mirror of https://github.com/TheAlgorithms/C
86 lines
1.8 KiB
C
86 lines
1.8 KiB
C
/**
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@file
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@author [Krishna Vedala](https://github.com/kvedala)
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@date 2 October, 2019
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@brief Compute \f$m^{mth}\f$ Fibonacci number using the formulae:
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\f{eqnarray*}{
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F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\
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F_{2n} &=& F_n\left(2F_{n-1} + F_n\right)
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\f}
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*/
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#include <locale.h>
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#include <stdio.h>
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#include <stdlib.h>
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/**
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* Get the \f$n^{th}\f$ and \f$n+1^{th}\f$ Fibonacci number using recursive
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* half-interval decimation.
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* \param [in] n index of Fibonacci number to get
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* \param [out] C left half interval value - end result here. Cannot be NULL
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* \param [out] D right half interval can be discarded at end and can be NULL
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*/
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void fib(unsigned long n, unsigned long *C, unsigned long *D)
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{
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// Out of Range checking
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// commented out since `n` is unsigned integer
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// if (n < 0)
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// {
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// printf("\nNo Such term !\n");
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// exit(0);
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// }
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unsigned long a, b, c, d;
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if (n == 0)
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{
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C[0] = 0;
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if (D) /* if D is not NULL */
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D[0] = 1;
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return;
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}
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fib(n >> 1, &c, &d); /* Compute F(n/2) */
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a = c * ((d << 1) - c);
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b = c * c + d * d;
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if (n % 2 == 0) /* If n is even */
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{
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C[0] = a;
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if (D)
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D[0] = b;
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return;
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}
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/**< If n is odd */
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C[0] = b;
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if (D) /* if D is not NULL */
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D[0] = a + b;
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return;
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}
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/**
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* main function
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*/
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int main(int argc, char *argv[])
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{
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unsigned long number, result;
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setlocale(LC_NUMERIC, ""); // format the printf output
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// Asks for the number/position of term in Fibonnacci sequence
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if (argc == 2)
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number = atoi(argv[1]);
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else
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{
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printf("Enter the value of n(n starts from 0 ): ");
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scanf("%lu", &number);
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}
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fib(number, &result, NULL);
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printf("The nth term is : %'lu \n", result);
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return 0;
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}
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