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CS 4613 Project 2

 CS 4613 E. K. Wong

Project 2: Futoshiki Spring 2020
Total number of points = 100. 
Project Description: Design and implement a program to solve 5 × 5 Futoshiki puzzles. The 
rules of the game are:
• The game board consists of 5 × 5 cells. Some of the cells already have numbers (1 to 5) 
assigned to them and there are inequality signs (< or >) between some of the cells (See 
Figure 1.)
• The goal is to find assignments (1 to 5) for the empty cells such that the inequality 
relationships between all pairs of adjacent cells with an inequality sign between them are 
satisfied. In addition, a digit can only appear once in every row and column; that is, the 
digits in every row and column must be different from each other (See Figure 2.) 
 
 
 
 
 
 Figure 1. Initial game board Figure 2. Solution
 
As the first step in your program, use Forward Checking to reduce the domain of empty cells, based 
on the values of cells that already have a number. If an empty cell has only one value left in its 
domain after domain reduction, you can repeat Forward Checking on the cell’s neighbors, and so 
on. If any empty cell has an empty domain after applying Forward Checking, then the puzzle does 
not have a solution and the program can stop here. Next, use the Backtracking Algorithm for CSPs
(in Figure 5 on page 3) to solve the puzzle. Implement the function SELECT-UNASSIGNED￾VARIABLE in the algorithm by using the most constrained variable (or minimum remaining values) 
heuristic, and in case of a tie, use the most constraining variable (or degree) heuristic as tie breaker.
If there are more than one variables left after applying the most constraining variable heuristic, you 
can arbitrarily choose a variable. There is no need to implement the least constraining value 
heuristic in the ORDER-DOMAIN-VALUES function; instead, simply order the domain values in 
increasing order (from 1 to 5.) To make it easier for you to implement the program, you do not 
have to implement the INFERENCE function inside the Backtracking Algorithm. 
Your program will read in values from an input text file and produce an output text file that contains 
the solution. The input file contains 16 rows (or lines) of integers. The first five rows contain the 
initial cell values of the game board, with each row containing five integers, ranging from 0 to 5.
Digit “0” indicates a blank cell. This is followed by a blank line. The next five rows contain the 
inequalities between horizontally-adjacent cells. A value of 0 indicates no inequality between two 
cells. This is followed by a blank line. The next four rows contain the inequalities between 
5
2
1
2 3 1 4 5
3 5 2 1 4
5 1 4 3 2
1 4 5 2 3
4 2 3 5 1
CS 4613 E. K. Wong
Project 2: Futoshiki Spring 2020
vertically-adjacent cells. Again, a value of 0 indicates no inequality between two cells. The input 
file for the initial game board in Figure 1 is as shown in Figure 3 below. The output file contains
five rows (or lines) of integers, representing the solution. Each row contains five integers, ranging 
from 1 to 5, separated by blanks. The output file (solution) for the initial game board in Figure 1 is 
as shown in Figure 4 below. 
Testing your program: I will provide three input test files on NYU Classes for you to test your 
program.
Recommended languages: Python, C++/C and Java. If you would like to use a different language, 
send me an email first.
Submit on NYU Classes by due date:
1. A text file that contains the source code. Put comments in your source code to make it easier 
for someone else to read your program. Points will be taken off if you do not have comments 
in your source code.
2. The output text files generated by your program. Name your output files Output1.txt, 
Output2.txt and Output3.txt.
3. A PDF file that contains instructions on how to run your program. If your program requires 
compilation, instructions on how to compile your program should also be provided. Also, copy 
and paste the output text files and your source code onto the PDF file (to make it easier for us 
to grade your project.) This is in addition to the source code file and output files that you have 
to submit separately (as described in 1 and 2 above.)
0 0 0 0 0
0 0 0 0 0
5 0 0 0 0
0 0 0 2 0
0 0 0 0 1
0 > 0 0
0 0 0 0
0 0 > 0
0 0 0 0
0 0 < 0
^ ^ 0 0 0
0 0 0 0 0
0 0 0 0 0
0 v 0 0 0 
Figure 3. Input file for the initial game board in Figure 1. Digit 0 indicates a blank cell. > and 
< are the greater than and less than characters on the keyboard. ^ is upper case 6 and v is the lower 
case letter v on the keyboard.
CS 4613 E. K. Wong
Project 2: Futoshiki Spring 2020
2 3 1 4 5
3 5 2 1 4
5 1 4 3 2
1 4 5 2 3
4 2 3 5 1
Figure 4. Output file containing the solution for the initial game board in Figure 1.
Figure 5. The Backtracking Algorithm for CSPs.
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