% You should be able to run this as
%
% CS121_sudoku(sudoku_file)
%
% The board_file should just be a 9x9 matrix of numbers.
% It should look like the one we provide.
%
% Example Run: CS121_sudoku('board.txt');
%
% Feel free to delete all example code.
%
% We referenced http://www.mathworks.com/matlabcentral/fileexchange/7676
% when setting this assignment up.

function sudoku_solver(sudoku_file) 
global fignr; fignr = figure; cla; draw_grid();

%% for loading from a plain text file as in 
start = load(sudoku_file);
current = start;
draw_board(start, current);

%% if loading from an excel spreadsheet use
% start = xlsread(sudoku_file);
% current = start;
% draw_board_xls(start, current);




%% This just pauses the board after it has been initially drawn
waitforbuttonpress

%% Example code: that marks squares with numbers that make the board invalid
% This does not try to check which squares are correctly labeled and is
% just used as an example to show you what functions you have available.
for i = 1:9
  for j = 1:9
    ss_r = ceil(i / 3); % because matlab indexes starting from 1
    ss_c = ceil(j / 3);
    if start(i, j) == 0 && (current(i, j) ~= 0) && ... % matlab uses ~ to signify not
        ~(is_subsquare_valid(ss_r, ss_c, current) ...
        && is_row_valid(i, current) ...
        && is_col_valid(j, current))
      draw_number(current(i, j), i, j, 'r');
    end
  end
end

%% Example code that checks if a board is solved
if(checksolved(current))
  disp('this board is a solved board');
end

%% Sudoku Solver
% if you are using this as your sudoku model then
%
% YOUR CODE SHOULD GO HERE
%
% Also you may add as many functions as you'd like.  You'll probably need
% to add a couple for readability and for however you decompose the
% problem
return 

%% Helper Functions
% Provided for your convenience.  You shouldn't need to
% change any code below here.  But feel free to read it and change it as
% see fit. Just be sure to document what you are doing.

% This function checks to see if the current board configuration is solved
function isvalid = checksolved(current)
isvalid = true;
for i = 1:3
  for j = 1:3
    r = 3*(i-1) + j; c = r;
    if( ~is_subsquare_solved(i, j, current) || ...
        ~is_row_solved(r, current) || ...
        ~is_col_solved(c, current) )
      isvalid = false;
      return
    end
  end
end
return 

% checks if the 3x3 subsquare in position
% r,c  (labeled by subsquare) is a valid subsquare
% meaning that there are no conflicts within the square
function isvalid = is_subsquare_valid(r, c, current)
rr = 3*r;
cc = 3*c;
subsquare = current(rr-2:rr, cc-2:cc);
subsquare = subsquare(:);
subsquare = subsquare(subsquare ~= 0);
isvalid = isequal(size(unique(subsquare)), size(subsquare));
return

function isvalid = is_row_valid(row, current)
r = current(row, :);
r = r(r ~= 0);
isvalid = isequal(size(unique(r)), size(r)); 
return

function isvalid = is_col_valid(col, current)
isvalid = is_row_valid(col, current');
return

% check to see if a particular subproblem is solved
function issolved = is_subsquare_solved(r, c, current)
rr = 3*r; cc = 3*c;
subsquare = current(rr-2:rr, cc-2:cc);
issolved = ~any(subsquare(:) == 0) ...
  && is_subsquare_valid(r, c, current);
return

function issolved = is_row_solved(r, current)
issolved = ~any(current(r, :) == 0) ...
  && is_row_valid(r, current);
return

function issolved = is_col_solved(c, current)
issolved = is_row_solved(c, current');
return

% This function writes the desired number in the sudoku square, as given by
% the desired row and column.  Also draws it in the specified color.
% If there was a previous number in that position then that object is removed 
% from the board so the new number can be cleanly placed
function draw_number(num, row, col, color)
[sx, sy, w, h] = position(row, col);
pos = [sx + w/2, sy + h/2, 0];

% erase current text at this position
% need to find a better way to do this, such as get the element at the
% current position
tt = get(get(gcf,'Children'), 'Children');
for i = 1:size(tt, 1)
  if strcmp(get(tt(i), 'Type'), 'text') == 0
    continue;
  end
  numpos = get(tt(i), 'Position');
  if(numpos == pos)
    delete(tt(i));
    break;
  end
end

text(pos(1), pos(2), num2str(num), 'fontsize', 20, 'color', color);
return

% For a given position (rows and cols start from the top left corner i.e. 
% row 1 is the top row and col 3 would be the third column from the left)
% on the sudoku board, this function will return the lower left corner 
% graphing coordinate position as sx,sy and the width and the height 
% of the rectangle as w, h
%
% rows correspond to y values, and columns correspond to x values on the
% graph
function [sx,sy,w,h]=position(row,col)
dx=1/9;
dy=1/9;
w=dx;
h=dy;
sx=(col-1)*dx;
sy=(9-row)*dy;
return

% This function draws the grid for the sudoku board and should only ever
% have to be called once.
function draw_grid()
hold on
xlabel('');
ylabel('');
set(gca,'xtick',[]);
set(gca,'ytick',[]);
set(gca,'pos',[0.01 0.01 0.98 0.98]);
for i = 1:10
  spos = (i-1)/9;
  width = 1;
  if( mod(i, 3) == 1 ), width = 3; end
  line( [spos, spos], [0 1], 'color', 'k', 'linewidth', width);
  line( [0, 1], [spos spos], 'color', 'k', 'linewidth', width);
end
return

% This function draws the numbers from start and current onto the board.
% -The start matrix should represent the initial starting configuration.
%  (starting board configuration numbers are drawn in black)
% -the current matrix should represent the current board configuration.
%  (current board configuration numbers are drawn in green)
function draw_board(start, current)
for i=1:9
  for j=1:9
    nr=start(i,j);
    if nr>0
      draw_number(nr, i, j, 'k');
    elseif current(i, j) ~= 0
      draw_number(current(i, j), i, j, 'g');
    end
  end
end
return

function draw_board_xls(start, current)
ns = isnan(start);
nc = isnan(current);
for i=1:9
  for j=1:9
    if ~ns(i, j)
      draw_number(nr, i, j, 'k');
    elseif ~nc(i, j)
      draw_number(current(i, j), i, j, 'g');
    end
  end
end
return