From d78b3827c176ab40cf254512844e46f2cd78b4eb Mon Sep 17 00:00:00 2001
From: Jonathan Chan <jonathanhwchan@gmail.com>
Date: Mon, 5 Dec 2016 02:44:09 -0800
Subject: [PATCH] Problem 35; corrected upper bound of prime-counting function
 in primes.c

---
 35       | Bin 0 -> 10040 bytes
 35.c     |  63 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 primes.c |  17 ++++++++-------
 3 files changed, 73 insertions(+), 7 deletions(-)
 create mode 100755 35
 create mode 100644 35.c

diff --git a/35 b/35
new file mode 100755
index 0000000000000000000000000000000000000000..1f28e1cf44102e26494e4a3757e5817d29010ad2
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diff --git a/35.c b/35.c
new file mode 100644
index 0000000..4b92268
--- /dev/null
+++ b/35.c
@@ -0,0 +1,63 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdbool.h>
+#include <math.h>
+#include "primes.h"
+
+int main () {
+    int bound = 1000000;
+
+    int* primes;
+    bool* primesTable;
+    int numPrimes = listOfPrimes (bound, &primes, &primesTable);
+
+    bool* circularPrimesTable = calloc (bound + 1, sizeof (bool));
+    for (int i = 0; i < numPrimes; i++) {
+        if (circularPrimesTable[primes[i]] != true) {
+            int n = primes[i];
+            int numOfDigits = floor (log10 (n)) + 1;
+            int* digits = malloc (sizeof (int) * numOfDigits);
+            for (int d = 0; d < numOfDigits; d++) {
+                digits[d] = n % 10;
+                n /= 10;
+            }
+
+            int* circles = malloc (sizeof (int) * numOfDigits);
+            for (int c = 0; c < numOfDigits; c++) {
+                circles[c] = 0;
+                for (int d = c; d < c + numOfDigits; d++) {
+                    circles[c] += digits[d % numOfDigits] * (int) pow (10, d - c);
+                }
+            }
+            free (digits);
+
+            bool circular = true;
+            for (int c = 0; c < numOfDigits; c++) {
+                if (primesTable[circles[c]] == false) {
+                    circular = false;
+                    break;
+                }
+            }
+            if (circular) {
+                for (int c = 0; c < numOfDigits; c++) {
+                    circularPrimesTable[circles[c]] = true;
+                }
+            }
+            free (circles);
+        } 
+    }
+
+    free (primes);
+    free (primesTable);
+
+    int sum = 0;
+    for (int i = 0; i <= bound; i++) {
+        if (circularPrimesTable[i]) {
+            sum++;
+            printf ("%d ", i);
+        }
+    }
+    free (circularPrimesTable);
+
+    printf ("\n%d\n", sum);
+}
diff --git a/primes.c b/primes.c
index d2f9f49..b6e517a 100644
--- a/primes.c
+++ b/primes.c
@@ -52,7 +52,7 @@ bool isPrimeMem (int n, int* primes) {
  *
  *  N.B. numOfPrimesUpper is an upper-bound of 
  *      the prime-counting function, given by 
- *      n/ln(n) * (1 + 3/2 * 1/ln(n))
+ *      n/ln(n) * 1.25506
  *
  *  runs in O(n * sqrt(n)/ln(n)) (not a tight bound)
  *
@@ -66,19 +66,22 @@ int listOfPrimes (int n, int** primes_ptr, bool** primesTable_ptr) {
         return 0;
     }
 
-    int numOfPrimesUpper = (int) (n/log(n) * 
-                    (1 + 3/2 * 1/log(n)));
+    int numOfPrimesUpper = (int) (n/log(n) * 1.25506); 
     *primes_ptr = malloc (sizeof (int) * numOfPrimesUpper);
     int numOfPrimes = 0;
     for (int i = 0; i <= n; i++) {
         if (isPrimeMem (i, *primes_ptr)) {
-            (*primes_ptr)[numOfPrimes++] = i;
+            (*primes_ptr)[numOfPrimes] = i;
             (*primesTable_ptr)[i] = true;
+            numOfPrimes++;
         }
     }
-    if (numOfPrimes < numOfPrimesUpper)
-        *primes_ptr = realloc (*primes_ptr, 
-                        sizeof (int) * numOfPrimes);
+    if (numOfPrimes < numOfPrimesUpper) {
+        int* tmp = realloc (*primes_ptr, 
+                            sizeof (int) * numOfPrimes);
+        if (tmp != NULL)
+            *primes_ptr = tmp;
+    }
     
     return numOfPrimes;
 }