Initial data commit

Task/Padovan-sequence/C/padovan-sequence.c

@@ -0,0 +1,98 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+
+/* Generate (and memoize) the Padovan sequence using
+ * the recurrence relationship */
+int pRec(int n) {
+    static int *memo = NULL;
+    static size_t curSize = 0;
+
+    /* grow memoization array when necessary and fill with zeroes */
+    if (curSize <= (size_t) n) {
+        size_t lastSize = curSize;
+        while (curSize <= (size_t) n) curSize += 1024 * sizeof(int);
+        memo = realloc(memo, curSize * sizeof(int));
+        memset(memo + lastSize, 0, (curSize - lastSize) * sizeof(int));
+    }
+
+    /* if we don't have the value for N yet, calculate it */
+    if (memo[n] == 0) {
+        if (n<=2) memo[n] = 1;
+        else memo[n] = pRec(n-2) + pRec(n-3);
+    }
+
+    return memo[n];
+}
+
+/* Calculate the Nth value of the Padovan sequence
+ * using the floor function */
+int pFloor(int n) {
+    long double p = 1.324717957244746025960908854;
+    long double s = 1.0453567932525329623;
+    return powl(p, n-1)/s + 0.5;
+}
+
+/* Given the previous value for the L-system, generate the
+ * next value */
+void nextLSystem(const char *prev, char *buf) {
+    while (*prev) {
+        switch (*prev++) {
+            case 'A': *buf++ = 'B'; break;
+            case 'B': *buf++ = 'C'; break;
+            case 'C': *buf++ = 'A'; *buf++ = 'B'; break;
+        }
+    }
+    *buf = '\0';
+}
+
+int main() {
+    // 8192 is enough up to P_33.
+    #define BUFSZ 8192
+    char buf1[BUFSZ], buf2[BUFSZ];
+    int i;
+
+    /* Print P_0..P_19 */
+    printf("P_0 .. P_19: ");
+    for (i=0; i<20; i++) printf("%d ", pRec(i));
+    printf("\n");
+
+    /* Check that functions match up to P_63 */
+    printf("The floor- and recurrence-based functions ");
+    for (i=0; i<64; i++) {
+        if (pRec(i) != pFloor(i)) {
+            printf("do not match at %d: %d != %d.\n",
+                i, pRec(i), pFloor(i));
+            break;
+        }
+    }
+    if (i == 64) {
+        printf("match from P_0 to P_63.\n");
+    }
+
+    /* Show first 10 L-system strings */
+    printf("\nThe first 10 L-system strings are:\n");
+    for (strcpy(buf1, "A"), i=0; i<10; i++) {
+        printf("%s\n", buf1);
+        strcpy(buf2, buf1);
+        nextLSystem(buf2, buf1);
+    }
+
+    /* Check lengths of strings against pFloor up to P_31 */
+    printf("\nThe floor- and L-system-based functions ");
+    for (strcpy(buf1, "A"), i=0; i<32; i++) {
+        if ((int)strlen(buf1) != pFloor(i)) {
+            printf("do not match at %d: %d != %d\n",
+                i, (int)strlen(buf1), pFloor(i));
+            break;
+        }
+        strcpy(buf2, buf1);
+        nextLSystem(buf2, buf1);
+    }
+    if (i == 32) {
+        printf("match from P_0 to P_31.\n");
+    }
+
+    return 0;
+}