Number Cross

1. About the Game (or Number Cross)

1. This puzzle consists of a NxM grid where every cells are labeled with a positive integer.

2. The goal of the game is to determine the color of each cells either Black or White.

3. The labeled numbers on top (or each column) is the total value of the black cells within the column.

4. The labeled numbers on right (or end of each row) is the total value of the white cells within the row.

5. Each cells has a value between 1 to 9

6. There are no initial colors given.

For example:

8 1
5 2 2
6 1 6
3 4 4

1. The number on top of 1st column represents sum of the black cells in {5,6,3}. Which we can assume 5 and 3 are black cells.
2. The second number is 1 that we know among {2,1,4}, 1 is the only black cells. so the black cells are {5,1,3} and others are white cells.

2. How to Run

1. Needs to install z3

2. Designed for linux/unix environment

3. Inputs are only fed by standard input

./a.out < input

3. Input

a. the name of the file isn't important

b. but the format should keep following:

i. first row has to indicate the sum of black cells on each column

ii. the last cell of each row (excluding the first row) should indicate the sum of white cells on each row.

iii. there should be no line feed after last line. (please keep this)

4. Output/Results

a. If it is unsatisfiable result, the program will provide a error message.

b. A file name 'formula' will be created, when program is executed. this file contains z3 input details.

c. A file name 'output' will be created, when program is succesfully runned. this file will show a table of 0 and 1, which each of them representing white and black cells.

5. Warnings

a. error will occur when there is a additional line feed at the end of the program.

b. Error, if z3 is not installed.

6. Quick Tryout

1. gcc hw1.c
2. ./a.out < input

Or

1. ./Makefile
2. ./answer.out < input