explenation of recusion based on factoral example

JonathanHinds.md

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+Jonathan Hinds
+Code Sample: RecursionExampleDirectory
+
+//pre: n >= 0
+//method fact takes in an int >= 0
+public static int fact(int n)
+{
+  //initialize the result to 0
+  int result = 0;
+  //if the number entered is 0
+  if(n == 0)
+    //set result to 1
+    result = 1;
+  //if the number entered is not 0
+  else
+    //the result is set = to the original input * the result
+    //of fact if you subtract 1 from the original input
+    result = n * fact(n-1);
+    //
+  return result;
+}
+
+the fact method takes in an integer ( n ) which must be greater than 0
+and outputs an integer ( result ) which is a product of n * (n - 1).
+This method recursively calls itself, multiplying itself by 1 less of
+what its original input was and exiting once ( n ) the input is 0, the
+code then continues in order downward to the return of the result.
+this means, 5 goes in, 5 isn't 0 so we call fact again on n-1
+this means, 4 goes in, 4 isn't 0 so we call fact again on n-1
+this means, 3 goes in, 3 isn't 0 so we call fact again on n-1
+... and so forth until 0 goes in.
+Once 0 goes in, we see that n == 0; set result to 1 and move outward returning
+the result to the previous time fact was called.
+this means when n == 0, return 1 to the previous time it was calculated.
+the previous time it was calculated ( n + 1 ) n was == 1. before that n == 2
+before that n == 3 each time multiplying itself by what it was previously.
+Recursion can be used to execute a task any number of times until a specific
+result is shown. This would be used in place of a for or while loop
+when its unknown how many times the method needs to run. In the event
+that the exit condition is never specified or never met - recursion will
+take place infinitely until a memory error occurs.