“魔方"算法 [英] 'Magic Square' algorithm

问题描述

作为一项实验，我正在尝试创建一个幻方程序，用九个数字检查每个可能的方格.对于那些不知道的人来说，幻方是一个由 1-9 数字组成的 3x3 网格，其中每行、每列和对角线的总和为 15.例如:

As an experiment, I'm trying to create a magic square program that checks every possible square with nine numbers. For those who do not know, a magic square is a 3x3 grid of numbers 1-9, where each row, column, and diagonal add up to 15. For example:

我将如何使用 Lua 使用表格检查每个方块?我从下表开始:

How would I go about checking each square using a table with Lua? I'm starting with the following table:

local sq = {
    1, 1, 1,
    1, 1, 1
    1, 1, 1
}

我将如何以正确的顺序检查每张桌子?我能够在纸上画出我的想法，但我不完全确定如何将其转换为代码.我已经创建了检查正方形是否神奇"的函数(如下)，但我不确定如何以正确的方式增加每个数字.

How would I go about checking each table in the correct order? I'm able to draw out my thinking on paper, but I'm not completely sure how to translate it to code. I already created the function to check if the square is 'magic' (following), but I'm not sure how to increase each number in the correct fashion.

local isMagic = function(s)
    return (
        s[1] + s[2] + s[3] == 15 and
        s[4] + s[5] + s[6] == 15 and
        s[7] + s[8] + s[9] == 15 and
        s[1] + s[4] + s[7] == 15 and
        s[2] + s[5] + s[8] == 15 and
        s[3] + s[6] + s[9] == 15 and
        s[1] + s[5] + s[9] == 15 and
        s[3] + s[5] + s[7] == 15
    )
end 

推荐答案

根据我在这里看到的，共有三种模式:

Based on what I am seeing here, there are three patterns:

1) if we can define step by 3, we compare columns: 
sum(tab[x] for x in range(step)) == sum(tab[x] for x in xrange(step+1,step*2))== sum(tab[x] for x in xrange(2*step+1,step*3))

2) raws:
sum(tab[x] for x in range(step*step) if x%step==0) == sum(tab[x] for x in range(step*step) if x%step==1)== sum(tab[x] for x in range(step*step) if x%step==2) ===> till we x%step== step-1

3) Diagonales: 
sum(tab[x] for x in range(step*step) if x%(step+1)==0) == sum(tab[x] for x in range(step*step) if x%(step+1)==step-1) 

这篇关于“魔方"算法的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！