RelationClassifier | Topcoder Archive

Problem Statement

Weiwei is studying math. Unfortunately, math is very hard for him. Today, the teacher asked Weiwei to determine if a relation is a bijection or not.

Formally, a relation is a set of ordered pairs of elements. The teacher gave Weiwei one such relation. You are also given a description of this relation: int[]s domain and range. For each valid i, the relation contains the ordered pair (domain[i], range[i]).

Let X be the set of elements that appear at least once in domain. Similarly, let Y be the set of elements that appear at least once in range. We say that an element x of X is paired to an element y of Y if the relation contains the ordered pair (x, y).

We will say that our relation is a bijection if each element of X is paired to exactly one element of Y, and each element of Y is paired to exactly one element of X.

If Weiwei's relation is a bijection, return "Bijection" (quotes for clarity). Otherwise, return "Not". Note that the return value is case-sensitive.

Definition

Class:: RelationClassifier
Method:: isBijection
Parameters:: int[], int[]
Returns:: String
Method signature:: String isBijection(int[] domain, int[] range)
(be sure your method is public)

Constraints

domain will contain between 1 and 10 elements, inclusive.
range will contain the same number of elements as domain.
Each element of domain and range will be between 1 and 100, inclusive.
No two pairs (domain[i], range[i]) will be identical.

Examples

```
{1, 1}
```
```
{2, 3}
```
```
Returns: "Not"
```
Since 1 in X is paired with both 2 and 3 in Y, the given relation is not a bijection.
```
{4, 5}
```
```
{2, 2}
```
```
Returns: "Not"
```
Since both 4 and 5 in X are paired with 2 in Y, the given relation is not a bijection.
```
{1}
```
```
{2}
```
```
Returns: "Bijection"
```
A single ordered pair is always a bijection.

{1, 2, 3, 4, 5}

{1, 2, 3, 4, 5}

Returns: "Bijection"

{14, 12, 10, 13, 20, 18, 9, 17, 14, 9}

{18, 6, 8, 15, 2, 14, 10, 13, 13, 15}

Returns: "Not"

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