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

$T2$

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 ) ) {//redprint( 1, 1, 2, 2 );print( n, 1, n, 2 );//yellowfor( int i = 1;i < n;i ++ )print( i, 1, i + 1, 1 );//bluefor( int i = 3;i <= n;i ++ )for( int j = 2;j < m;j ++ )print( i, j, i, j + 1 );//greenfor( int i = 3;i <= n;i ++ )if( ( n - i + 1 ) & 1 )print( i, m, i - 1, m );elseprint( i, 2, i - 1, 2 );//pinkfor( int i = 2;i <= m;i ++ )print( 1, i, 2, i ); //orangefor( int i = 2;i < m;i ++ )if( i & 1 )print( 2, i, 2, i + 1 );elseprint( 1, i, 1, i + 1 );} else {if( n & 1 ) swap( n, m ), flag = 1;//redprint( 1, 1, 1, 2 );print( n, 1, n, 2 );//yellowfor( int i = 1;i < n;i ++ )print( i, 1, i + 1, 1 );//bluefor( int i = 1;i <= n;i ++ )for( int j = 2;j < m;j ++ )print( i, j, i, j + 1 );//greenfor( int i = 1;i < n;i ++ )if( i & 1 )print( i, m, i + 1, m );elseprint( 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 {//yellowprint( 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 );//greenfor( int i = 5;i <= m - 4;i ++ )print( 1, i, 2, i ), print( 2, i, 3, i );//pinkfor( int i = 5;i <= m - 4;i ++ )if( i & 1 )print( 2, i, 2, i + 1 );//blueprint( 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 ) ) {//redprint( 1, 1, 2, 2 );print( 1, m, 2, m - 1 );//yellowfor( int i = 1;i < m;i ++ )print( 1, i, 1, i + 1 );//greenfor( int i = 1;i <= m;i ++ )print( 1, i, 2, i );//bluefor( int i = 1;i <= m;i ++ )if( i & 1 )print( 2, i, 2, i + 1 );for( int i = 2;i <= n - 2;i ++ ) {//pinkprint( i, 1, i + 1, 1 );print( i, m, i + 1, m );if( i & 1 ) {//greyprint( i, 2, i + 1, 2 );print( i, m - 1, i + 1, m - 1 );//orangefor( int j = 1;j < m;j ++ )print( i, j, i, j + 1 );//purplefor( int j = 1;j < m;j ++ )print( i + 1, j, i + 1, j + 1 );}else {//blackfor( int j = 3;j <= m - 2;j ++ )print( i, j, i + 1, j );}}//redprint( n, 1, n - 1, 2 );print( n, m, n - 1, m - 1 );//yellowfor( int i = 1;i < m;i ++ )print( n, i, n, i + 1 );//greenfor( int i = 1;i <= m;i ++ )print( n, i, n - 1, i );//bluefor( 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 ) {//redprint( 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 );//yellowfor( int i = 1;i < m;i ++ )print( 1, i, 1, i + 1 );//greenfor( int i = 4;i <= m;i ++ )print( 1, i, 2, i );//bluefor( int i = 4;i <= m;i ++ )if( ! ( i & 1 ) )print( 2, i, 2, i + 1 );for( int i = 2;i <= n - 2;i ++ ) {//pinkprint( i, 1, i + 1, 1 );print( i, m, i + 1, m );if( i & 1 ) {//greyprint( i, m - 1, i + 1, m - 1 );//orangefor( int j = 1;j < m;j ++ )print( i, j, i, j + 1 );//purplefor( int j = 1;j < m;j ++ )print( i + 1, j, i + 1, j + 1 );}else {//blackfor( int j = 2;j <= m - 2;j ++ )print( i, j, i + 1, j );}}//redprint( 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 );//yellowfor( int i = 1;i < m;i ++ )print( n, i, n, i + 1 );//greenfor( int i = 4;i <= m;i ++ )print( n, i, n - 1, i );//bluefor( int i = 4;i <= m;i ++ )if( ! ( i & 1 ) )print( n - 1, i, n - 1, i + 1 );}else {//redprint( 1, 1, 2, 2 );print( 2, 1, 2, 2 );print( 2, 3, 2, 4 );print( 1, m, 2, m - 1 );//yellowfor( int i = 1;i < m;i ++ )print( 1, i, 1, i + 1 );//greenfor( int i = 1;i <= m;i ++ )print( 1, i, 2, i );//bluefor( int i = 4;i <= m;i ++ )if( ! ( i & 1 ) )print( 2, i, 2, i + 1 );for( int i = 2;i <= n - 2;i ++ ) {//pinkprint( i, 1, i + 1, 1 );print( i, m, i + 1, m );if( i & 1 ) {//greyprint( i, 2, i + 1, 2 );print( i, 4, i + 1, 4 );print( i, m - 1, i + 1, m - 1 );//orangefor( int j = 1;j < m;j ++ )print( i, j, i, j + 1 );//purplefor( int j = 1;j < m;j ++ )print( i + 1, j, i + 1, j + 1 );}else {//blackprint( i, 3, i + 1, 3 );for( int j = 5;j <= m - 2;j ++ )print( i, j, i + 1 , j);}}//redprint( 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 );//yellowfor( int i = 1;i < m;i ++ )print( n, i, n, i + 1 );//greenfor( int i = 1;i <= m;i ++ )print( n, i, n - 1, i );//bluefor( 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();elsesubtask3_1();flag = 0;}return 0;
}