Question

How can I analyze a recursive source codes by hand?

For example, I have devised a technique for analyzing iterative source code by hand like this:

int fact(int n) 
{ 
 int f = 0; 
 int i = 0; 
 if (n<=1)  
 {  
  return 1; 
 } 

 f = 1; 
 i = 2; 
 for (i=2; i<=n ; i++) 
 { 
  f *= i; 
 } 

 return f; 
}

---------------------------
  i         f       new-f
---------------------------
---------------------------
---------------------------

For each ‘i’ I can analyze and calculate the values of old-f and new-f by hand and fill up the table to see if the routine is working correctly.

But how can I analyze recursive routines by hand?

int fact(int number) {
    int temp;

    if(number <= 1) return 1;

    temp = number * fact(number - 1);
    return temp;
}

Answer 1

Since recursion stores values on the stack you need to analyze it 2-way

1st pass is: do the recursion until the termination condition is reached.

2nd pass: collect the values until the stack is empty.

1st down  2nd up
---------------------------------
n = 6     tmp = 6 * 120 = 720 <- result
n = 5     tmp = 5 * 24 = 120
n = 4     tmp = 4 * 6 = 24
n = 3     tmp = 3 * 2 = 6
n = 2     tmp = 2 * 1 = 2
n = 1     end