Merge branch 'project_euler/problem_16' into project_euler/master

# Conflicts:
#	DIRECTORY.md

project_euler/Problem 16/sol1.c

@@ -0,0 +1,55 @@
+#include <stdio.h>
+#include <math.h>
+#include <stdlib.h>
+#include <stdint.h>
+
+int main(int argc, char **argv)
+{
+    const double tmp = log(10) / log(2); /* required to get number of digits */
+    unsigned long MAX_NUM_DIGITS;
+    uint8_t *digits = NULL;              /* array to store individual digits. index 0 = units place */
+    int N = 1000, sum = 0;
+
+    if (argc == 2)
+        N = atoi(argv[1]);
+
+    MAX_NUM_DIGITS = (N + tmp) / tmp;
+    
+    digits = calloc(MAX_NUM_DIGITS, sizeof(uint8_t));
+    digits[0] = 1;
+
+    if (!digits)
+    {
+        perror("Unable to allocate memory!");
+        return -1;
+    }
+
+    for (int i = 0; i < N; i++)
+    {
+        int carry = 0;
+        for (int j = 0; j < MAX_NUM_DIGITS; j++)
+        {
+            digits[j] = (digits[j] << 1) + carry;   /* digit * 2 + carry */
+            // printf("\t value: %d\t", digits[j]);
+            if (digits[j] > 9)
+            {
+                carry = 1;
+                digits[j] -= 10;
+            } else
+                carry = 0;
+            // printf("carry: %d\t value: %d\n", carry, digits[j]);
+            
+            /* accumulate sum for last multiplication */
+            if (i == N - 1)
+                sum += digits[j];
+        }
+    }
+
+    printf("2^%d = ", N);
+    for(int i = MAX_NUM_DIGITS - 1; i >= 0; i--)
+        putchar(digits[i] + 0x30);
+    printf("\n\t Sum: %d\t Num. digits: %lu\n", sum, MAX_NUM_DIGITS);
+
+    free(digits);
+    return 0;
+}