MagicalSquare | Topcoder Archive

Problem Statement

You are going to fill 9 strings into the cells of a 3x3 square. Rows of the square are numbered 0 to 2 from top to bottom, and columns of the square are numbered 0 to 2 from left to right. Let S[i][j] be the string you'll enter into the cell in row i, column j. The strings S[i][j] do not have to be distinct. It is also allowed to use empty strings.

You are given two String[]s rowStrings and columnStrings. For each i, the concatenation of strings in row i must be equal to rowStrings[i]. The same must hold for columns and columnStrings. Formally, the strings in the cells must satisfy the following conditions:

For all 0<=i<=2, S[i][0]+S[i][1]+S[i][2] = rowStrings[i].
For all 0<=j<=2, S[0][j]+S[1][j]+S[2][j] = columnStrings[j].

Here, '+' represents a string concatenation.

Return the number of ways in which the strings S[i][j] can be chosen so that all conditions are satisfied.

Definition

Class:: MagicalSquare
Method:: getCount
Parameters:: String[], String[]
Returns:: long
Method signature:: long getCount(String[] rowStrings, String[] columnStrings)
(be sure your method is public)

Constraints

rowStrings and columnStrings will each contain exactly 3 elements.
Each element of rowStrings will contain between 0 and 50 characters, inclusive.
Each element of columnStrings will contain between 0 and 50 characters, inclusive.
rowStrings and columnStrings will contain only lowercase letters ('a'-'z').

Examples

```
{"f", "o", "x"}
```
```
{"f", "o", "x"}
```
```
Returns: 1
```
The only valid way to choose the strings: --- --- --- | f | | | --- --- --- | | o | | --- --- --- | | | x | --- --- --- That is, S[0][0]="f", S[1][1]="o", S[2][2]="x", and all other S[i][j] are empty.
```
{"x", "x", "x"}
```
```
{"x", "", "xx"}
```
```
Returns: 3
```
These are the three valid possibilities: --- --- --- --- --- --- --- --- --- | x | | | | | | x | | | | x | --- --- --- --- --- --- --- --- --- | | | x | | x | | | | | | x | --- --- --- --- --- --- --- --- --- | | | x | | | | x | | x | | | --- --- --- --- --- --- --- --- ---
```
{"cd", "cd", "cd"}
```
```
{"dvd", "dvd", "dvd"}
```
```
Returns: 0
```
In this case there is no way to satisfy all conditions.

{"abab", "ab", "abab"}

{"abab", "ab", "abab"}

Returns: 11

{"qwer", "asdf", "zxcv"}

{"qaz", "wsx", "erdfcv"}

Returns: 1

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