Add id0091 faster

Makefile

@@ -32,7 +32,7 @@ all: \
 	id0068$(E) id0069$(E) id0070$(E) id0071$(E) id0072$(E) id0073$(E) \
 	id0074$(E) id0075$(E) id0076$(E) id0077$(E) id0078$(E) id0079$(E) \
 	id0080$(E) id0081$(E) id0082$(E) id0083$(E) id0084$(E) id0085$(E) \
-	id0086$(E) id0087$(E) id0089$(E)
+	id0086$(E) id0087$(E) id0089$(E) id0091$(E) id0092$(E)
 
 libeuler$(A): $(call RECURSE,lib,*.c)
 	$(RM) *.o
@@ -306,5 +306,11 @@ id0087$(E): src/id0087.c libeuler$(A)
 id0089$(E): src/id0089.c libeuler$(A)
 	$(CC) $(CFLAGS) $< -o $@ $(LEULER) $(LM)
 
+id0091$(E): src/id0091.c libeuler$(A)
+	$(CC) $(CFLAGS) $< -o $@ $(LEULER) $(LM)
+
+id0092$(E): src/id0092.c libeuler$(A)
+	$(CC) $(CFLAGS) $< -o $@ $(LEULER) $(LM)
+
 clean:
 	$(RM) *$(A) *.o

README.md

@@ -122,6 +122,8 @@ which is licensed under the GNU Lesser General Public License v3.0 (`LGPL-3.0`).
 | 86 | [Cuboid Route](src/id0086.c) | Geometry | Minimum | |
 | 87 | [Prime Power Triples](src/id0087.c) | Number theory | Count | [Hash set](https://en.wikipedia.org/wiki/Hash_table) |
 | 89 | [Roman Numerals](src/id0089.c) | Numeral systems | Difference | [Roman numerals](https://en.wikipedia.org/wiki/Roman_numerals) |
+| 91 | [Right Triangles with Integer Coordinates](src/id0091.c) | Geometry | Count | |
+| 92 | [Square Digit Chains](src/id0092.c) | Number theory | Count | |
 
 ## LeetCode
 
@@ -142,6 +144,7 @@ which is licensed under the GNU Lesser General Public License v3.0 (`LGPL-3.0`).
 |  62  |                       [Unique Paths](src/lc0062.c)                       | Combinatorics | Binomial coefficient | `binomial`            |
 |  69  |                         [Sqrt(x)](src/lc0069.c)                          |  Mathematics  |     Square root      | `sqrt`                |
 |  75  |                       [Sort Colors](src/lc0075.c)                        |    Sorting    |         Sort         | `qsort`               |
+| 273 | [Integer to English Words](src/lc0273.c) | Mathematics | String | `words_to_string` |
 | 367  |                   [Valid Perfect Square](src/lc0367.c)                   |  Mathematics  |       Boolean        | `math_is_polygonal`   |
 | 2119 |             [A Number After a Double Reversal](src/lc2119.c)             |  Mathematics  |       Boolean        | `math_reverse`        |
 | 2400 | [Number of Ways to Reach a Position After Exactly k Steps](src/lc2400.c) | Combinatorics | Binomial coefficient | `mod_binomial_range`            |

src/id0091.c

@@ -0,0 +1,33 @@
+// Licensed under the MIT License.
+
+// Right Triangles with Integer Coordinates
+
+#include "../lib/euler.h"
+#include "../lib/euclidean.h"
+
+int main(void)
+{
+    int count = 0;
+    clock_t start = clock();
+
+    for (int x = 1; x <= 50; x++)
+    {
+        for (int y = 1; y <= 50; y++)
+        {
+            int d = gcd(x, y);
+            int min = x * d / y;
+            int other = (50 - y) * d / x;
+
+            if (other < min)
+            {
+                min = other;
+            }
+
+            count += 2 * min;
+        }
+    }
+
+    count += 50 * 50 * 3;
+
+    return euler_submit(91, count, start);
+}

src/id0092.c

@@ -0,0 +1,65 @@
+// Licensed under the MIT License.
+
+// Square Digit Chains
+
+#include "../lib/euler.h"
+
+int math_sum_of_square_digits(long n, int results[])
+{
+    if (n < 568 && results[n])
+    {
+        return results[n];
+    }
+
+    long result = 0;
+
+    for (long k = n; k; k /= 10)
+    {
+        int d = k % 10;
+
+        result += d * d;
+    }
+
+    return result;
+}
+
+int math_square_digit_chain(long m, int results[])
+{
+    long n = m;
+
+    while (n != 1 && n != 89)
+    {
+        n = math_sum_of_square_digits(n, results);
+    }
+
+    return n;
+}
+
+int main(void)
+{
+    long count = 0;
+    int results[568] = { 0 };
+    clock_t start = clock();
+
+    for (long m = 1; m < 568; m++)
+    {
+        results[m] = math_square_digit_chain(m, results);
+
+        if (results[m] == 89)
+        {
+            count++;
+        }
+    }
+
+    for (long m = 1; m < 10000000l; m++)
+    {
+        long n = math_square_digit_chain(m, results);
+
+        if (n == 89)
+        {
+            count++;
+        }
+    }
+
+    return euler_submit(91, count, start);
+}