Algorithm

This problem is very confusing because you are asked to create code that creates code. To see what's really asked, just remove all the code and let only the permutations. Ah! it looks more easy, isn't it? The point is to generate permutations with only one check between each var.

Simply create a recursive function : put a, then put b before and after a, then for both cases, put c before, in between and after the two letters, and so on. When you've eventually put all the variables, you have generated a permutation. Simply add the pascal code in between and you are done!

Trick

Beware of the name of the variables and the number of ';' allowed.

If you are in trouble with the multi-entry input, read my how to read input.

Additional Input

110.in

Additional Output

110.out

Background

Sorting holds an important place in computer science. Analyzing and implementing various sorting algorithms forms an important part of the education of most computer scientists, and sorting accounts for a significant percentage of the world's computational resources. Sorting algorithms range from the bewilderingly popular Bubble sort, to Quicksort, to parallel sorting algorithms and sorting networks. In this problem you will be writing a program that creates a sorting program (a meta-sorter).

The Problem 

• They must begin with program sort(input,output);

• They must declare storage for exactly n integer variables. The names of the variables must come from the first n letters of the alphabet (a,b,c,d,e,f).

• A single readln statement must read in values for all the integer variables.

• Other than writeln statements, the only statements in the program are if then else statements. The boolean conditional for each if statement must consist of one strict inequality (either < or >) of two integer variables. Exactly n! writeln statements must appear in the program.

• Exactly three semi-colons must appear in the programs
  1. after the program header: program sort(input,output);

  2. after the variable declaration: ...: integer;

  3. after the readln statement: readln(...);

• No redundant comparisons of integer variables should be made. For example, during program execution, once it is determined that a < b, variables a and b should not be compared again.

• Every writeln statement must appear on a line by itself.

• The programs must compile. Executing the program with input consisting of any arrangement of any n distinct integer values should result in the input values being printed in sorted order.

For those unfamiliar with Pascal syntax, the example at the end of this problem completely defines the small subset of Pascal needed.

The Input 

1 n 8

The Output 

Sample Input 

1

3

Sample Output 

program sort(input,output);
var
a,b,c : integer;
begin
  readln(a,b,c);
  if a < b then
    if b < c then
      writeln(a,b,c)
    else if a < c then
      writeln(a,c,b)
    else
      writeln(c,a,b)
  else
    if a < c then
      writeln(b,a,c)
    else if b < c then
      writeln(b,c,a)
    else
      writeln(c,b,a)
end.

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