Understanding this C function

Question

I'm trying to understand how this function works, I have studied several algorithms to generate sudoku puzzles and found out this one.

Tested the function and it does generates a valid 9x9 Latin Square (Sudoku) Grid. My problem is that I can't understand how the function works, i do know the struct is formed by to ints, p and b , p will hold the number for the cell in the table, But after that I don't understand why it creates more arrays (tab 1 and tab2) and how it checks for a latin square =/ etc , summarizing , I'm completely lost.

I'm not asking for a line by line explanation, the general concept behind this function. would help me a lot !

Thanks again <3

int sudoku(struct sudoku tabla[9][9],int x,int y)
{
int tab[9] = {1,1,1,1,1,1,1,1,1};
        int i,j;
  for(i=0;i<y;++i)
  {
        tab[tabla[x][i].p-1]=0; 

  for(i=0;i<x;++i)
  { 
        tab[tabla[i][y].p-1]=0;
  }
  for(i=(3*(x/3));i<(3*(x/3)+3);++i)
  { 
        for(j=(3*(y/3));j<y;++j)
        {
         tab[tabla[i][j].p-1]=0; 
        }
  }
    int n=0;
   for(i=0;i<9;++i)
   {
    n=n+tab[i];
   }

    int *tab2; 
    tab2=(int*)malloc(sizeof(int)*n);

    j=0; 
    for(i=0;i<9;++i)
    { if(tab[i]==1)
      {
       tab2[j]=i+1;
            j++;
      }
    }
    int ny, nx;
    if(x==8)
    {
        ny=y+1; 
        nx=0;   
    }
    else
    {
        ny=y; 
        nx=x+1;
    }

    while(n>0)
    {
        int los=rand()%n;
        tabla[x][y].p=tab2[los];

        tab2[los]=tab2[n-1]; 

        n--;

        if(x==8 && y==8)
        {
            return 1;
        }

        if (sudoku(tabla,nx,ny)==1)
        {
           return 1;
        } 

    }
    return 0;
}

EDIT Great, I now understand the structure, thanks lijie's answer. What I still don't understand is the part that tries out the values in random order). I don't understand how it checks if the random value placement is valid without calling the part of the code that checks if the movement is legal, also, after placing the random numbers is it necessary to check if the grid is valid again? –

Answer 1

Basically, the an invocation of the function fills in the positions at and "after" (x, y) in the table tabla, and the function assumes that the positions "prior" to (x, y) are filled, and returns whether a legal "filling in" of the values is possible.

The board is linearized via increasing x, then y.

The first part of the function finds out the values that are legal at (x, y), and the second part tries out the values in a random order, and attempts fills out the rest of the board via a recursive call.

There isn't actually a point in having tab2 because tab can be reused for that purpose, and the function leaks memory (since it is never freed, but aside from these, it works).

Does this make sense to you?

EDIT

The only tricky area in the part that checks for legal number is the third loop (checking the 3x3 box). The condition for j is j < y because those values where j == y are already checked by the second loop.

EDIT2

I nitpick, but the part that counts n and fills tab2 with the legal values should really be

int n = 0;
for (i = 0; i < 9; ++i) if (tab[i]) tab[n++] = i+1;

hence omitting the need for tab2 (the later code can just use tab and n instead of tab2). The memory leak is thusly eliminated.

EDIT

Note that the randomness is only applied to valid values (the order of trying the values is randomized, not the values themselves).

The code follows a standard exhaustive search pattern: try each possible candidate value, immediately returning if the search succeeds, and backtracking with failure if all the candidate values fail.

Answer 2

Try to solve sudoku yourself, and you'll see that there is inherent recursion in finding a solution to it. So, you have function that calls itself until whole board is solved.

As for code, it can be significantly simplified, but it will be for the best if you try to write one yourself.

EDIT:

Here is one from java, maybe it will be similar to what you are trying to do.

Answer 3

A quick description of the principles - ignoring the example you posted. Hopefully with the idea, you can tie it to the example yourself.

The basic approach is something that was the basis of a lot of "Artificial Intelligence", at least as it was seen until about the end of the 80s. The most general solution to many puzzles is basically to try all possible solutions.

So, first you try all possible solutions with a 1 in the top-left corner, then all possible solutions with a 2 in the top-left corner and so on. You recurse to try the options for the second position, third position and so on. This is called exhaustive search - or "brute force".

Trouble is it takes pretty much forever - but you can short-cut a lot of pointless searching.

For example, having placed a 1 in the top-left corner, you recurse. You place a 1 in the next position and recurse again - but now you detect that you've violated two rules (two ones in a row, two ones in a 3x3 block) even without filling in the rest of the board. So you "backtrack" - ie exit the recursion to the previous level and advance to putting a 2 in that second position.

This avoids a lot of searching, and makes things practical. There are further optimisations, as well, if you keep track of the digits still unused in each row, column and block - think about the intersection of those sets.

What I described is actually a solution algorithm (if you allow for some cells already being filled in). Generating a random solved sudoku is the same thing but, for each digit position, you have to try the digits in random order. This also leaves the problem of deciding which cells to leave blank while ensuring the puzzle can still be solved and (much harder) designing puzzles with a level-of-difficulty setting. But in a way, the basic approach to those problems is already here - you can test whether a particular set of left-blank spaces is valid by running the solution algorithm and finding if (and how many) solutions you get, for example, so you can design a search for a valid set of cells left blank.

The level-of-difficulty thing is difficult because it depends on a human perception of difficulty. Hmmm - can I fit "difficult" in there again somewhere...

One approach - design a more sophisticated search algorithm which uses typical human rules-of-thumb in preference to recursive searching, and which judges difficulty as the deepest level of recursion needed. Some rules of thumb might also be judged more advanced than others, so that using them more counts towards difficulty. Obviously difficulty is subjective, so there's no one right answer to how precisely the scoring should be done.

That gives you a measure of difficulty for a particular puzzle. Designing a puzzle directly for a level of difficulty will be hard - but when trying different selections of cells to leave blank, you can try multiple options, keep track of all the difficulty scores, and at the end select the one that was nearest to your target difficulty level.