add explanations for problem 34

Author: tca19

problem_026-050/problem_034.c

@@ -1,7 +1,15 @@
 #include <stdio.h>
 #include <stdint.h>
 
-#define MAX 2177280
+/* The upper search bound is 2540160. If the upper bound has 6 digits, the
+ * maximum factorial sum that can be obtained is 6*9! = 2177280 > 999999. So
+ * every numbers between 1 and 999999 can be a curious number. If the upper
+ * bound has 7 digits, the maximum achievable sum is 7*9! = 2540160, so all
+ * the numbers after 2540160 can not be a curious number as the sum of the
+ * factorial of its digits will be less than 2540160 so less than itself
+ * (therefore not equal).
+ */
+#define MAX 2540160
 
 int32_t factorial[] = {
 	1,        /* 0! */
@@ -16,6 +24,8 @@ int32_t factorial[] = {
 	362880    /* 9! */
 };
 
+/* is_sum_factorial: return 1 if n is equal to the sum of the factorial of its
+ * digits. */
 int32_t is_sum_factorial(int32_t n)
 {
 	int32_t sum, i;
@@ -29,6 +39,8 @@ int32_t main(void)
 {
 	int32_t n, answer;
 
+	/* start at 3 because 1! and 2! are no included according to the problem
+	 * statement. */
 	for (n = 3, answer = 0; n <= MAX; ++n)
 		if (is_sum_factorial(n))
 			answer += n;