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Competition Arena > RectangleAvoidingColoring

RectangleAvoidingColoring

Member SRM 485 · 2010-03-12 · by ivan_metelsky

Member SRM 485 · 2010-03-12 · by ivan_metelsky · Brute Force, Simple Math
Class Name: RectangleAvoidingColoring
Return Type: long
Method Name: count
Arg Types: (vector<string>)
Problem Statement

Problem Statement

There is an N x M board divided into 1 x 1 cells. The rows of the board are numbered from 0 to N-1, and the columns are numbered from 0 to M-1. The cell located in row r and column c has coordinates (r, c).

In a coloring of the board, each cell on the board is colored white or black. A coloring is called rectangle-avoiding if it is impossible to choose 4 distinct cells of the same color so that their centers form a rectangle whose sides are parallel to the sides of the board. In other words, a coloring is rectangle-avoiding if, for each a, b, c, and d with 0 <= a < b < N, 0 <= c < d < M, there is at least one white cell and at least one black cell among the cells (a, c), (a, d), (b, c) and (b, d).

You are given a String[] board representing a board. The j-th character of the i-th element of board represents cell (i, j), and it can be 'W', 'B' or '?'. Here, 'W' indicates a white cell, 'B' indicates a black cell and '?' indicates an uncolored cell. For each uncolored cell, you may choose to color it either white or black. Return the number of different rectangle-avoiding colorings that can be achieved. If it is impossible to achieve a rectangle-avoiding coloring, return 0.

Notes

  • Two colorings are different if there is a cell on the board that is colored white in one coloring and black in the other coloring.
  • The answer will always fit into a 64-bit signed integer data type.

Constraints

  • board will contain between 1 and 50 elements, inclusive.
  • Each element of board will contain between 1 and 50 characters, inclusive.
  • All elements of board will contain the same number of characters.
  • Each character in each element of board will be 'W', 'B' or '?'.
Examples
0)
{"??",
 "??"}
Returns: 14

Since each cell can be black or white, there are 2^4 = 16 ways to color this board. Of them, only 2 monochromatic colorings are not rectangle-avoiding, so the answer is 16 - 2 = 14.

1)
{"B?",
 "?B"}
Returns: 3

It is the same board as in previous example, but colors for some cells are already predefined. There are 4 ways to color the remaining cells and in one of them the board becomes completely black. Therefore the answer is 4 - 1 = 3.

2)
{"WW",
 "WW"}
Returns: 0

This board is already colored and the coloring is not rectangle-avoiding.

3)
{"??B??",
 "W???W",
 "??B??"}
Returns: 12
4)
{"??",
 "W?",
 "W?",
 "?W",
 "W?"}
Returns: 16

Submissions are judged against all 206 archived test cases, of which 5 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class RectangleAvoidingColoring with a public method long long count(vector<string> board) · 206 test cases · 2 s / 256 MB per case

Submitting as anonymous