2021-4-1 多校省选模拟赛

考试复盘

$T1$

我可太喜欢这种不要脑子的莽试题了！！

考场上猜的结论$d>3$无解

$d=1,d=2$的填法也试出来了

$d=3$只试出来了$n,m$是$3$的倍数的填法

但是另外的情况就$GG$了

最后交上去竟然还敲挂了(ˉ▽ˉ；)…乌鸡鲅鱼

这道题应该是这一段考试以来唯几接近整正解的题目了

思考的：大讨论，猜结论

扫描二维码关注公众号，回复： 13138662 查看本文章

$T2$

发现了很多小性质，想到了与根号有关的因子上面去

但是，呃emmmmmm~~

我不知道这个集合应该怎么填

所以找到的那些小性质并没有什么卵用

（和善的微笑

思考的：质数/因子有关的各种算法，$DP$

$T3$

考场上敲得暴力——又挂了w(ﾟДﾟ)waz

链想的树形$DP$但是也没打，没想明白

看到无环的部分分也想不出做法

思考的：$tarjan$强连通，树形$DP$，暴力，后缀数组（纯粹是看到了字符串比较

nmd

大讨论好哇b（￣▽￣）d

• $n,m,d$都是奇数

  $-1$

• $d>3$

  $-1$

  在考场上肯定是猜的结论，就是反复试啊，就是连不出来

  从$(1,1)$先开始满足，要往外连$>3$条线，肯定跨越了一个小正方格

  感性理解都感觉最后几行会有点被困住连不出去

• $d=1$

  • 点数为奇数

    $-1$

  • 点数为偶数

    相邻两个连边即可

• $d=2$

  • 点数为奇数
    
  • 点数为偶数
    

• $d=3$

  • $n=3$

    • $m=4$

      $-1$

    • $m=6$
      

    • $otherwise$

      排除掉两边的对称，中间一定是偶数列，两两配对即可
      

  • $n,m$为偶数
    

  • $otherwise$

    • $m=5$
      
    • $otherwise$
      

代码虽然有三百多行，7K大，但是是非常不动脑子的莽敲，请不要感到害怕，ㄟ(▔=▔)ㄏ

#include <cstdio>
#include <iostream>
using namespace std;
int T, n, m, d;
bool flag;

void print( int x1, int y1, int x2, int y2 ) {
    
    
	if( flag ) printf( "%d %d %d %d\n", y1, x1, y2, x2 );
	else printf( "%d %d %d %d\n", x1, y1, x2, y2 );
}

void subtask1() {
    
    
	printf( "%d\n", ( n * m ) >> 1 );
	if( n & 1 ) swap( n, m ), flag = 1;
	for( int i = 1;i <= n;i ++ )
		for( int j = 1;j <= m;j ++ )
			if( i & 1 )
				print( i, j, i + 1, j );
}

void subtask2() {
    
    
	printf( "%d\n", ( n * m * d ) >> 1 );
	if( ( n & 1 ) && ( m & 1 ) ) {
    
    
		//red
		print( 1, 1, 2, 2 );
		print( n, 1, n, 2 );
		//yellow
		for( int i = 1;i < n;i ++ )
			print( i, 1, i + 1, 1 );
		//blue
		for( int i = 3;i <= n;i ++ )
			for( int j = 2;j < m;j ++ )
				print( i, j, i, j + 1 );
		//green
		for( int i = 3;i <= n;i ++ )
			if( ( n - i + 1 ) & 1 )
				print( i, m, i - 1, m );
			else
				print( i, 2, i - 1, 2 );
		//pink
		for( int i = 2;i <= m;i ++ )
			print( 1, i, 2, i ); 
		//orange
		for( int i = 2;i < m;i ++ )
			if( i & 1 )
				print( 2, i, 2, i + 1 );
			else
				print( 1, i, 1, i + 1 );
	} 
	else {
    
    
		if( n & 1 ) swap( n, m ), flag = 1;
		//red
		print( 1, 1, 1, 2 );
		print( n, 1, n, 2 );
		//yellow
		for( int i = 1;i < n;i ++ )
			print( i, 1, i + 1, 1 );
		//blue
		for( int i = 1;i <= n;i ++ )
			for( int j = 2;j < m;j ++ )
				print( i, j, i, j + 1 );
		//green
		for( int i = 1;i < n;i ++ )
			if( i & 1 )
				print( i, m, i + 1, m );
			else
				print( i, 2, i + 1, 2 ); 
	}
}

void subtask3_0() {
    
    
	if( n != 3 ) swap( n, m ), flag = 1;
	if( m == 4 ) {
    
    
		printf( "-1\n" );
		return;
	}
	printf( "%d\n", ( n * m * d ) >> 1 );
	//red	
	print( 1, 1, 2, 1 );
	print( 2, 1, 3, 1 );
	print( 1, m, 2, m );
	print( 2, m, 3, m );
	for( int i = 1;i < m;i ++ )
		print( 1, i, 1, i + 1 ), print( 3, i, 3, i + 1 );
	if( m == 6 ) {
    
    
		print( 1, 1, 2, 2 );
		print( 2, 1, 2, 2 );
		print( 3, 1, 2, 2 );
		print( 1, 2, 2, 3 );
		print( 3, 2, 2, 3 );
		print( 3, 3, 2, 3 );
		print( 1, 6, 2, 5 );
		print( 2, 6, 2, 5 );
		print( 3, 6, 2, 5 );
		print( 1, 5, 2, 4 );
		print( 1, 4, 2, 4 );
		print( 3, 5, 2, 4 );
		print( 1, 3, 3, 4 );
	}
	else {
    
    
		//yellow
		print( 1, 1, 2, 2 );
		print( 2, 1, 2, 2 );
		print( 3, 1, 2, 2 );
		print( 1, 2, 2, 3 );
		print( 1, 3, 2, 3 );
		print( 3, 2, 2, 3 );
		print( 1, 4, 2, 4 );
		print( 3, 3, 2, 4 );
		print( 3, 4, 2, 4 );
		//green
		for( int i = 5;i <= m - 4;i ++ )
			print( 1, i, 2, i ), print( 2, i, 3, i );
		//pink
		for( int i = 5;i <= m - 4;i ++ )
			if( i & 1 )
				print( 2, i, 2, i + 1 );
		//blue
		print( 1, m, 2, m - 1 );
		print( 2, m, 2, m - 1 );
		print( 3, m, 2, m - 1 );
		print( 1, m - 1, 2, m - 2 );
		print( 1, m - 2, 2, m - 2 );
		print( 3, m - 1, 2, m - 2 );
		print( 1, m - 3, 2, m - 3 );
		print( 3, m - 3, 2, m - 3 );
		print( 3, m - 2, 2, m - 3 );
	}
}

void subtask3_1() {
    
    
	printf( "%d\n", ( n * m * d ) >> 1 );
	if( ! ( n & 1 ) && ! ( m & 1 ) ) {
    
    
		//red
		print( 1, 1, 2, 2 );
		print( 1, m, 2, m - 1 );
		//yellow
		for( int i = 1;i < m;i ++ )
			print( 1, i, 1, i + 1 );
		//green
		for( int i = 1;i <= m;i ++ )
			print( 1, i, 2, i );
		//blue
		for( int i = 1;i <= m;i ++ )
			if( i & 1 )
				print( 2, i, 2, i + 1 );
		for( int i = 2;i <= n - 2;i ++ ) {
    
    
			//pink
			print( i, 1, i + 1, 1 );
			print( i, m, i + 1, m );
			if( i & 1 ) {
    
    
				//grey
				print( i, 2, i + 1, 2 );
				print( i, m - 1, i + 1, m - 1 );
				//orange
				for( int j = 1;j < m;j ++ )
					print( i, j, i, j + 1 );
				//purple
				for( int j = 1;j < m;j ++ )
					print( i + 1, j, i + 1, j + 1 );
			}
			else {
    
    
				//black
				for( int j = 3;j <= m - 2;j ++ )
					print( i, j, i + 1, j );
			}
		}
		//red
		print( n, 1, n - 1, 2 );
		print( n, m, n - 1, m - 1 );
		//yellow
		for( int i = 1;i < m;i ++ )
			print( n, i, n, i + 1 );
		//green
		for( int i = 1;i <= m;i ++ )
			print( n, i, n - 1, i );
		//blue
		for( int i = 1;i <= m;i ++ )
			if( i & 1 )
				print( n - 1, i, n - 1, i + 1 );
	}
	else {
    
    
		if( n & 1 ) swap( n, m ), flag = 1;
		if( m == 5 ) {
    
    
			//red
			print( 1, 1, 2, 2 );
			print( 1, 1, 2, 1 );
			print( 2, 1, 2, 2 );
			print( 1, 2, 2, 3 );
			print( 1, 3, 2, 3 );
			print( 1, m, 2, m - 1 );
			//yellow
			for( int i = 1;i < m;i ++ )
				print( 1, i, 1, i + 1 );
			//green
			for( int i = 4;i <= m;i ++ )
				print( 1, i, 2, i );
			//blue
			for( int i = 4;i <= m;i ++ )
				if( ! ( i & 1 ) )
					print( 2, i, 2, i + 1 );
			for( int i = 2;i <= n - 2;i ++ ) {
    
    
				//pink
				print( i, 1, i + 1, 1 );
				print( i, m, i + 1, m );
				if( i & 1 ) {
    
    
					//grey
					print( i, m - 1, i + 1, m - 1 );
					//orange
					for( int j = 1;j < m;j ++ )
						print( i, j, i, j + 1 );
					//purple
					for( int j = 1;j < m;j ++ )
						print( i + 1, j, i + 1, j + 1 );
				}
				else {
    
    
					//black
					for( int j = 2;j <= m - 2;j ++ )
						print( i, j, i + 1, j );
				}
			}
			//red
			print( n, 1, n - 1, 1 );
			print( n, 1, n - 1, 2 );
			print( n - 1, 1, n - 1, 2 );
			print( n, 2, n - 1, 3 );
			print( n, 3, n - 1, 3 );
			print( n, m, n - 1, m - 1 );
			//yellow
			for( int i = 1;i < m;i ++ )
				print( n, i, n, i + 1 );
			//green
			for( int i = 4;i <= m;i ++ )
				print( n, i, n - 1, i );
			//blue
			for( int i = 4;i <= m;i ++ )
				if( ! ( i & 1 ) )
					print( n - 1, i, n - 1, i + 1 );
		}
		else {
    
    
			//red
			print( 1, 1, 2, 2 );
			print( 2, 1, 2, 2 );
			print( 2, 3, 2, 4 );
			print( 1, m, 2, m - 1 );
			//yellow
			for( int i = 1;i < m;i ++ )
				print( 1, i, 1, i + 1 );
			//green
			for( int i = 1;i <= m;i ++ )
				print( 1, i, 2, i );
			//blue
			for( int i = 4;i <= m;i ++ )
				if( ! ( i & 1 ) )
					print( 2, i, 2, i + 1 );
			for( int i = 2;i <= n - 2;i ++ ) {
    
    
				//pink
				print( i, 1, i + 1, 1 );
				print( i, m, i + 1, m );
				if( i & 1 ) {
    
    
					//grey
					print( i, 2, i + 1, 2 );
					print( i, 4, i + 1, 4 );
					print( i, m - 1, i + 1, m - 1 );
					//orange
					for( int j = 1;j < m;j ++ )
						print( i, j, i, j + 1 );
					//purple
					for( int j = 1;j < m;j ++ )
						print( i + 1, j, i + 1, j + 1 );
				}
				else {
    
    
					//black
					print( i, 3, i + 1, 3 );
					for( int j = 5;j <= m - 2;j ++ )
						print( i, j, i + 1 , j);
				}
			}
			//red
			print( n, 1, n - 1, 2 );
			print( n - 1, 1, n - 1, 2 );
			print( n - 1, 3, n - 1, 4 );
			print( n, m, n - 1, m - 1 );
			//yellow
			for( int i = 1;i < m;i ++ )
				print( n, i, n, i + 1 );
			//green
			for( int i = 1;i <= m;i ++ )
				print( n, i, n - 1, i );
			//blue
			for( int i = 4;i <= m;i ++ )
				if( ! ( i & 1 ) )
					print( n - 1, i, n - 1, i + 1 );
		}
	}
}

int main() {
    
    
	freopen( "nmd.in", "r", stdin );
	freopen( "nmd.out", "w", stdout );
	scanf( "%d", &T );
	while( T -- ) {
    
    
		scanf( "%d %d %d", &n, &m, &d );
		if( ( d > 3 ) || ( ( d & 1 ) && ( n & 1 ) && ( m & 1 ) ) )
			printf( "-1\n" );
		else if( d == 1 )
			subtask1();
		else if( n == 1 || m == 1 )
			printf( "-1\n" );
		else if( d == 2 )
			subtask2();
		else if( n == 2 || m == 2 )
			printf( "-1\n" );
		else if( n == 3 || m == 3 )
			subtask3_0();
		else
			subtask3_1();
		flag = 0;
	}
	return 0;
}