Merge branch 'sorting/shell_sort' into project_euler/master2

* sorting/shell_sort:
  add stats for algo 2 and use milliseconds
  create a duplicate array
  added new shell-sort algorithm
  updating DIRECTORY.md
  +a much faster fibonacci computation algorithm
  print hashes in HEX
  add commandline option to FibonacciDP.c
  print hashes in HEX
  add commandline option to FibonacciDP.c

DIRECTORY.md

@@ -185,6 +185,7 @@
   * [Factorial Trailing Zeroes](https://github.com/TheAlgorithms/C/blob/master/misc/factorial_trailing_zeroes.c)
   * [Fibonacci](https://github.com/TheAlgorithms/C/blob/master/misc/Fibonacci.c)
   * [Fibonacci Dp](https://github.com/TheAlgorithms/C/blob/master/misc/Fibonacci_DP.c)
+  * [Fibonacci Fast](https://github.com/TheAlgorithms/C/blob/master/misc/Fibonacci_fast.c)
   * [Gcd](https://github.com/TheAlgorithms/C/blob/master/misc/GCD.c)
   * [Is Armstrong](https://github.com/TheAlgorithms/C/blob/master/misc/is_Armstrong.c)
   * [Large Factorials](https://github.com/TheAlgorithms/C/blob/master/misc/Large_Factorials.c)

hash/test_program.c

@@ -8,15 +8,13 @@
 
 int main(void)
 {
-    char s[] = "name";
+    char s[] = "hello";
 
     /* actual tests */
-    printf("sdbm: %s --> %lld\n", s, sdbm(s));
-    printf("djb2: %s --> %lld\n", s, djb2(s));
-    printf("xor8: %s --> %i\n", s, xor8(s)); /* 8 bit */
-    printf("adler_32: %s --> %i\n", s, adler_32(s)); /* 32 bit */
-    printf("crc32: %s --> %i\n", s, crc32(s));
-    
+    printf("sdbm: %s --> %llX\n", s, sdbm(s));
+    printf("djb2: %s --> %llX\n", s, djb2(s));
+    printf("xor8: %s --> %X\n", s, xor8(s)); /* 8 bit */
+    printf("adler_32: %s --> %X\n", s, adler_32(s)); /* 32 bit */
 
     return 0;
-}
+}

misc/Fibonacci_DP.c

@@ -31,12 +31,17 @@ int fib(int n)
   return f[n]; 
 } 
   
-int main(){
+int main(int argc, char *argv[])
+{
 	int number;
 
 	//Asks for the number/position of term in Fibonnacci sequence
-	printf("Enter the value of n(n starts from 0 ): ");
-	scanf("%d", &number);
+    if (argc == 2)
+        number = atoi(argv[1]);
+    else {
+        printf("Enter the value of n(n starts from 0 ): ");
+        scanf("%d", &number);
+    }
 	
 	printf("The nth term is : %d \n", fib(number));
 	

misc/Fibonacci_fast.c

@@ -0,0 +1,76 @@
+/**
+    @file Fibonacci_fast.c
+    @author: Krishna Vedala
+    @date 2 October, 2019
+    @brief Compute \f$m^{mth}\f$ Fibonacci number using the formulae:
+    \f{eqnarray*}{
+        F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\ 
+        F_{2n}   &=& F_n\left(2F_{n-1} + F_n\right)
+   \f}
+*/
+
+#include<stdio.h> 
+#include<stdlib.h>
+#include<locale.h>
+
+/**
+    Returns the \f$n^{th}\f$ and \f$n+1^{th}\f$ Fibonacci number.
+    The return variables are C & D respectively.
+ */
+void fib(unsigned long n, unsigned long *C, unsigned long *D) 
+{ 
+    //Out of Range checking 
+    if(n < 0){
+        printf("\nNo Such term !\n");
+        exit(0);
+    }
+    
+    unsigned long a, b, c, d;
+    
+    if (n == 0)
+    {
+        C[0] = 0;
+        if(D)
+            D[0] = 1;
+        return;
+    }
+
+    fib(n >> 1, &c, &d); /**< Compute F(n/2) */
+
+    a = c * ((d << 1) - c);
+    b = c * c + d * d;
+    if (n % 2 == 0)   /**< If n is even */
+    {
+        C[0] = a;
+        if(D)
+            D[0] = b;
+        return;
+    }
+    
+    /**< If n is odd */
+    C[0] = b;
+    if(D)
+        D[0] = a + b;
+    return;
+} 
+  
+int main(int argc, char *argv[])
+{
+	unsigned long number, result;
+    
+    setlocale(LC_NUMERIC, "");  // format the printf output
+
+	//Asks for the number/position of term in Fibonnacci sequence
+    if (argc == 2)
+        number = atoi(argv[1]);
+    else {
+        printf("Enter the value of n(n starts from 0 ): ");
+        scanf("%lu", &number);
+    }
+    
+    fib(number, &result, NULL);
+    
+	printf("The nth term is : %'lu \n", result);
+	
+	return 0;
+}

sorting/shell_Sort.c

@@ -2,7 +2,7 @@
 #include <stdlib.h>
 #include <time.h>
 
-#define ELEMENT_NR 20
+#define ELEMENT_NR 20000
 #define ARRAY_LEN(x) (sizeof(x) / sizeof((x)[0]))
 const char *notation = "Shell Sort Big O Notation:\
 						\n--> Best Case: O(n log(n)) \
@@ -37,10 +37,38 @@ void shellSort(int array[], int len)
                 swap(&array[j], &array[j + gap]);
 }
 
+/**
+ * Optimized algorithm - takes half the time as other
+ **/
+void shell_sort2(int array[], int LEN)
+{
+    const int gaps[] = {701, 301, 132, 57, 23, 10, 4, 1};
+    const int gap_len = 8;
+    int i, j, g;
+
+    for (g = 0; g < gap_len; g++)
+    {
+        int gap = gaps[g];
+        for (i = gap; i < LEN; i++)
+        {
+            int tmp = array[i];
+
+            for (j = i; j >= gap && (array[j - gap] - tmp) > 0; j -= gap)
+                array[j] = array[j - gap];
+            array[j] = tmp;
+        }
+    }
+#ifdef DEBUG
+    for (i = 0; i < LEN; i++)
+        printf("%s\t", data[i]);
+#endif
+}
+
 int main(int argc, char *argv[])
 {
     int i;
     int array[ELEMENT_NR];
+    int array2[ELEMENT_NR];
     int range = 500;
     int size;
     clock_t start, end;
@@ -48,7 +76,10 @@ int main(int argc, char *argv[])
 
     srand(time(NULL));
     for (i = 0; i < ELEMENT_NR; i++)
+    {
         array[i] = rand() % range + 1;
+        array2[i] = array[i];
+    }
 
     size = ARRAY_LEN(array);
 
@@ -62,7 +93,19 @@ int main(int argc, char *argv[])
     show_data(array, size);
 
     printf("%s\n", notation);
-    printf("Time spent sorting: %f\n", time_spent);
+    printf("Time spent sorting: %.4g ms\n", time_spent * 1e3);
+
+    printf("--------------------------\n");
+    start = clock();
+    shell_sort2(array2, size);
+    end = clock();
+    time_spent = (double)(end - start) / CLOCKS_PER_SEC;
+
+    printf("Data Sorted\n");
+    show_data(array2, size);
+
+    printf("%s\n", notation);
+    printf("Time spent sorting: %.4g ms\n", time_spent * 1e3);
 
     return 0;
 }