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92 lines
2.0 KiB
C++
92 lines
2.0 KiB
C++
/*
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* C++ Program to Find Fibonacci Numbers using Matrix Exponentiation
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*/
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#include <cstring>
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#include <iostream>
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#include <cstdlib>
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#define ll long long
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using namespace std;
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/*
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* function to multiply two matrices
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*/
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void multiply(ll F[2][2], ll M[2][2])
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{
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ll x = F[0][0] * M[0][0] + F[0][1] * M[1][0];
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ll y = F[0][0] * M[0][1] + F[0][1] * M[1][1];
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ll z = F[1][0] * M[0][0] + F[1][1] * M[1][0];
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ll w = F[1][0] * M[0][1] + F[1][1] * M[1][1];
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F[0][0] = x;
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F[0][1] = y;
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F[1][0] = z;
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F[1][1] = w;
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}
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/*
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* function to calculate power of a matrix
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*/
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void power(ll F[2][2], int n)
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{
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if (n == 0 || n == 1)
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return;
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ll M[2][2] = {{1,1},{1,0}};
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power(F, n / 2);
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multiply(F, F);
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if (n % 2 != 0)
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multiply(F, M);
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}
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/*
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* function that returns nth Fibonacci number
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*/
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ll fibo_matrix(ll n)
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{
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ll F[2][2] = {{1,1},{1,0}};
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if (n == 0)
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return 0;
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power(F, n - 1);
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return F[0][0];
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}
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/*
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* Main
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*/
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int main()
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{
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int n;
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while (1)
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{
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cout<<"Enter the integer n to find nth fibonnaci no.(0 to exit): ";
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cin>>n;
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if (n == 0)
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break;
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cout<<fibo_matrix(n)<<endl;
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}
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return 0;
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}
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/*
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Enter the integer n to find nth fibonnaci no.(0 to exit): 1
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1
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Enter the integer n to find nth fibonnaci no.(0 to exit): 2
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1
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Enter the integer n to find nth fibonnaci no.(0 to exit): 3
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2
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Enter the integer n to find nth fibonnaci no.(0 to exit): 4
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3
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Enter the integer n to find nth fibonnaci no.(0 to exit): 5
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5
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Enter the integer n to find nth fibonnaci no.(0 to exit): 6
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8
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Enter the integer n to find nth fibonnaci no.(0 to exit): 7
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13
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Enter the integer n to find nth fibonnaci no.(0 to exit): 8
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21
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Enter the integer n to find nth fibonnaci no.(0 to exit): 9
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34
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Enter the integer n to find nth fibonnaci no.(0 to exit): 10
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55
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Enter the integer n to find nth fibonnaci no.(0 to exit): 0
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------------------
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(program exited with code: 1)
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Press return to continue
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