Add more solutions

Added solutions for problem 206 in C and python, and for problem
357 in C.

C/p206.c

@@ -0,0 +1,60 @@
+/* Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
+ * where each “_” is a single digit.*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+
+int main(int argc, char **argv)
+{
+   int i, found = 0;
+   /* Since the square of n has 19 digits, n must be at least 10^9.*/
+   long int n = 1e9, p;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   while(!found)
+   {
+      /* If the square on n ends with 10, n must be divisible by 10.*/
+      n += 10;
+      p = n * n;
+
+      /* A square divisible by 10 is also divisible by 100.*/
+      if(p % 100 != 0)
+      {
+         continue;
+      }
+
+      /* Check if the digits of the square correspond to the given pattern.*/
+      i = 9;
+      p /= 100;
+
+      while(p > 0)
+      {
+         if(p % 10 != i)
+         {
+            break;
+         }
+         p /= 100;
+         i--;
+      }
+
+      if(p == 0)
+      {
+         found = 1;
+      }
+   }
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 206\n");
+   printf("Answer: %d\n", n);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}

C/p357.c

@@ -0,0 +1,78 @@
+/* Consider the divisors of 30: 1,2,3,5,6,10,15,30.
+ * It can be seen that for every divisor d of 30, d+30/d is prime.
+ *
+ * Find the sum of all positive integers n not exceeding 100 000 000
+ * such that for every divisor d of n, d+n/d is prime.*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+#define N 100000000
+
+int check_d_nd_prime(int n);
+
+int *primes;
+
+int main(int argc, char **argv)
+{
+   int i;
+   long int sum = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   if((primes = sieve(N+2)) == NULL)
+   {
+      fprintf(stderr, "Error! Sieve function returned NULL\n");
+      return 1;
+   }
+
+   for(i = 2; i <= N; i += 2)
+   {
+      /* Every number is divisible by 1, so 1+n/1=n+1 must be prime.*/
+      if(primes[i+1] && check_d_nd_prime(i))
+      {
+         sum += i;
+      }
+   }
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 357\n");
+   printf("Answer: %ld\n", sum);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int check_d_nd_prime(int n)
+{
+   int i, limit;
+
+   /* To get all divisors, it's sufficient to loop up to the square root
+    * of the number, because for every divisor d smaller than sqrt(n) n/d
+    * is also a divisor larger than sqrt(n).*/
+   limit = floor(sqrt(n));
+
+   for(i = 2; i <= limit; i++)
+   {
+      if(n % i == 0)
+      {
+         /* We only need to check the property for i and not n/i. 
+          * If d=n/i, we would have to check if n/i+n/(n/i)=n/i+i is prime.*/
+         if(!primes[i+n/i])
+         {
+            return 0;
+         }
+      }
+   }
+
+   return 1;
+}

Python/p206.py

@@ -0,0 +1,46 @@
+#!/usr/bin/python3
+
+# Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
+# where each “_” is a single digit.
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+#   Since the square of n has 19 digits, n must be at least 10^9.
+    n = 1000000000
+    found = 0
+
+    while not found:
+#       If the square on n ends with 10, n must be divisible by 10.
+        n = n + 10
+        p = n * n
+
+#       A square divisible by 10 is also divisible by 100.
+        if p % 100 != 0:
+            continue
+
+#       Check if the digits of the square correspond to the given pattern.
+        i = 9
+        p = p // 100
+
+        while p > 0:
+            if p % 10 != i:
+                break
+            p = p // 100
+            i = i - 1
+
+        if p == 0:
+            found = 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 206')
+    print('Answer: {}'.format(n))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()
+