1782 - Count Pairs Of Nodes\.

Hard

You are given an undirected graph defined by an integer n, the number of nodes, and a 2D integer array edges, the edges in the graph, where <code>edgesi = u_i, v_i</code> indicates that there is an undirected edge between <code>u_i</code> and <code>v_i</code>. You are also given an integer array queries.

Let incident(a, b) be defined as the number of edges that are connected to either node a or b.

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

• a < b

• incident(a, b) > queries[j]

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

Note that there can be multiple edges between the same two nodes.

Example 1:

Input: n = 4, edges = \[\[1,2],2,4,1,3,2,3,2,1], queries = 2,3

Output: 6,5

Explanation: The calculations for incident(a, b) are shown in the table above. The answers for each of the queries are as follows:

• answers0 = 6. All the pairs have an incident(a, b) value greater than 2.

• answers1 = 5. All the pairs except (3, 4) have an incident(a, b) value greater than 3.

Example 2:

Input: 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

Output: 10,10,9,8,6

Constraints:

• <code>2 <= n <= 2 * 10⁴</code>

• <code>1 <= edges.length <= 10⁵</code>

• <code>1 <= u_i, v_i<= n</code>

• <code>u_i != v_i</code>

• 1 <= queries.length <= 20

• 0 <= queries[j] < edges.length