ExactTreeEasy | Topcoder Archive

Problem Statement

You are given ints n and m. Construct any tree with exactly n nodes (labeled 0 through n-1) and exactly m leaves. For the given constraints on n and m a solution will always exist.

The return value should be a int[] containing a sequence of 2*(n-1) integers. If your tree has edges (a[0], b[0]), (a[1], b[1]), etc., the correct return value is the sequence {a[0], b[0], a[1], b[1], ...}. If there are multiple correct return values, you may return any of them.

Definition

Class:: ExactTreeEasy
Method:: getTree
Parameters:: int, int
Returns:: int[]
Method signature:: int[] getTree(int n, int m)
(be sure your method is public)

Notes

A tree is a connected acyclic graph. The leaf of a tree is a node of degree 1, i.e., a node that has exactly one outgoing edge.

Constraints

n will be between 3 and 50, inclusive.
m will be between 2 and n-1, inclusive.

Examples

```
4
```
```
2
```
```
Returns: {0, 1, 1, 2, 2, 3 }
```
We are supposed to construct a tree with 4 nodes and 2 leaves. One such tree is a simple path consisting of the edges 0-1, 1-2, and 2-3.
```
4
```
```
3
```
```
Returns: {0, 1, 1, 2, 1, 3 }
```
Now we have to construct a tree with 4 nodes and 3 leaves. The tree returned by our solution contains the edges 1-0, 1-2, and 1-3. The leaves are the nodes 0, 2, and 3.
```
3
```
```
2
```
```
Returns: {0, 1, 1, 2 }
```
```
5
```
```
3
```
```
Returns: {0, 1, 1, 2, 1, 3, 3, 4 }
```

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

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