C++ Program to Find Fibonacci Numbers using Matrix Exponentiation

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This C++ Program demonstrates the the computation of Fibonacci Numbers using Matrix Exponentiation.

Here is source code of the C++ Program to Find Fibonacci Numbers using Matrix Exponentiation. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. /* 
  2.  * C++ Program to Find Fibonacci Numbers using Matrix Exponentiation
  3.  */
  4. #include <cstring>
  5. #include <iostream>
  6. #include <cstdlib>
  7. #define ll long long
  8. using namespace std;
  9.  
  10. /* 
  11.  * function to multiply two matrices
  12.  */
  13. void multiply(ll F[2][2], ll M[2][2])
  14. {
  15.     ll x =  F[0][0] * M[0][0] + F[0][1] * M[1][0];
  16.     ll y =  F[0][0] * M[0][1] + F[0][1] * M[1][1];
  17.     ll z =  F[1][0] * M[0][0] + F[1][1] * M[1][0];
  18.     ll w =  F[1][0] * M[0][1] + F[1][1] * M[1][1];
  19.     F[0][0] = x;
  20.     F[0][1] = y;
  21.     F[1][0] = z;
  22.     F[1][1] = w;
  23. }
  24.  
  25.  /* 
  26.   * function to calculate power of a matrix
  27.   */
  28. void power(ll F[2][2], int n)
  29. {
  30.     if (n == 0 || n == 1)
  31.         return;
  32.     ll M[2][2] = {{1,1},{1,0}};
  33.     power(F, n / 2);
  34.     multiply(F, F);
  35.     if (n % 2 != 0)
  36.         multiply(F, M);
  37. }
  38.  
  39. /* 
  40.  * function that returns nth Fibonacci number 
  41.  */
  42. ll fibo_matrix(ll n)
  43. {
  44.     ll F[2][2] = {{1,1},{1,0}};
  45.     if (n == 0)
  46.         return 0;
  47.     power(F, n - 1);
  48.     return F[0][0];
  49. }
  50. /* 
  51.  * Main
  52.  */
  53. int main()
  54. {
  55.     int n;
  56.     while (1)
  57.     {
  58.         cout<<"Enter the integer n to find nth fibonnaci no.(0 to exit): ";
  59.         cin>>n;
  60.         if (n == 0)
  61.             break;
  62.         cout<<fibo_matrix(n)<<endl;
  63.     }
  64.     return 0;
  65. }

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$ g++ fibo_matrix.cpp
$ a.out
 
Enter the integer n to find nth fibonnaci no.(0 to exit): 1
1
Enter the integer n to find nth fibonnaci no.(0 to exit): 2
1
Enter the integer n to find nth fibonnaci no.(0 to exit): 3
2
Enter the integer n to find nth fibonnaci no.(0 to exit): 4
3
Enter the integer n to find nth fibonnaci no.(0 to exit): 5
5
Enter the integer n to find nth fibonnaci no.(0 to exit): 6
8
Enter the integer n to find nth fibonnaci no.(0 to exit): 7
13
Enter the integer n to find nth fibonnaci no.(0 to exit): 8
21
Enter the integer n to find nth fibonnaci no.(0 to exit): 9
34
Enter the integer n to find nth fibonnaci no.(0 to exit): 10
55
Enter the integer n to find nth fibonnaci no.(0 to exit): 0
 
------------------
(program exited with code: 1)
Press return to continue

Sanfoundry Global Education & Learning Series – 1000 C++ Programs.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn