count-unreachable-pairs-of-nodes-in-an-undirected-graph

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Algorithms

You are given an integer <code>n</code>. There is an undirected graph with <code>n</code> nodes, numbered from <code>0</code> to <code>n - 1</code>. You are given a 2D integer array <code>edges</code> where <code>edges[i] = [ai, bi]</code> denotes that there exists an undirected edge connecting nodes <code>ai</code> and <code>bi</code>.

Return the number of pairs of different nodes that are unreachable from each other.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-3.png" style="width: 267px; height: 169px;" />
<pre>
Input: n = 3, edges = [[0,1],[0,2],[1,2]]
Output: 0
Explanation: There are no pairs of nodes that are unreachable from each other. Therefore, we return 0.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-2.png" style="width: 295px; height: 269px;" />
<pre>
Input: n = 7, edges = [[0,2],[0,5],[2,4],[1,6],[5,4]]
Output: 14
Explanation: There are 14 pairs of nodes that are unreachable from each other:
[[0,1],[0,3],[0,6],[1,2],[1,3],[1,4],[1,5],[2,3],[2,6],[3,4],[3,5],[3,6],[4,6],[5,6]].
Therefore, we return 14.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= edges.length &lt;= 2 * 105</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= ai, bi &lt; n</code></li>
	<li><code>ai != bi</code></li>
	<li>There are no repeated edges.</li>
</ul>

countPairs

Count Unreachable Pairs of Nodes in an Undirected Graph

Number of Islands

number-of-islands

岛屿数量

Depth-First Search

Breadth-First Search

Union Find

Graph

给你一个整数&nbsp;<code>n</code>&nbsp;，表示一张&nbsp;无向图&nbsp;中有 <code>n</code>&nbsp;个节点，编号为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;。同时给你一个二维整数数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [ai, bi]</code>&nbsp;表示节点&nbsp;<code>ai</code> 和&nbsp;<code>bi</code>&nbsp;之间有一条&nbsp;无向&nbsp;边。

请你返回 无法互相到达&nbsp;的不同 点对数目&nbsp;。

&nbsp;

示例 1：

<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-3.png" style="width: 267px; height: 169px;">

<pre>输入：n = 3, edges = [[0,1],[0,2],[1,2]]
输出：0
解释：所有点都能互相到达，意味着没有点对无法互相到达，所以我们返回 0 。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-2.png" style="width: 295px; height: 269px;">

<pre>输入：n = 7, edges = [[0,2],[0,5],[2,4],[1,6],[5,4]]
输出：14
解释：总共有 14 个点对互相无法到达：
[[0,1],[0,3],[0,6],[1,2],[1,3],[1,4],[1,5],[2,3],[2,6],[3,4],[3,5],[3,6],[4,6],[5,6]]
所以我们返回 14 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= edges.length &lt;= 2 * 105</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= ai, bi &lt; n</code></li>
	<li><code>ai != bi</code></li>
	<li>不会有重复边。</li>
</ul>