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Task/Ascending-primes/C/ascending-primes.c

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+/*
+ *  Ascending primes
+ *
+ *  Generate and show all primes with strictly ascending decimal digits.
+ *
+ *
+ *  Solution
+ *
+ *  We only consider positive numbers in the range 1 to 123456789. We would
+ *  get 7027260 primes, because there are so many primes smaller than 123456789
+ *  (see also Wolfram Alpha).On the other hand, there are only 511 distinct
+ *  nonzero positive integers having their digits arranged in ascending order.
+ *  Therefore, it is better to start with numbers that have properly arranged
+ *  digitsand then check if they are prime numbers.The method of generating
+ *  a sequence of such numbers is not indifferent.We want this sequence to be
+ *  monotonically increasing, because then additional sorting of results will
+ *  be unnecessary. It turns out that by using a queue we can easily get the
+ *  desired effect. Additionally, the algorithm then does not use recursion
+ *  (although the program probably does not have to comply with the MISRA
+ *  standard). The problem to be solved is the queue size, the a priori
+ *  assumption that 1000 is good enough, but a bit magical.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdbool.h>
+#include <math.h>
+
+#if UINT_MAX < 123456789
+#error "we need at least 9 decimal digits (32-bit integers)"
+#endif
+
+
+#define MAXSIZE 1000
+
+unsigned queue[MAXSIZE];
+unsigned primes[MAXSIZE];
+
+unsigned begin = 0;
+unsigned end = 0;
+unsigned n = 0;
+
+
+bool isPrime(unsigned n)
+{
+    if (n == 2)
+    {
+        return true;
+    }
+    if (n == 1 || n % 2 == 0)
+    {
+        return false;
+    }
+    unsigned root = sqrt(n);
+    for (unsigned k = 3; k <= root; k += 2)
+    {
+        if (n % k == 0)
+        {
+            return false;
+        }
+    }
+    return true;
+}
+
+
+int main(int argc, char argv[])
+{
+    for (int k = 1; k <= 9; k++)
+    {
+        queue[end++] = k;
+    }
+
+    while (begin < end)
+    {
+        int value = queue[begin++];
+        if (isPrime(value))
+        {
+            primes[n++] = value;
+        }
+        for (int k = value % 10 + 1; k <= 9; k++)
+        {
+            queue[end++] = value * 10 + k;
+        }
+    }
+
+    for (int k = 0; k < n; k++)
+    {
+        printf("%u ", primes[k]);
+    }
+
+    return EXIT_SUCCESS;
+}