MATLAB——解数独

数独

数独是一种逻辑游戏，玩家需要根据9x9盘面的已知数字，推理出剩余所有空格的数字，并满足每一行、每一列和每个粗线宫(3x3)内均含1~9,不重复。

MATLAB中有关函数

M = dlmread(filename,delimiter) 使用指定的分隔符，将该文件的数据读取到矩阵M中，并将重复的分隔符视为单个的分隔符

disp(x) 显示变量x的值，而不打印变量名称

代码实现

文件目录

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)
%检查（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)
%按九宫格检查(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)
%按列检查(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)
%按行检查(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 (想要破解的数独矩阵)

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)
%按编号逐一填充，递归
    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

效果图

参考链接：https://youtu.be/La57P8wNnLA