SumK | Topcoder Archive

Problem Statement

Some numbers can be expressed as the sum of k consecutive numbers. 9 = -1 + 0 + 1 + 2 + 3 + 4 so 9 can be expressed as the sum of 6 consecutive numbers. Your program will be given a collection of values and a positive k, and it will report how many of the values in the collection could be expressed as the sum of k consecutive numbers.

Definition

Class:: SumK
Method:: count
Parameters:: int, int[]
Returns:: int
Method signature:: int count(int k, int[] values)
(be sure your method is public)

Notes

If a value is repeated, count it each time it appears if it is a sum of k.
Values may be negative or zero, but k will be positive.

Constraints

k is between 1 and 1,000,000,000 (inclusive)
each element in values is between -1,000,000,000 and 1,000,000,000 (inclusive)
the number of elements in values is between 0 and 50 (inclusive)

Examples

```
3
```
```
{-987,5,0}
```
```
Returns: 2
```
-987 = -330 + -329 + -328, 5 is not the sum of 3 consecutive values, 0 = -1 + 0 + 1
```
1000
```
```
{0,-500,499500,499501,17,-500}
```
```
Returns: 3
```
-500 + -499 + ... + 499 = -500, 0 + 1 + ... + 999 = 499500, and neither 499501 nor 17 nor 0 can be expressed as the sum of 1000 consecutive values. (-500 is counted twice since it appears twice in values.)
```
1
```
```
{3,4,5,-1000000000}
```
```
Returns: 4
```
Each value is the sum of itself
```
2
```
```
{}
```
```
Returns: 0
```
```
2
```
```
{-999999999}
```
```
Returns: 1
```

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