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section_3/precomputation/README.md

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+# Section 3 - Pre-computation
+
+Time versus space.
+
+This is the essential battle that programmers face. In order to go
+faster, more memory is used. In order to economize on memory, more
+computation is needed.
+
+This duality is demonstrated in no better way than comparing a
+calculated method (economizing space at the expense of time) versus an
+entirely precomputed method (sacrificing space to reduce time).
+
+In this section, we will demonstrate three methods of calculating
+factorials from 0 to 15.
+
+* Iteratively
+
+* Recursively
+
+* By pre-computation
+
+Certainly, for the purposes of this demonstration, it is not necessary
+to implement both iterative and recursive methods. We do so for fun and
+for any lessons the reader can glean.
+

section_3/precomputation/main.c

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+#include <stdio.h>
+
+#define MIN     1
+#define MAX     15
+
+long Iterative(long n);
+long Recursive(long n);
+long Precomputed(long n);
+
+int main() {
+    long (*func[])(long) = {
+        Iterative,
+        Recursive,
+        Precomputed,
+        NULL
+    };
+
+    printf("%3s %13s %13s %13s\n", 
+        "N", "Iterative", "Recursive", "Precomputed");
+
+    for (long n = MIN; n <= MAX; n++) {
+        printf("%3ld ", n);
+        int i = 0;
+        while (func[i] != NULL) {
+            printf("%13ld ", (*func[i])(n));
+            i++;
+        }
+        printf("\n");
+    }
+
+    return 0;
+}
+
+/*  Iterative() - this function computes the factorial of a long integer
+    by  counting  down,  multiplying each time the value computed in the
+    previous iteration.
+
+    The maximum value of the parameter is NOT enforced here, having been
+    checked by the calling function.
+*/
+
+long Iterative(long n) {
+    long retval = 1;
+    for (long i = 1; i <= n; i++) {
+        retval *= i;
+    }
+    return retval;
+}
+
+/*  Recursive() - this function computes the factorial of a long integer
+	recursively.  At each point, the current value of n in multiplied by
+    the return value  of  calling  the function with its parameter being
+    reduced by b1.
+
+	The maximum value of the parameter is NOT enforced here, having been
+	checked by the calling function.
+*/
+
+long Recursive(long n) {
+    long retval;
+    if (n <= 1)
+        retval = 1;
+    else
+        retval = n * Recursive(n - 1);
+        
+    return retval;
+}
+
+long v[] = {
+	1,
+	1,
+	2,
+	6,
+	24,
+	120,
+	720,
+	5040,
+	40320,
+	362880,
+	3628800,
+	39916800,
+	479001600,
+	6227020800,
+	87178291200,
+	1307674368000
+};
+
+/*  Precomputed() - this  function  computes  the  factorial  of  a long
+    integer using pre-computation. The values of  the  parameter over  a
+    predefined  range  are computed  prior  to the  first  call  of  the
+    factorial function.  These values  are stored in a table and fetched
+    using the parameter as an index.
+
+	The maximum value of the parameter is NOT enforced here, having been
+	checked by the calling function.
+*/
+
+long Precomputed(long n) {
+    if (n < 0 || n > 15)
+        return 1;
+
+	return v[n];
+}