C. Karen and Game
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

On the way to school, Karen became fixated on the puzzle game on her phone!

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  • row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row".
  • col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column".

If there are multiple optimal solutions, output any one of them.

Examples
input
Copy
3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1
output
Copy
4
row 1
row 1
col 4
row 3
input
Copy
3 3
0 0 0
0 1 0
0 0 0
output
Copy
-1
input
Copy
3 3
1 1 1
1 1 1
1 1 1
output
Copy
3
row 1
row 2
row 3
Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

Note that this is not the only solution; another solution, among others, is col 1col 2col 3.


题意:每次操作能使得一行或者一列都-1,给定一个矩阵n*m,问是否能使得所有元素都为0,如果不行,输出-1; 否则输出最小的操作数

思路:
判断每次操作是行减还是列减,看哪个贡献大就选哪个。
#include<bits/stdc++.h> #define PI acos(-1.0) using namespace std; typedef long long ll; const int N=2e5+5; const int MOD=1e9+9; const int INF=0x3f3f3f3f; int a[200][200],n,m; vector <pair<string,int> > ans; bool checkrow(int i,int j){ for(int jj=1;jj<=m;jj++) if(a[i][jj]==0) return false; return true; } bool checkcol(int i,int j){ for(int ii=1;ii<=n;ii++) if(a[ii][j]==0) return false; return true; } int main(void){ cin >>n >>m ; for(int i=1;i<=n;++i) for(int j=1;j<=m;j++) scanf("%d",&a[i][j]); for(int i=1;i<=n;i++){ for(int j=1;j<=m;j++){ if(a[i][j]==0) continue; while(a[i][j]){ bool row=checkrow(i,j); bool col=checkcol(i,j); if(row && col){ if(n>m){ for(int ii=1;ii<=n;ii++) a[ii][j]--; ans.push_back(make_pair("col",j)); } else{ for(int jj=1;jj<=m;jj++) a[i][jj]--; ans.push_back(make_pair("row",i)); } } else if(row && !col){ for(int jj=1;jj<=m;jj++) a[i][jj]--; ans.push_back(make_pair("row",i)); } else if(!row && col){ for(int ii=1;ii<=n;ii++) a[ii][j]--; ans.push_back(make_pair("col",j)); } else if(!row && !col) break; } } } for(int i=1;i<=n;i++){ for(int j=1;j<=m;j++){ if(a[i][j]!=0){ cout << -1 << endl; return 0; } } } cout <<(int) ans.size()<<endl; for(int i=0;i<(int)ans.size();++i){ cout << ans[i].first <<" "<<ans[i].second <<endl; } return 0; }