Count Pairs Of Nodes
<p>You are given an undirected graph defined by an integer <code>n</code>, the number of nodes, and a 2D integer array <code>edges</code>, the edges in the graph, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an <strong>undirected</strong> edge between <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>. You are also given an integer array <code>queries</code>.</p>

<p>Let <code>incident(a, b)</code> be defined as the <strong>number of edges</strong> that are connected to <strong>either</strong> node <code>a</code> or <code>b</code>.</p>

<p>The answer to the <code>j<sup>th</sup></code> query is the <strong>number of pairs</strong> of nodes <code>(a, b)</code> that satisfy <strong>both</strong> of the following conditions:</p>

<ul>
	<li><code>a &lt; b</code></li>
	<li><code>incident(a, b) &gt; queries[j]</code></li>
</ul>

<p>Return <em>an array </em><code>answers</code><em> such that </em><code>answers.length == queries.length</code><em> and </em><code>answers[j]</code><em> is the answer of the </em><code>j<sup>th</sup></code><em> query</em>.</p>

<p>Note that there can be <strong>multiple edges</strong> between the same two nodes.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1700-1799/1782.Count%20Pairs%20Of%20Nodes/images/winword_2021-06-08_00-58-39.png" style="width: 529px; height: 305px;" />
<pre>
<strong>Input:</strong> n = 4, edges = [[1,2],[2,4],[1,3],[2,3],[2,1]], queries = [2,3]
<strong>Output:</strong> [6,5]
<strong>Explanation:</strong> The calculations for incident(a, b) are shown in the table above.
The answers for each of the queries are as follows:
- answers[0] = 6. All the pairs have an incident(a, b) value greater than 2.
- answers[1] = 5. All the pairs except (3, 4) have an incident(a, b) value greater than 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5, edges = [[1,5],[1,5],[3,4],[2,5],[1,3],[5,1],[2,3],[2,5]], queries = [1,2,3,4,5]
<strong>Output:</strong> [10,10,9,8,6]
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= edges.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n</code></li>
	<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>
	<li><code>1 &lt;= queries.length &lt;= 20</code></li>
	<li><code>0 &lt;= queries[j] &lt; edges.length</code></li>
</ul>
Graph; Array; Hash Table; Two Pointers; Binary Search; Counting; Sorting
class Solution:
    def countPairs(
        self, n: int, edges: List[List[int]], queries: List[int]
    ) -> List[int]:
        cnt = [0] * n
        g = defaultdict(int)
        for a, b in edges:
            a, b = a - 1, b - 1
            a, b = min(a, b), max(a, b)
            cnt[a] += 1
            cnt[b] += 1
            g[(a, b)] += 1

        s = sorted(cnt)
        ans = [0] * len(queries)
        for i, t in enumerate(queries):
            for j, x in enumerate(s):
                k = bisect_right(s, t - x, lo=j + 1)
                ans[i] += n - k
            for (a, b), v in g.items():
                if cnt[a] + cnt[b] > t and cnt[a] + cnt[b] - v <= t:
                    ans[i] -= 1
        return ans
