Add more solutions

Added solutions for problems from 41 to 5, both in C and python

C/p041.c

@@ -0,0 +1,48 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+int count_digits(int n);
+
+int main(int argc, char **argv)
+{
+   int i, found = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   for(i = 7654321; !found && i > 0; i -= 2)
+   {
+
+      if(is_pandigital(i, count_digits(i)) && is_prime(i))
+      {
+         printf("Project Euler, Problem 41\n");
+         printf("Answer: %d\n", i);
+         found = 1;
+      }
+   }
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int count_digits(int n)
+{
+   int i = 0;
+
+   while(n > 0)
+   {
+      i++;
+      n /= 10;
+   }
+
+   return i;
+}

C/p042.c

@@ -0,0 +1,96 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+
+int is_triang(int n);
+
+int main(int argc, char **argv)
+{
+   int i, j, n, len, value, count = 0;
+   char *line, **words;
+   double elapsed;
+   FILE *fp;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   if((fp = fopen("words.txt", "r")) == NULL)
+   {
+      fprintf(stderr, "Error while opening file %s\n", "words.txt");
+      return 1;
+   }
+
+   fscanf(fp, "%ms", &line);
+
+   fclose(fp);
+
+   n = 1;
+   len = strlen(line);
+
+   for(i = 0; i < len; i++)
+   {
+      if(line[i] == ',')
+      {
+         n++;
+      }
+   }
+
+   if((words = (char **)malloc(n*sizeof(char *))) == NULL)
+   {
+      fprintf(stderr, "Error while allocating memory\n");
+      return 1;
+   }
+
+   words[0] = strtok(line, ",\"");
+
+   for(i = 1; i < n; i++)
+   {
+      words[i] = strtok(NULL, ",\"");
+   }
+
+   for(i = 0; i < n; i++)
+   {
+      value = 0;
+      len = strlen(words[i]);
+
+      for(j = 0; j < len; j++)
+      {
+         value += (words[i][j] - 'A' + 1);
+      }
+
+      if(is_triang(value))
+      {
+         count++;
+      }
+   }
+
+   free(line);
+   free(words);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec-start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 42\n");
+   printf("Answer: %d\n", count);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int is_triang(int n)
+{
+   int i, j;
+
+   for(i = 1, j = 1; j <= n; i++, j += i)
+   {
+      if(n == j)
+      {
+         return 1;
+      }
+   }
+
+   return 0;
+}

C/p043.c

@@ -0,0 +1,118 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+
+void permute(int *v, int i, int n);
+void swap(int *a, int *b);
+int has_property(int *v);
+
+long int sum = 0;
+
+int main(int argc, char **argv)
+{
+   int n[10] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   permute(n, 0, 9);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 43\n");
+   printf("Answer: %ld\n", sum);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+void permute(int *v, int i, int n)
+{
+   int j;
+
+   if(i == n)
+   {
+      if(has_property(v))
+      {
+         sum += v[0] * 1e9 + v[1] * 1e8 + v[2] * 1e7 + v[3] * 1e6 + v[4] * 1e5 + v[5] * 1e4 + v[6] * 1e3 + v[7] * 1e2 + v[8] * 1e1 + v[9];
+      }
+   }
+   else
+   {
+      for(j = i; j <= n; j++)
+      {
+         swap((v+i), (v+j));
+         permute(v, i+1, n);
+         swap((v+i), (v+j));
+      }
+   }
+}
+
+void swap(int *a, int *b)
+{
+   int tmp;
+
+   tmp = *a;
+   *a = *b;
+   *b = tmp;
+}
+
+int has_property(int *v)
+{
+   long int value;
+
+   value = v[1] * 100 + v[2] * 10 + v[3];
+
+   if(value % 2 != 0)
+   {
+      return 0;
+   }
+
+   value = v[2] * 100 + v[3] * 10 + v[4];
+
+   if(value % 3 != 0)
+   {
+      return 0;
+   }
+
+   value = v[3] * 100 + v[4] * 10 + v[5];
+
+   if(value % 5 != 0)
+   {
+      return 0;
+   }
+
+   value = v[4] * 100 + v[5] * 10 + v[6];
+
+   if(value % 7 != 0)
+   {
+      return 0;
+   }
+
+   value = v[5] * 100 + v[6] * 10 + v[7];
+
+   if(value % 11 != 0)
+   {
+      return 0;
+   }
+
+   value = v[6] * 100 + v[7] * 10 + v[8];
+
+   if(value %13 != 0)
+   {
+      return 0;
+   }
+
+   value = v[7] * 100 + v[8] * 10 + v[9];
+
+   if(value % 17 != 0)
+   {
+      return 0;
+   }
+
+   return 1;
+}

C/p044.c

@@ -0,0 +1,44 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+int main(int argc, char **argv)
+{
+   int n, m, pn, pm, found = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   n = 2;
+
+   while(!found)
+   {
+      pn = n * (3 * n - 1) / 2;
+
+      for(m = 1; m < n; m++)
+      {
+         pm = m * (3 * m - 1) / 2;
+
+         if(is_pentagonal(pn+pm) && is_pentagonal(pn-pm))
+         {
+            found = 1;
+            break;
+         }
+      }
+      n++;
+   }
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 44\n");
+   printf("Answer: %d\n", pn-pm);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}

C/p045.c

@@ -0,0 +1,39 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+int main(int argc, char **argv)
+{
+   int found = 0;
+   long int i, n;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   i = 143;
+
+   while(!found)
+   {
+      i++;
+      n = i * (2 * i - 1);
+      
+      if(is_pentagonal(n))
+      {
+         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 45\n");
+   printf("Answer: %ld\n", n);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}

C/p046.c

@@ -0,0 +1,73 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+#define N 10000
+
+int goldbach(int n);
+
+int *primes;
+
+int main(int argc, char **argv)
+{
+   int i, found = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   primes = sieve(N);
+
+   for(i = 3; !found && i < N; i += 2)
+   {
+      if(!primes[i])
+      {
+         if(!goldbach(i))
+         {
+            found = 1;
+         }
+      }
+   }
+
+   free(primes);
+   
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 46\n");
+   printf("Answer: %d\n", i-2);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int goldbach(int n)
+{
+   int i, j, tmp;
+
+   for(i = 2; i < n; i++)
+   {
+      if(primes[i])
+      {
+         j = 1;
+
+         do
+         {
+            tmp = i + 2 * j * j;
+
+            if(tmp == n)
+            {
+               return 1;
+            }
+
+            j++;
+         }while(tmp < n);
+      }
+   }
+
+   return 0;
+}

C/p047.c

@@ -0,0 +1,77 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+#define N 150000
+
+int count_distinct_factors(int n);
+   
+int *primes;
+
+int main(int argc, char **argv)
+{
+   int i, found = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   primes = sieve(N);
+
+   for(i = 645; !found && i < N - 3; i++)
+   {
+      if(!primes[i] && !primes[i+1] && !primes[i+2] && !primes[i+3])
+      {
+         if(count_distinct_factors(i) == 4 && count_distinct_factors(i+1) == 4 &&
+               count_distinct_factors(i+2) == 4 && count_distinct_factors(i+3) == 4)
+         {
+            found = 1;
+         }
+      }
+   }     
+
+   free(primes);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 47\n");
+   printf("Answer: %d\n", i-1);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int count_distinct_factors(int n)
+{
+   int i, count=0;
+
+   if(n % 2 == 0)
+   {
+      count++;
+
+      do
+      {
+         n /= 2;
+      }while(n % 2 == 0);
+   }
+
+   for(i = 3; n > 1; i += 2)
+   {
+      if(primes[i] && n % i == 0)
+      {
+         count++;
+
+         do
+         {
+            n /= i;
+         }while(n % i == 0);
+      }
+   }
+
+   return count;
+}

C/p048.c

@@ -0,0 +1,40 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+#include <gmp.h>
+
+int main(int argc, char **argv)
+{
+   int i;
+   double elapsed;
+   struct timespec start, end;
+   mpz_t power, sum;
+   char *res;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   mpz_init_set_ui(sum, 0);
+   mpz_init(power);
+
+   for(i = 1; i <= 1000; i++)
+   {
+      mpz_ui_pow_ui(power, i, i);
+      mpz_add(sum, sum, power);
+   }
+
+   res = mpz_get_str(NULL, 10, sum);
+   
+   mpz_clears(power, sum, NULL);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 48\n");
+   printf("Answer: %s\n", res+strlen(res)-10);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}

C/p049.c

@@ -0,0 +1,79 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+#define N 10000
+
+int check_digits(int a, int b);
+
+int *primes;
+
+int main(int argc, char **argv)
+{
+   int i, j, found = 0;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   primes = sieve(N);
+
+   for(i = 1489; i < N && !found; i++)
+   {
+      if(primes[i])
+      {
+         for(j = 1; j < 4255; j++)
+         {
+            if(i + 2 * j < N && primes[i+j] && primes[i+2*j] &&
+                  check_digits(i, i+j) && check_digits(i, i+2*j))
+            {
+               found = 1;
+               break;
+            }
+         }
+      }
+   }
+
+   free(primes);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 49\n");
+   printf("Answer: %d%d%d\n", i-1, i-1+j, i-1+2*j);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}
+
+int check_digits(int a, int b)
+{
+   int i;
+   int digits1[10] = {0}, digits2[10] = {0};
+
+   while(a > 0)
+   {
+      digits1[a%10]++;
+      a /= 10;
+   }
+
+   while(b > 0)
+   {
+      digits2[b%10]++;
+      b /= 10;
+   }
+
+   for(i = 0; i < 10; i++)
+   {
+      if(digits1[i] != digits2[i])
+      {
+         return 0;
+      }
+   }
+
+   return 1;
+}

C/p050.c

@@ -0,0 +1,56 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#include "projecteuler.h"
+
+#define N 1000000
+
+int main(int argc, char **argv)
+{
+   int i, j, max = 0, max_p = 0, sum, count;
+   int *primes;
+   double elapsed;
+   struct timespec start, end;
+
+   clock_gettime(CLOCK_MONOTONIC, &start);
+
+   primes = sieve(N);
+
+   for(i = 2; i < N; i++)
+   {
+      if(primes[i])
+      {
+         count = 1;
+         sum = i;
+
+         for(j = i + 1; j < N && sum < N; j++)
+         {
+            if(primes[j])
+            {
+               sum += j;
+               count++;
+
+               if(sum < N && primes[sum] && count > max)
+               {
+                  max = count;
+                  max_p = sum;
+               }
+            }
+         }
+      }
+   }
+
+   free(primes);
+
+   clock_gettime(CLOCK_MONOTONIC, &end);
+
+   elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
+
+   printf("Project Euler, Problem 50\n");
+   printf("Answer: %d\n", max_p);
+
+   printf("Elapsed time: %.9lf seconds\n", elapsed);
+
+   return 0;
+}