# 99 questions/Solutions/62B

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Revision as of 06:35, 22 November 2010 by Drb226 (talk | contribs) (rewrite a little shorter and (imho) clearer)

Collect the nodes at a given level in a list

A node of a binary tree is at level N if the path from the root to the node has length N-1. The root node is at level 1. Write a predicate atlevel/3 to collect all nodes at a given level in a list.

```
atlevel :: Tree a -> Int -> [a]
atlevel Empty _ = []
atlevel (Branch v l r) n
| n == 1 = [v]
| n > 1 = atlevel l (n-1) ++ atlevel r (n-1)
| otherwise = []
```

Another possibility is to decompose the problem:

```
levels :: Tree a -> [[a]]
levels Empty = repeat []
levels (Branch a l r) = [a] : zipWith (++) (levels l) (levels r)
atlevel :: Tree a -> Int -> [a]
atlevel t n = levels t !! (n-1)
```