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Quoting Wikipedia :
"Sudoku is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes (also called blocks or regions) contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid."
The rules for an N2 X N2 sudoku are as follows :
- The board is consists of N2 rows and N2 columns.
- Numbers between 1 and N2(inclusive) are to be filled in each row such that :
- All numbers in each row are distinct.
- All numbers in each column are distinct.
- All numbers in the sub-matrix having rows from (i*N + 1) to(i + 1)*N, and columns from (j*N + 1) to (j + 1)*N both inclusive, should be distinct. 0 <= i,j <= N-1. Rows and columns are 1 indexed. Each such sub-matrix is called a "box" or "region".
For this problem, you are required to solve a general N2X N2 sudoku puzzle. Given a partially filled sudoku board, you have to fill it in as "perfect" a manner as possible.
The first line contains N,K.
The following K lines contain 3 numbers: x, y and d. 1 <= x,y,d <= N^2.
This means that a number d is present on the board at position (x,y)
2 <= N <= 30
0 <= K <= N4
At most 50% of the board will be covered at the start.
All positions (x,y) in the input will be unique.
The output consists of N2 rows having N2 numbers each. Each number should be between 1 and N2 (inclusive) and separated by a space. If the initial grid has a number d at position (x,y), then even the output should have the number d at position (x,y).
- For each row and every number K in the range 1 to N2 that is missing from the row, incurs a penalty of 1.
- For each column and every number K in the range 1 to N2 that is missing from the column, incurs a penalty of 1.
- Similary, for each box and every number K in the range 1 to N2 that is missing from the box, incurs a penalty of 1.
A box (as explained above) is a N X N square and the grid can be divided into N2 such non-overlapping boxes.
2 4 1 2 1 2 4 4 3 3 1 4 1 3
2 1 3 4 1 2 4 4 3 4 1 2 3 2 4 1
(0 + 1 + 0 + 0) + (1 + 1 + 1 + 1) + (2 + 2 + 1 + 1) = 11
|Time Limit:||3 sec|
|Source Limit:||50000 Bytes|
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