## Description

In this homework we will work with a variation on Star Battles, however we will modify one of the rules. As

such, you should read the entire handout carefully. Star Battles in various forms have seen some popularity,

so there is lots of material available online.

You may not search for, study, or use any outside code related to

Star Battles (or variants of Star Battles). You are welcome to find additional puzzles to experiment with and

try to solve by hand. Some examples of puzzles are “Trees” (S=1, uses trees instead of stars as a symbol),

“Two Not Touch” (S=2), and more generally “Star Battles“ (S=1, S=2, S=3 examples).

The basic goal is to consider a two dimensional grid in which each square belongs to exactly one contiguous

group of squares. We will refer to these groups as zones. Some puzzles use background colors to make this

more clear, we will use single letter labels for our zones (see Input File) below.

The goal in our version is

that for a positive integer S, we should place stars (we will use @ instead) such that:

1. Each zone should have exactly S stars.

2. No two stars can be adjacent (touching), not even diagonally!

3. Each row can have up to S stars in it.

4. Each column can have up to S stars in it.

## Star Battle Arguments

Your program will accept five command line arguments.

Execution looks like: ./a.out [input file] [output file] [stars per zone] [output mode] [solution mode]

Input File

The input file describes the puzzle.

The first two integers are the number of rows and then number of

columns. Next that, we describe one zone at a time by first giving the label (letter) for zone and the number

of squares in the zone. After each label and square count, the file contains a series of (x,y) coordinates for

the zone. We define (0, 0) as the bottom left of the puzzle.

You can assume zones always have at least 1

square, and that every input has at least 1 zone.

The input file custom1.txt and a visualization of the puzzle’s initial state is:

4 3

L 6

0 0

1 0

0 1

1 1

0 2

1 2

X 6

2 0

2 1

2 2

0 3

1 3

2 3

= Zone L

= Zone X

Output Mode

The output mode will either be count in which case you will only print the number of solutions you found

(just the first line of output from the example in the section below), or print in which case you should print

the count and print all solutions.

Solution Mode

The solution mode will either be one solution meaning you should only find up to one solution, or it will be

all solutions meaning you should find all solutions that satisfy the inputs.

Output Formatting

Partial output for the custom1.txt puzzle with S = 1 is:

Number of solutions: 17

Solution 1:

LLX

LL@

@LX

XXX

Solution 2:

LLX

L@X

LLX

XX@

[see out_custom1_1_all.txt for full output]

To ensure full credit on the homework server, please format your solution exactly as shown above. Solutions

may appear in any order, but the first line must start with Number of solution(s): then a space and the

number of solutions. Each solution should start with a line that starts with Solution followed by one row

of the grid per line, with (0, 0) being located in the bottom left. For any square that has a star, you should

print @. For all other squares, you should print the letter of the zone the square belongs to.

## Additional Requirements: Recursion, Order Notation, & Extra Puzzles

You must use recursion in a non-trivial way in your solution to this homework. As always, we recommend you

work on this program in logical steps. Partial credit will be awarded for each component of the assignment.

Your program should do some error checking when reading in the input to make sure you understand the

file format.

IMPORTANT NOTE: This problem is computationally expensive, even for medium-sized puzzles

with too much freedom! Be sure to create your own simple test cases as you debug your program.

To help with runtime, your program should be written to do the three following things (also discussed in the

HW6 Discussion lecture videos):

1. Start with the smallest zones first, and work up to the bigger zones in a puzzle

2. Stop considering a partial solution if we’ve seen it before (keep a history of states)

3. Stop considering a partial solution if it is no longer solveable

To get started, we recommend starting by solving sporcle1.txt first, since for S = 1, only one solution

exists. After that, you may either want to move to twonot1.txt to handle S > 1, or you may want to move

to custom1.txt (Still S = 1 but has many solutions).

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Once you have finished your implementation, analyze the performance of your algorithm using order notation.

What important variables control the complexity of a particular problem? In your README.txt file write

a concise paragraph (< 200 words) justifying your answer. Also include a simple table summarizing the

running time and number of solutions found by your program on each of the provided examples.

You should include 1-3 new puzzles that either helped you test corner cases or experiment with the running

time of your program. Make sure to describe these puzzles in your README.

You can use any technique we have covered in Lectures 1-14, Homework 1-5, and Lab 1-7. This means you

cannot use STL pair, map, set, etc. on this homework assignment.

You must do this assignment on your own, as described in the “Collaboration Policy & Academic Integrity”

handout. If you did discuss this assignment, problem solving techniques, or error messages, etc. with anyone,

please list their names in your README.txt file.

NOTE: If you earn 7 points on the homework submission server for tests 3 through 10 by 11:59pm on

Wednesday, March 16, you will earn a one day extension on HW6.

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