Add id0068 (c and python)

.editorconfig

@@ -1,3 +1,5 @@
+# Licensed under the MIT License.
+
 [*]
 cpp_indent_braces=false
 cpp_indent_multi_line_relative_to=innermost_parenthesis

.gitattributes

@@ -1 +1,3 @@
+# Licensed under the MIT License.
+
 *.sh text eol=lf

.gitignore

@@ -1,3 +1,5 @@
+# Licensed under the MIT License.
+
 a.out
 *.exe
 *.o

Makefile

@@ -1,3 +1,5 @@
+# Licensed under the MIT License.
+
 CC = gcc
 CFLAGS = -O3 -pedantic -std=c99 -Wall -Wextra
 
@@ -263,5 +265,8 @@ id0065.o: src/id0065.c euler.o lp_string.o
 id0066.o: src/id0066.c euler.o math.o
 	$(CC) $(CFLAGS) $< -o $@ euler.o math.o -lgmp -lm
 
+id0068.o: src/id0068.c euler.o list.o math.o permutation_iterator.o 
+	$(CC) $(CFLAGS) $< -o $@ euler.o list.o math.o permutation_iterator.o -lm
+
 clean:
 	rm -rf *.o

README.md

@@ -1,3 +1,5 @@
+<!-- Licensed under the MIT License. -->
+
 # Project Euler
 
 Efficient Project Euler solutions in C language
@@ -17,7 +19,8 @@ languages. The most difficult problems are implemented in 10 languages.
 
 | Difficulty | Language                   |
 | :--------: | -------------------------- |
-|            | [C](tools/test.sh)         |
+| (Trivial)  | [Shell](tools/test.sh)     |
+|   \> 0%    | [C](tools/test.sh)         |
 |   \> 10%   | [Python](tools/test.py.sh) |
 |   \> 20%   | [C\#](tools/test.cs.ps1)   |
 
@@ -113,4 +116,4 @@ which is licensed under the GNU Lesser General Public License v3.0 (`LGPL-3.0`).
 | 63  |   [Powerful Digit Counts](src/id0063.c)   |         Number theory          |  Count  |                                                                                                                                        |
 | 64  |  [Odd Period Square Roots](src/id0064.c)  |            Algebra             |  Count  | [Continued fraction expansion](https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion)           |
 | 65  |     [Convergents of e](src/id0065.c)      | Arbitrary-precision arithmetic |  Count  |                                                                                                                                        |
-| 66  |   [Diophantine Equation](src/id0066.c)    | Arbitrary-precision arithmetic | Maximum | [Pell\'s equation](https://mathworld.wolfram.com/PellEquation.html) |
+| 66  |   [Diophantine Equation](src/id0066.c)    | Arbitrary-precision arithmetic | Maximum | [Pell\'s equation](https://mathworld.wolfram.com/PellEquation.html)                                                                    |

lib/euler.h

@@ -64,7 +64,17 @@ long math_gcd(long a, long b);
  * @param a the exponent.
  * @return The number of digits in the expanded expression `b^a`.
 */
-int math_length(int b, int a);
+long long math_length(long long b, long long a);
+
+/**
+ * Concatenates two integers.
+ * 
+ * @param left  the left digits.
+ * @param right the right digits.
+ * @return An integer formed by writing out the digits of `left` immediately
+ *         followed by the digits of `right`.
+*/
+long long math_concat(long long left, long long right);
 
 /**
  * Reverses the digits of a given value.

lib/factor_iterator.c

@@ -22,7 +22,7 @@ void factor_next(FactorIterator iterator)
     {
         iterator->current = *iterator->iterator.current;
         iterator->remainder = 0;
-        iterator->currentCount = 1;
+        iterator->exponent = 1;
 
         return;
     }
@@ -34,12 +34,12 @@ void factor_next(FactorIterator iterator)
 
     iterator->current = *iterator->iterator.current;
     iterator->remainder /= iterator->current;
-    iterator->currentCount = 1;
+    iterator->exponent = 1;
 
     while (iterator->remainder % iterator->current == 0)
     {
         iterator->remainder /= iterator->current;
-        iterator->currentCount++;
+        iterator->exponent++;
     }
 }
 
@@ -50,7 +50,7 @@ int factor_divisor_count(long long n, Sieve primes)
 
     for (factor_begin(&it, n, primes); !factor_end(&it); factor_next(&it))
     {
-        result *= it.currentCount + 1;
+        result *= it.exponent + 1;
     }
 
     return result;
@@ -63,7 +63,7 @@ int factor_divisor_sum(long long n, Sieve primes)
 
     for (factor_begin(&it, n, primes); !factor_end(&it); factor_next(&it))
     {
-        result *= (pow(it.current, it.currentCount + 1) - 1) / (it.current - 1);
+        result *= (pow(it.current, it.exponent + 1) - 1) / (it.current - 1);
     }
 
     return result;

lib/factor_iterator.h

@@ -8,7 +8,7 @@ struct FactorIterator
     struct SieveIterator iterator;
     long long current;
     long long remainder;
-    int currentCount;
+    int exponent;
 };
 
 /** Iterates over the prime factors of a positive integer. */

lib/math.c

@@ -16,7 +16,12 @@ bool math_is_polygonal(int s, long x, long* approxN)
     return n == localApproxN;
 }
 
-int math_length(int b, int a)
+long long math_length(long long b, long long a)
 {
-    return 1 + (int)(a * log10(b));
+    return 1 + a * log10(b);
+}
+
+long long math_concat(long long left, long long right)
+{
+    return left * pow(10, math_length(right, 1)) + right;
 }

src/id0018.c

@@ -9,13 +9,13 @@
 #define BUFFER_SIZE 512
 #define MAX_HEIGHT 100
 
-int main(int count, LPString args[])
+int main(int argc, LPString argv[])
 {
     int id;
 
-    if (count == 2)
+    if (argc == 2)
     {
-        id = strtol(args[1], NULL, 10);
+        id = strtol(argv[1], NULL, 10);
     }
     else
     {

src/id0060.c

@@ -9,11 +9,6 @@
 #include "../lib/sieve.h"
 #define MAX_SEARCH 10000
 
-long math_concat(int a, int b)
-{
-    return a * pow(10, math_length(b, 1)) + b;
-}
-
 bool math_is_prime_pair(Sieve primes, int a, int b)
 {
     long concat = math_concat(a, b);

src/id0060.py

@@ -7,11 +7,9 @@
 from time import time
 
 MAX_SEARCH = 10000
-
-def math_concat(a: int, b: int) -> int: return a * 10 ** (int(log10(b)) + 1) + b
 
 def math_is_prime_pair(a: int, b: int) -> int: 
-    return isprime(math_concat(a, b)) and isprime(math_concat(b, a))
+    return isprime(int(str(a) + str(b))) and isprime(int(str(b) + str(a)))
 
 start = time()
 primes = list(primerange(2, MAX_SEARCH))

src/id0067.sh

@@ -0,0 +1,5 @@
+# Licensed under the MIT License.
+
+# Maximum Path Sum II
+
+./../id0018.o 67

src/id0068.c

@@ -0,0 +1,62 @@
+// Licensed under the MIT License.
+
+// Magic 5-gon Ring
+
+#include <math.h>
+#include "../lib/euler.h"
+#include "../lib/permutation_iterator.h"
+
+int main(void)
+{
+    long long max = 0;
+    long long r[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
+    struct List l;
+    struct PermutationIterator it;
+    clock_t start = clock();
+
+    list_from_array(&l, r, 10);
+
+    for (permutation_begin(&it, &l); !it.end; permutation_next(&it))
+    {
+        if (r[0] > r[3] || r[0] > r[5] || r[0] > r[7] || r[0] > r[9] ||
+            (r[3] != 10 && r[5] != 10 && r[7] != 10 && r[9] != 10))
+        {
+            continue;
+        }
+
+        int sum = r[0] + r[1] + r[2];
+
+        if (r[2] + r[3] + r[4] != sum || r[4] + r[5] + r[6] != sum ||
+            r[6] + r[7] + r[8] != sum || r[8] + r[9] + r[1] != sum)
+        {
+            continue;
+        }
+
+        long long value = math_concat(r[0], r[1]);
+
+        value = math_concat(value, r[2]);
+
+        value = math_concat(value, r[3]);
+        value = math_concat(value, r[2]);
+        value = math_concat(value, r[4]);
+
+        value = math_concat(value, r[5]);
+        value = math_concat(value, r[4]);
+        value = math_concat(value, r[6]);
+
+        value = math_concat(value, r[7]);
+        value = math_concat(value, r[6]);
+        value = math_concat(value, r[8]);
+
+        value = math_concat(value, r[9]);
+        value = math_concat(value, r[8]);
+        value = math_concat(value, r[1]);
+
+        if (value > max)
+        {
+            max = value;
+        }
+    }
+
+    return euler_submit(68, max, start);
+}

src/id0068.py

@@ -0,0 +1,31 @@
+# Licensed under the MIT License.
+
+# Magic 5-gon Ring
+
+from itertools import permutations
+from time import time
+
+maxString = ""
+start = time()
+
+for l in permutations([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]):
+    if l[0] > l[3] or l[0] > l[5] or l[0] > l[7] or l[0] > l[9]: continue
+    if l[3] != 10 and l[5] != 10 and l[7] != 10 and l[9] != 10: continue
+
+    sum = l[0] + l[1] + l[2]
+
+    if l[2] + l[3] + l[4] != sum or l[4] + l[5] + l[6] != sum: continue
+    if l[6] + l[7] + l[8] != sum or l[8] + l[9] + l[1] != sum: continue
+
+    string = "".join(map(str, [
+        l[0], l[1], l[2], 
+        l[3], l[2], l[4], 
+        l[5], l[4], l[6], 
+        l[7], l[6], l[8], 
+        l[9], l[8], l[1]
+    ]))
+
+    if string > maxString:
+        maxString = string
+
+print(f"0068{maxString:>64}    {time() - start:.6f}")

tools/test.c.sh

@@ -55,5 +55,3 @@ for i in {0060..0066};
 do
     ./../id${i}.o
 done
-
-cat ./../data/id0067.txt | ./../id0018.o 67

tools/test.py.sh

@@ -2,7 +2,14 @@
 
 python3 ../src/id0051.py
 
-for i in {0060..0066};
+for i in {0060..0062};
 do
     python3 ../src/id${i}.py
 done
+
+for i in {0064..0066};
+do
+    python3 ../src/id${i}.py
+done
+
+python3 ../src/id0068.py

tools/test.sh

@@ -58,4 +58,5 @@ done
 
 python3 ../src/id0065.py
 ./../id0066.o
-cat ./../data/id0067.txt | ./../id0018.o 67
+cat ./../data/id0067.txt | ./../src/id0067.sh
+./../id0068.o