MATLAB——解數獨

數獨

數獨是一種邏輯游戲，玩家需要根據9x9盤面的已知數字，推理出剩余所有空格的數字，並滿足每一行、每一列和每個粗線宮(3x3)內均含1~9,不重復。

MATLAB中有關函數

M = dlmread(filename,delimiter) 使用指定的分隔符，將該文件的數據讀取到矩陣M中，並將重復的分隔符視為單個的分隔符

disp(x) 顯示變量x的值，而不打印變量名稱

代碼實現

文件目錄

check3_by_3.m   
check_cell.m
check_col.m
check_row.m
data.txt
shudu.m
slove.m

check3_by_3.m

function res = check3_by_3(matrix,i,j,num)
%檢查（i,j）能否放num
    res = true;
    block_row = floor((i - 1) / 3) + 1;
    block_col = floor((j - 1) / 3) + 1;
    
    block_row_to = block_row * 3;
    block_row_from = block_row_to - 2;
    block_col_to = block_col * 3;
    block_col_from = block_col_to - 2;
    
    for row = block_row_from : block_row_to
        for col = block_col_from : block_col_to
            if matrix(row,col) == num
                res = false;
                break;
            end
        end
    end
end

check_cell.m

function res = check_cell(matrix,i,j,num)
%按九宮格檢查(i,j)能否放num
    if check_row(matrix,i,j,num) && check_col(matrix,i,j,num) && check3_by_3(matrix,i,j,num)
        res = true;
    else
        res = false;
    end
end

check_col.m

function res = check_col(matrix,i,j,num)
%按列檢查(i,j)能否放num
    res = true;
    for row = 1 : 9
        if matrix(row,j) == num
            res = false;
            break;
        end
    end
end

check_row.m

function res = check_row(matrix,i,j,num)
%按行檢查(i,j)能否放num
    res = true;
    for col = 1 : 9
        if matrix(i,col) == num
            res = false;
            break;
        end
    end
end

data.txt (想要破解的數獨矩陣)

5 3 0 0 7 0 0 0 0
6 0 0 1 9 5 0 0 0 
0 9 8 0 0 0 0 6 0
8 0 0 0 6 0 0 0 3
4 0 0 8 0 3 0 0 1
7 0 0 0 2 0 0 0 6
0 6 0 0 0 0 2 8 0
0 0 0 4 1 9 0 0 5
0 0 0 0 8 0 0 7 9

shudu.m (主程序)

matrix = dlmread('data3.txt','');
disp(matrix);
solve(matrix,1);

slove.m

function solve(matrix,id)
%按編號逐一填充，遞歸
    if id > 81
        disp(matrix);
    else
        row = floor((id - 1) / 9) + 1;
        col = mod((id - 1),9) + 1;
    
        if matrix(row,col) ~= 0
            solve(matrix,id + 1);
        else
            for i = 1 : 9
                if check_cell(matrix,row,col,i) == true
                matrix(row,col) = i;
                solve(matrix,id + 1);
                end
            end
        end
   end
end

效果圖

參考鏈接：https://youtu.be/La57P8wNnLA