Merge branch 'project_euler/problem_25' into project_euler/master2

* project_euler/problem_25:
  solution using arbitrary number of digits took 11ms

project_euler/Problem 25/sol1.c

@@ -0,0 +1,109 @@
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <time.h>
+
+#define MAX_DIGITS 1000
+
+/**
+ * Function to add arbitraty length decimal integers stored in an array.
+ * a + b = c = new b
+ **/
+unsigned int add_numbers(uint8_t *a, uint8_t *b, uint8_t *c, int N)
+{
+    uint8_t carry = 0;
+    unsigned int i;
+
+    for (i = 0; i < N; i++)
+    {
+        // printf("\t%d + %d + %d ", a[i], b[i], carry);
+        c[i] = carry + a[i] + b[i];
+        if (c[i] > 9) /* check for carry */
+        {
+            carry = 1;
+            c[i] -= 10;
+        }
+        else
+            carry = 0;
+        // printf("= %d, %d\n", carry, c[i]);
+    }
+
+    while (carry != 0)
+    {
+        // printf("\t\t...adding new digit\n");
+        // printf("\t0 + %d + %d ", b[i], carry);
+        c[i] = carry + c[i];
+        if (c[i] > 9)
+        {
+            carry = 1;
+            c[i] -= 10;
+        }
+        else
+            carry = 0;
+        // printf("= %d, %d\n", carry, c[i]);
+        i++;
+    }
+    return i;
+}
+
+int print_number(uint8_t *number, int N)
+{
+    int start_pos = N - 1;
+
+    /* skip all initial zeros */
+    while (number[start_pos] == 0)
+        start_pos--;
+
+    for (int i = start_pos; i >= 0; i--)
+        putchar(number[i] + 0x30);
+
+    return 0;
+}
+
+unsigned int get_digits(uint8_t *number)
+{
+    unsigned int digits = MAX_DIGITS;
+    while (number[digits] == 0)
+        digits--;
+    return digits;
+}
+
+int main(int argc, char *argv[])
+{
+    uint8_t fn[MAX_DIGITS + 1]; /* array to store digits of a large number */
+    uint8_t fn1[MAX_DIGITS + 1];
+    uint8_t sum[MAX_DIGITS + 1];
+
+    memset(fn, 0, MAX_DIGITS);
+    memset(fn1, 0, MAX_DIGITS);
+    memset(sum, 0, MAX_DIGITS);
+
+    fn[0] = 1;
+    fn1[1] = 1;
+
+    unsigned int index = 1, digit_count = 1;
+
+    clock_t start_time = clock();
+    do
+    {
+        digit_count = add_numbers(fn, fn1, sum, digit_count);
+        // digit_count = get_digits(sum);
+
+        // printf("%5u (%u) (%u) ", index, digit_count, get_digits(sum));
+        // print_number(sum, digit_count);
+        // putchar('\n');
+
+        if (digit_count == MAX_DIGITS)
+            break;
+        memcpy(fn, fn1, MAX_DIGITS);
+        memcpy(fn1, sum, MAX_DIGITS);
+        index++;
+    } while (digit_count < MAX_DIGITS);
+    clock_t end_time = clock();
+
+    printf("Time taken: %.4g ms\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC);
+    printf("The nth term for %d digits: %u \n", MAX_DIGITS, index--);
+    print_number(sum, digit_count);
+
+    return 0;
+}