Find Minimum Diameter After Merging Two Trees
<p>There exist two <strong>undirected </strong>trees with <code>n</code> and <code>m</code> nodes, numbered from <code>0</code> to <code>n - 1</code> and from <code>0</code> to <code>m - 1</code>, respectively. You are given two 2D integer arrays <code>edges1</code> and <code>edges2</code> of lengths <code>n - 1</code> and <code>m - 1</code>, respectively, where <code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the first tree and <code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the second tree.</p>

<p>You must connect one node from the first tree with another node from the second tree with an edge.</p>

<p>Return the <strong>minimum </strong>possible <strong>diameter </strong>of the resulting tree.</p>

<p>The <strong>diameter</strong> of a tree is the length of the <em>longest</em> path between any two nodes in the tree.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3203.Find%20Minimum%20Diameter%20After%20Merging%20Two%20Trees/images/example11-transformed.png" /></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>We can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.</p>
</div>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3203.Find%20Minimum%20Diameter%20After%20Merging%20Two%20Trees/images/example211.png" />
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

<p><strong>Explanation:</strong></p>

<p>We can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>
	<li><code>edges1.length == n - 1</code></li>
	<li><code>edges2.length == m - 1</code></li>
	<li><code>edges1[i].length == edges2[i].length == 2</code></li>
	<li><code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>
	<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt; m</code></li>
	<li>The input is generated such that <code>edges1</code> and <code>edges2</code> represent valid trees.</li>
</ul>
Tree; Depth-First Search; Breadth-First Search; Graph
function minimumDiameterAfterMerge(edges1: number[][], edges2: number[][]): number {
    const d1 = treeDiameter(edges1);
    const d2 = treeDiameter(edges2);
    return Math.max(d1, d2, Math.ceil(d1 / 2) + Math.ceil(d2 / 2) + 1);
}

function treeDiameter(edges: number[][]): number {
    const n = edges.length + 1;
    const g: number[][] = Array.from({ length: n }, () => []);
    for (const [a, b] of edges) {
        g[a].push(b);
        g[b].push(a);
    }
    let [ans, a] = [0, 0];
    const dfs = (i: number, fa: number, t: number): void => {
        for (const j of g[i]) {
            if (j !== fa) {
                dfs(j, i, t + 1);
            }
        }
        if (ans < t) {
            ans = t;
            a = i;
        }
    };
    dfs(0, -1, 0);
    dfs(a, -1, 0);
    return ans;
}
