问题描述

link如何解决如下矩阵生成难题？注意一定要用link实现。

将1~N*N放入一个N*N的矩阵，要求矩阵每行每列以及对角线的和相等。请问怎么实现？注意一定要用link实现。

解决方案

 using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication2
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = 3;
            var result = solve(n, new int[] { }).First();
            for (int i = 0; i < n; i++)
            {
                Console.WriteLine(string.Join("t", result.Skip(i * n).Take(n).Select(x => x.ToString())));
            }
        }

        static IEnumerable<int[]> solve(int n, int[] current)
        {
            if (current.Length == n * n)
            {
                yield return current;
                yield break;
            }
            foreach (int item in Enumerable.Range(1, n * n).Where(x => !current.Contains(x) && foo(n, current, x)))
            {
                foreach (var i in solve(n, current.Concat(new int[] { item }).ToArray()))
                    yield return i;
            }
        }

        static bool foo(int n, int[] current, int next)
        {
            int[] arr = current.Concat(new int[] { next }).Concat(Enumerable.Repeat(0, n * n - current.Length - 1)).ToArray();
            int sum3 = 0, sum4 = 0;
            for (int i = 0; i < n; i++)
            {
                int sum1 = 0, sum2 = 0;
                for (int j = 0; j < n; j++)
                {
                    sum1 += arr[i * n + j];
                    sum2 += arr[j * n + i];
                }
                if (new int[] { sum1, sum2 }.Any(x => x > n * n / 2 + 1)) return false;
                sum3 += arr[i * n + i];
                sum4 += arr[i * n + (n - i)];
            }
            if (new int[] { sum3, sum4 }.Any(x => x > n * n / 2 + 1)) return false;
            return true;
        }
    }
}