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long_comps_topcoder  Problem Statement
Contest: 2007 TopCoder Collegiate Challenge Marathon Online Round 1
Problem: Scruffle

Problem Statement

    

Scruffle is a single player word game, played on a rectangular board. The goal of the game is to score as many point as possible by placing words on the board. The board contains obstacles in some of the cells; no word may be placed to overlap with one of these obstacles. The player is given a list of available words; each word may be placed on the board only once. A word may be placed horizontally or vertically and must read from left to right or top to bottom. A word may be placed such that it overlaps with an already placed word, in which case the overlapping letters of the words must be the same. A word may not go off the edge of the board. When placing a word, at least one of its letters must not overlap with any previously placed word.

Each letter is worth a specific amount of points.

  • The letters A, E, I, L, N, O, R, S, T and U is worth 1 point.
  • The letters D and G are worth 2 points.
  • The letters B, C, M and P are worth 3 points.
  • The letters F, H, V, W and Y are worth 4 points.
  • The letter K is worth 5 points.
  • The letters J and X are worth 8 points.
  • The letters Q and Z are worth 10 points.

Each cell of the board can contain one of the following:

  • # : The cell contains an obstacle, no word may overlap with this cell.
  • 0-9 : Letter multiplier. The score of the letter that is placed on this cell will be multiplied by the given number. Ex. If the cell contains a 5 and the player places a letter B on the cell, the score for that placement will be 5 * 3 = 15.
  • D : Double word multiplier. The score of the word placed over this cell will be multiplied by 2. The score of the letter placed on this cell will be just the letter points (Letter multiplier of 1.). If a word overlaps with more than one word multiplier, the word score will be cumulative. Ex. If the score of a word before applying the word multiplier is 12 and the word overlaps with 2 D’s, then the total score for the placement will be 12 * 2 * 2 = 48.
  • T : Triple word multiplier. The score of the word placed over this cell will be multiplied by 3. This multiplier works cumulatively with the double word multiplier.

The score for each word placement will be calculated independently from previously placed words. All letter and word multipliers that form part of the placement will be used in the calculation. Pseudo code for calculating the score of a word placement:

letterScore = 0
wordMultiplier = 1
for each letter in the word
	cell = cell where this letter will be placed
	if cell contains a D
		letterScore = letterScore + worth of letter
		wordMultiplier = wordMultiplier * 2
	else if cell contains a T
		letterScore = letterScore + worth of letter
		wordMultiplier = wordMultiplier * 3
	else
		letterScore = letterScore + worth of letter * letter multiplier of cell
	end 
score for placement = letterScore * wordMultiplier

You will play the game by writing a single method play. The play method will take a String[] that contains the definition of the board and a String[] that contains a list of all the available words. The method will be called only once. You must return a String[] that contains all your word placements. Each element contains a single placement. Words will be placed on the board in the same order as in your return. The format of a placement is the direction of the placement followed by the 0-based index of the word that must be placed, followed by the (x, y) 0-based position where the first letter of the word must be placed. The direction character must be a H for horizontal placement or a V for vertical placement. Ex. “H 10 5 3” indicates the horizontal placement of the word at index 10, and the placement starts at position (5, 3) of the board.

Your score for a test case will be the sum of all the scores for each placement. You will receive a score of 0 when you perform an invalid placement or when the method runs out of time. Your final score will be found by taking the sum over test cases of (your score)/(highest score).

Test case generation

All random values are computed uniformly and ranges are stated inclusively. The horizontal dimension X of the board will be chosen between 10 and 100. The vertical dimension Y of the board will be chosen between 10 and 100.

A fraction 0 <= B <= 0.2 of the cells are blocked with obstacles, a fraction 0 <= D <= 0.05 of the cells are doubles ('D'), and a fraction 0 <= T <= 0.02 of the cells are triples ('T'). All these cells are selected randomly, with a new random selection being made if a selected cell was already previously marked. The remaining cells are filled with numbers '0'-'9'.

The number of words W will be chosen between 10 and 10000. Words will then be randomly selected from the English dictionary. The same word may appear more than once in the list given to your method. See the notes section for a link to the words of our dictionary.

 

Definition

    
Class:Scruffle
Method:play
Parameters:String[], String[]
Returns:String[]
Method signature:String[] play(String[] board, String[] words)
(be sure your method is public)
    
 

Notes

-There are 50 non-example tests.
-The complete list of words can be downloaded from here. The words between length 1 and 8 were extracted.
-Each word will only contain uppercase characters between A and Z.
-Each word may be placed on the board only once.
 

Constraints

-The memory limit is 1024MB.
-The time limit is 30 seconds.
 

Examples

0)
    
5#17475928
9158971908
61662#6593
29#2909138
15950557T7
858912#029
098668#528
025121716#
9D31739229
##D683##74
Number of words=15
DOPAMINE
CUTISES
IMAGOS
COCOANUT
SOLECISM
GLOM
INBRED
DABSTERS
YARN
CRABBIER
HOPPLING
UNRIPPED
FUSIONS
DOPED
AGONY

The following placements results in a score of 802.

V 10 1 1 ( Placement score = 130 )

H 9 2 1 ( Placement score = 73 )

V 0 0 1 ( Placement score = 64 )

H 11 2 0 ( Placement score = 79 )

V 12 3 2 ( Placement score = 48 )

H 2 4 4 ( Placement score = 126 )

V 6 2 4 ( Placement score = 102 )

H 13 4 3 ( Placement score = 52 )

V 14 4 5 ( Placement score = 54 )

H 5 6 2 ( Placement score = 35 )

V 8 5 6 ( Placement score = 39 )

The resulting board looks like this:

.#UNRIPPED
DHCRABBIER
OO.F.#GLOM
PP#UDOPED.
APISIMAGOS
MLNIA.#...
IIBOGY#...
NNRNOA...#
EGESNR....
##D.YN##..
1)
    
45907606097855716D07
22402890009467790483
D89#4409987128989678
1377T90D832410496926
D866513417D673621357
40377191947836T24494
76873205#46981717311
146593608D04142D1886
709702200D7957680836
2948926139D647794687
Num of words=20
2)
    
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Number of words=10000
3)
    
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