FractionCounting | Topcoder Archive

Problem Statement

Consider the following set (see notes for clarification):

  S = {  p/q  |   w <= p <= x,  y <= q <= z  }

Given w, x, y, and z return the number of distinct elements in S.

Definition

Class:: FractionCounting
Method:: howMany
Parameters:: int, int, int, int
Returns:: int
Method signature:: int howMany(int w, int x, int y, int z)
(be sure your method is public)

Notes

S is the set of all rational numbers whose numerators are between w and x inclusive, and whose denominators are between y and z inclusive.

Constraints

x and z will be between 1 and 100, inclusive.
w will be between 1 and x, inclusive.
y will be between 1 and z, inclusive.

Examples

```
1
```
```
1
```
```
1
```
```
1
```
```
Returns: 1
```
Only the value 1/1 is being considered.
```
1
```
```
10
```
```
1
```
```
1
```
```
Returns: 10
```
Here S contains the values 1,...,10.
```
1
```
```
2
```
```
1
```
```
2
```
```
Returns: 3
```
Here the values are 1/1, 1/2, 2/1, and 2/2. Since 2/2 = 1/1 the answer is 3.
```
2
```
```
4
```
```
2
```
```
4
```
```
Returns: 7
```
```
1
```
```
100
```
```
1
```
```
100
```
```
Returns: 6087
```

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