A more complex example

Now that we understand the simpler example, let us consider a slightly more complex example:

The indentation shows how the statements are nested. Lines 6 and 7 are the most nested statements. They are nested within the prechecking loop that begins on line 5 and ends on line 8.

Note that the assignment statements on lines 4 and 9 are ``peers'' of the prechecking loop that begins on line 5 and ends on line 8.

Everything from line 4 to line 9 are nested inside the outer prechecking loop.

It may be helpful to show a diagram of this algorithm. Figure 1 represents the same logic in a trail-map format.

Figure 1: Graphical representation of algorithm 2.

Of course, no explanation is complete without a trace! Table 1 traces this algorithm.

Table 1: Partial trace of algorithm 2.

line#	x	y	s	comments
pre	?	?	?	we know nothing about the variables
1	0	?	?	x is initialized
2	0	?	0	s is initialized
3	0	?	0	$x = 0 < 3$ is true, get into the outer loop
4	0	0	0	initialize y
5	0	0	0	$y = 0 < 2$ is true, get into the inner loop
6	0	1	0	y is incremented
7	0	1	1	s gets 0(s) + 1(y) + 0(x), loop back!
5	0	1	1	$y = 1 < 2$ is true, get into the inner loop
6	0	2	1	y is incremented again
7	0	2	3	s gets 1(s) + 2(y) + 0(x), loop back
5	0	2	3	$y = 2 < 2$ is false, exit inner loop
9	1	2	3	x is incremented, loop back to the beginning of the outer loop
3	1	2	3	$x = 1 < 3$ is true, get into the outer loop
...	...	...	...