# Minimum Height Trees

{% embed url="<https://leetcode.com/problems/minimum-height-trees>" %}

### Problem

> A tree is an undirected graph in which any two vertices are connected by *exactly* one path. In other words, any connected graph without simple cycles is a tree.
>
> Given a tree of `n` nodes labelled from `0` to `n - 1`, and an array of `n - 1` `edges` where `edges[i] = [ai, bi]` indicates that there is an undirected edge between the two nodes `ai` and `bi` in the tree, you can choose any node of the tree as the root. When you select a node `x` as the root, the result tree has height `h`. Among all possible rooted trees, those with minimum height (i.e. `min(h)`)  are called **minimum height trees** (MHTs).
>
> Return *a list of all **MHTs'** root labels*. You can return the answer in **any order**.
>
> The **height** of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
>
> &#x20;
>
> **Example 1:**
>
> ![](https://assets.leetcode.com/uploads/2020/09/01/e1.jpg)
>
> <pre data-overflow="wrap"><code>Input: n = 4, edges = [[1,0],[1,2],[1,3]]
> <strong>Output: [1]
> </strong><strong>Explanation: As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT.
> </strong></code></pre>
>
> **Example 2:**
>
> ![](https://assets.leetcode.com/uploads/2020/09/01/e2.jpg)
>
> <pre><code>Input: n = 6, edges = [[3,0],[3,1],[3,2],[3,4],[5,4]]
> <strong>Output: [3,4]
> </strong></code></pre>

### Pseudocode

```
- topo approach, trime all the leaves to find the core nodes
- need to review this solution
```

### Solution

```javascript
// from solutions
// https://leetcode.com/problems/minimum-height-trees/solutions/427802/javascript-bfs-solution/
var findMinHeightTrees = function (n, edges) {
  if (!edges || n < 2) return [0];
  let graph = [];
  // parse edges
  for (let [x, y] of edges) {
    graph[x] = graph[x] || [];
    graph[y] = graph[y] || [];
    graph[x].push(y);
    graph[y].push(x);
  }
  let leaves = [];
  // init leaf nodes
  graph.map((pts, i) => pts.length === 1 && leaves.push(i));
  while (n > 2) {
    n = n - leaves.length;
    let nxt_leaves = [];
    for (let leave of leaves) {
      // remove leaf node and itself in related nodes
      tmp = graph[leave].pop();
      graph[tmp].splice(graph[tmp].indexOf(leave), 1);
      // save new leaf node
      graph[tmp].length === 1 && nxt_leaves.push(tmp);
    }
    leaves = nxt_leaves;
  }
  return leaves;
};

```

### Time and Space Complexity

#### Time

* What did the code do
* Total -

#### Space

* What did the code do
* Total -


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://grind75-notes.gitbook.io/notes/week-7/minimum-height-trees.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.