Assignment 3 - For-Loops and While-Loops.

You hand in this assignment by showing it to the lecturer when it is completed. For-Loops and While-Loops can be translated into each other and this will be done in this exercise in order to train the skills in using them. Nevertheless, there is a philosophical idea behind these two types of loops:

A for-loop has the intention to model that one executes a specific task a certain number of times which is known prior to starting the work. The for-loop has a counting variable which is used to count the number of times a loop is executed. Here an example.
```
           var x; var y=0;
           for (x=0;x<1000;x=x+1) { y = y+x*x; } 
```
This for-loop computes the sum 0^2+1^2+2^2+3^2+...+998^2+999^2 of the first 1000 square numbers and stores the result in a variable y. The loop-variable is x. It is initialized with 0 and after each execution of the loop body "y=y+x*x", the variable x is updated by adding one to it.
A while-loop has the intention to model that one runs a loop as long as a certain condition is true where one does not know when this condition becomes false. Such a condition could for example come from user-input.
```
          while (window.confirm("Do you want to play?"))
            { tictactoe(); } 
```
The function "tictactoe()" is not shown here, but a later assignment deals with how to implement this game on a computer. In the case that the user has to play the game once first and is then asked whether he wants to continue, one can use a do-while-loop (also just called do-loop).
```
          do { tictactoe(); }
          while (window.confirm("Do you like to continue to play?")); 
```

For-loops are more flexible than it looks like. For example, one can start at any value and go to any value and even do weird updates like in the following: for (x=64;x<1000;x=x+x) { .... }. In this case the variable has at the first time the value 64, in the second run through the loop the value 128, in the third 256, in the fourth 512. Then, after that loop, the value is 1024 and no longer smaller than 1000, so the loop is just ran four times. This flexibility allows even to simulate while-loops by for-loops as follows:

          while (cond) { commands; }

becomes

     var u;
          for (u=cond;u;u=cond) { commands; }

where u is a new variable and the condition is always copied into u. As long as u is true, the for-loop is executed. Of course, assigning the value of the condition "cond" to u is a bit non-standard and a while-loop would be a much better style in this case as it is much easier to understand here. The translations in this assignment will therefore give more natural for-loops, provided they are done properly.

The opposite direction is much easier to do. The above for-loop

           var x; var y=0;
           for (x=0;x<1000;x=x+1) { y = y+x*x; }

can be translated into the following while-loop.

           var x=0; var y=0;
           while (x<1000) { y = y+x*x; x=x+1; }

Note that the initialization "x=0" has to be before the while-loop, here it is move into the variable-declaration. Furthermore, the update-command "x=x+1;" has to become the last statement of the body of the loop, that is, it has to be appended to the stuff between the braces "{" and "}". The condition between the two semicolons of the header starting with "for" af the for-loop becomes the condition of the while-loop.

Downloading the assignment.
Log on your UNIX account and go into the correct directory.

        cd public_html

Download this page onto your computer and place it on your webpage.

        wget http://www.comp.nus.edu.sg/~gem1501/assignment03.html
        chmod 755 *.html

The wget command copies a file into your page.
The chmod-command enables you to look with your browser at the downloaded assignment.
Use an editor like pico, vi or vim to look at the file. You can type the file name as well like

        pico assignment03.html

so that the editor knows which file to edit and where to save the changes.

The task In the following text, there are functions fa, wa, fb, wb, fc, wc, fd, wd and so on. The "f"-version has always a for-loop and the w-version a while-loop. In each case, one of the functions always returns 0. Please adjust this function such that it does the same as its counterpart. The input x is always a natural number from the set {0,1,2,3,...}.

Java Script Starts Here.

Java Script Ends Here.