# `gno.land/p/moul/x/daily/disjointset/v0`

**Union-find (disjoint-set forest)** — `New`, `Find`, `Union`, `Connected`,
`Size`, `Groups`, `Partition`, `MaxN`.

Tracks a partition of `[0, n)` into disjoint groups and answers "same group?" in
near-constant time.

```go
import "gno.land/p/moul/x/daily/disjointset/v0"

d := disjointset.New(10)
d.Union(0, 1)
d.Union(1, 3)
d.Connected(0, 3)   // true
d.Groups()          // 8
d.Partition()       // [[0 1 3] [2] [4] ...]
```

**Both optimisations, because they only work together:** path compression
flattens the tree on every `Find`, union by rank keeps the shallower tree under
the deeper one. With both, operations are O(α(n)) — inverse Ackermann,
effectively constant. With neither, a chain of unions degrades to O(n) per
query, which on chain is the difference between a cheap call and running out of
gas. `Find` compresses **iteratively**: a deep chain would otherwise risk the
call stack.

`Partition` returns groups sorted ascending and ordered by their smallest
member, so the result is **identical regardless of the order unions were
applied** — that determinism is what makes it safe to put in a `Render`.

Out-of-range indices return `-1`/`false`/`0` rather than panicking, and are
connected to nothing — not even to themselves.

**Live demo:** [`r/moul/x/daily/disjointsetdemo`](https://github.com/moul/gno-contracts/tree/main/r/moul/x/daily/disjointsetdemo/v0)
· render it at [`/r/moul/x/daily/disjointsetdemo/v0`](https://gno.land/r/moul/x/daily/disjointsetdemo/v0).

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Part of **[moul/gno-contracts](https://github.com/moul/gno-contracts)** — moul's versioned gno.land contracts. See the repository for the full catalog, build/test tooling, and usage.

> 🧪 **Highly experimental — potentially vibe-coded.** Not audited; may break, change, or be removed at any time. Do not use with anything of value. Full disclaimer: [DISCLAIMER](https://github.com/moul/gno-contracts/blob/main/DISCLAIMER.md).

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