ArithmeticProgression | Topcoder Archive

Problem Statement

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In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2. An arithmetic sequence can always be represented as a_n=a0+n*d.

You will be given a sequence seq, where seq_i = [a_i+1] for some nondecreasing arithmetic sequence a (both indices are 0-based). [x] denotes the floor function (see Notes). The sequence a is defined as a0+i*d. Return the minimal possible value for d. If no possible value exists for d, return -1 instead.

Definition

Class:: ArithmeticProgression
Method:: minCommonDifference
Parameters:: int, int[]
Returns:: double
Method signature:: double minCommonDifference(int a0, int[] seq)
(be sure your method is public)

Notes

[x] denotes the floor function of x which returns the highest integer less than or equal to x. For example, [3.4] = 3, [0.6] = 0, [-1.2] = -2 and [-0.6] = -1.
Your return value must be accurate to within an absolute or relative tolerance of 1E-9.

Constraints

seq will contain between 0 and 50 elements, inclusive.
Each element of seq will be between -10^6 and 10^6, inclusive.
a0 will be between -10^6 and 10^6, inclusive.

Examples

```
0
```
```
{6, 13, 20, 27}
```
```
Returns: 6.75
```
```
1
```
```
{2, 3, 4, 5, 6}
```
```
Returns: 1.0
```
```
3
```
```
{}
```
```
Returns: 0.0
```
Since the sequence a is nondecreasing, d must be at least 0.
```
3
```
```
{3, 3, 3, 3, 4}
```
```
Returns: 0.2
```
```
1
```
```
{-3}
```
```
Returns: -1.0
```
```
0
```
```
{6, 14}
```
```
Returns: -1.0
```

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