main() 
+{ 
+
+
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int t;
+    cin>>t;
+    while(t--)
+    {
+        int dim,n;
+        cin>>n;
+        cout << fib(n)<<endl; 
+    } 
+
+
+
+
+    return 0; 
+} 
+
+// This code is contributed by Parag Varshney