# Talk:Tying the Knot

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There's a conceptually much simpler way build a circular structure, though it has a substantial performance overhead (n^2) the first time you run through the nodes:

```mkDLList list = head result where
(result, n) = (zipWith mknode list [0..], length list)
mknode x i  = DLList (result !! ((i - 1) `mod` n) ) x (result !! (i + 1 `mod` n) )
```

Since we already have the result - the list of all the relevant nodes - we just simply point to the items at the right points on the list. When we do it this way, it's obvious what is going on from just a basic understanding of laziness, then we see a huge waste of operations in the repeat list traversing, and look for some way to make it O(n). The trick, of course, being tying the knot.

With a slight tweak, this also serves as a simple method for defining arbitrary graphs, which is best given a different sort of optimization.

WarDaft 17:25, 11 April 2012 (UTC)