CSU 1730（构造）

1730: Tractatus Logico-Philosophicus

Time Limit: 1 Sec  Memory Limit: 128 MB  Special Judge
Submit: 45  Solved: 26

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Description

This book is written by Ludwig Josef Johann Wittgenstein;

There are seven main propositions in the text. These are:

The world is everything that is the case.

What is the case (a fact) is the existence of states of affairs.

A logical picture of facts is a thought.

A thought is a proposition with a sense.

A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)

The general form of a proposition is the general form of a truth function, which is:  . This
is the general form of a proposition.

Whereof one cannot speak, thereof one must be silent.

Wittgenstein deduced our world was made up of logical word or logical picture.

There was a Conclution found by Wittgenstein that The most experienced Gods have to find a magic
matrix of the size n × n (n is
even number) to make our world .Matrix should contain integers from 0 to n - 1,
main diagonal should contain only zeroes and matrix should be symmetric. Moreover, all numbers in each row and cloumn should be different. You found
this secret after reading <<Tractatus Logico-Philosophicus>>.So output the world.

Input

The first line contains one integer T(1≤ T ≤ 10), There are T cases;

The next T lines contains one integer n( 2≤ n ≤ 1000) , n is even number.

Output

Output n lines with n numbers each for each case— the required matrix. Separate numbers with spaces. If there are several solutions, output any.

Sample Input

2
2
4

Sample Output

0 1
1 0
0 1 3 2
1 0 2 3
3 2 0 1
2 3 1 0

HINT

Source

题意：构造一个n*n的矩阵，使得每行每列没有重复的元素

题解：其实是非常简单的一个构造呀！只要胆大敢交就能AC，观察一下样例就可以找打一些规律，对角线的数字相同，然后矩阵的第一行的数字为0。。。。。n-1，然后按照规则构造就可以了，原本比赛1个多小时就敲好了，输入6，发现无法得到符合题意的矩阵，我不信，就把6的全排列跑了一边，还是不行，于是就没有交了，但是队友说6确实构造不出来，你尝试交一下，让后就AC了。。。。。。。。我也不知道原理。。迷之AC

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<string>
#include<bitset>
#include<utility>
#include<functional>
#include<iomanip>
#include<sstream>
#include<ctime>
using namespace std;

#define N int(2e3+10)
#define inf int(0x3f3f3f3f)
#define mod int(1e9+7)
typedef long long LL;

#ifdef CDZSC
#define debug(...) fprintf(stderr, __VA_ARGS__)
#else
#define debug(...)
#endif

int g

;

int main()
{
#ifdef CDZSC
freopen("i.txt", "r", stdin);
//freopen("o.txt","w",stdout);
int _time_jc = clock();
#endif
int t,n;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
for(int i=1;i<n;i++)
{
g[i][0]=i;
g[i][n-1]=n-i-1;
}
for(int i=1;i<n;i++)
{
int k=i;
int p=0;
while(k>0)
{
g[k-1][p+1]=g[k][p];
k-=1;
p+=1;
}
}
for(int i=n-1;i>=1;i--)
{
int k=i;
int p=n-1;
while(k<n)
{
g[k+1][p-1]=g[k][p];
k+=1;
p-=1;
}
}
for(int i=0;i<n;i++)
g[i][i]=0;
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(j)printf(" ");
printf("%d",g[i][j]);
}
printf("\n");
}
}
#ifdef CDZSC
debug("time: %d\n", int(clock() - _time_jc));
#endif
return 0;
}

1730: Tractatus Logico-Philosophicus

Time Limit: 1 Sec  Memory Limit: 128 MB  Special Judge
Submit: 45  Solved: 26

[Submit][Status][Web
Board]

Description

This book is written by Ludwig Josef Johann Wittgenstein;

There are seven main propositions in the text. These are:

The world is everything that is the case.

What is the case (a fact) is the existence of states of affairs.

A logical picture of facts is a thought.

A thought is a proposition with a sense.

A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)

The general form of a proposition is the general form of a truth function, which is:  . This
is the general form of a proposition.

Whereof one cannot speak, thereof one must be silent.

Wittgenstein deduced our world was made up of logical word or logical picture.

There was a Conclution found by Wittgenstein that The most experienced Gods have to find a magic
matrix of the size n × n (n is
even number) to make our world .Matrix should contain integers from 0 to n - 1,
main diagonal should contain only zeroes and matrix should be symmetric. Moreover, all numbers in each row and cloumn should be different. You found
this secret after reading <<Tractatus Logico-Philosophicus>>.So output the world.

Input

The first line contains one integer T(1≤ T ≤ 10), There are T cases;

The next T lines contains one integer n( 2≤ n ≤ 1000) , n is even number.

Output

Output n lines with n numbers each for each case— the required matrix. Separate numbers with spaces. If there are several solutions, output any.

Sample Input

2
2
4

Sample Output

0 1
1 0
0 1 3 2
1 0 2 3
3 2 0 1
2 3 1 0

HINT

Source