NiceTable | Topcoder Archive

Problem Statement

You are given a String[] t that describes a rectangular table of zeroes and ones. Each character in t is either '0' or '1'.

We say that a table is nice if there are two sequences x, y of zeroes and ones such that for each valid pair of indices i, j we have t[i][j] = x[i] xor y[j].

Some technical remarks:

The number of elements in x should be equal to the number of rows of the table, i.e., the number of elements in t.
The number of elements in y should be equal to the number of columns of the table, i.e., the length of each string in t.
The operation xor (exclusive or) is defined as follows: 0 xor 0 = 0, 1 xor 1 = 0, 0 xor 1 = 1, and 1 xor 0 = 1.

Verify whether the given table is nice. Return "Nice" if it is nice and "Not nice" otherwise. Note that the return value is case-sensitive.

Definition

Class:: NiceTable
Method:: isNice
Parameters:: String[]
Returns:: String
Method signature:: String isNice(String[] t)
(be sure your method is public)

Constraints

t will contain between 1 and 5 elements, inclusive.
Each element of t will contain between 1 and 5 characters, inclusive.
All elements of t will contain the same number of characters.
Each element of t will consist only of characters '0' and '1'.

Examples

```
{"01",
 "10"}
```
```
Returns: "Nice"
```
One valid choice is to choose x = y = {1, 0}.
```
{"01",
 "11"}
```
```
Returns: "Not nice"
```
Assume that t is nice. The sequences x and y have to satisfy the following constraints: x[0] xor y[0] = 0 x[0] xor y[1] = 1 x[1] xor y[0] = 1 x[1] xor y[1] = 1 From the first constraint we see that x[0] = y[0]. From the second and the third constraint we can then derive that we must also have x[1] = y[1]. But then the fourth constraint is not satisfied, which is a contradiction. Therefore, this t is not nice.
```
{"0100",
 "1011",
 "0100"}
```
```
Returns: "Nice"
```
Here, one valid choice is x = {1, 0, 1} and y = {1, 0, 1, 1}.

{"11",
 "10",
 "11",
 "11",
 "11"}

Returns: "Not nice"

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