SequenceSums | Topcoder Archive

Problem Statement

Given a number N and a length L, find the shortest list of at least L consecutive non-negative integers whose sum is N. If the length of that list is 100 or smaller, return the sequence as a int[] in ascending order. If there is no such sequence or its length is larger than 100, return { }.

Definition

Class:: SequenceSums
Method:: sequence
Parameters:: int, int
Returns:: int[]
Method signature:: int[] sequence(int N, int L)
(be sure your method is public)

Constraints

N will be between 1 and 1000000000, inclusive.
L will be between 2 and 100, inclusive.

Examples

```
18
```
```
2
```
```
Returns: {5, 6, 7 }
```
18 can be expressed as 5 + 6 + 7 or 3 + 4 + 5 + 6. Both of these lists contain more than 2 elements, so you should return the shortest among them.
```
18
```
```
4
```
```
Returns: {3, 4, 5, 6 }
```
Now the correct answer is 3 + 4 + 5 + 6 because 5 + 6 + 7 contains less than 4 elements.
```
18
```
```
5
```
```
Returns: { }
```
Both possible presentations of 18 contain less than 5 elements, so there's no answer for this case.

Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

1000000000

Returns: {199999998, 199999999, 200000000, 200000001, 200000002 }

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