2508 - Add Edges to Make Degrees of All Nodes Even.

Hard

There is an undirected graph consisting of n nodes numbered from 1 to n. You are given the integer n and a 2D array edges where <code>edgesi = a_i, b_i</code> indicates that there is an edge between nodes <code>a_i</code> and <code>b_i</code>. The graph can be disconnected.

You can add at most two additional edges (possibly none) to this graph so that there are no repeated edges and no self-loops.

Return true if it is possible to make the degree of each node in the graph even, otherwise return false.

The degree of a node is the number of edges connected to it.

Example 1:

Input: n = 5, edges = [1,2,2,3,3,4,4,2,1,4,2,5]

Output: true

Explanation: The above diagram shows a valid way of adding an edge. Every node in the resulting graph is connected to an even number of edges.

Example 2:

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

Output: true

Explanation: The above diagram shows a valid way of adding two edges.

Example 3:

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

Output: false

Explanation: It is not possible to obtain a valid graph with adding at most 2 edges.

Constraints:

• <code>3 <= n <= 10⁵</code>

• <code>2 <= edges.length <= 10⁵</code>

• edges[i].length == 2

• <code>1 <= a_i, b_i<= n</code>

• <code>a_i != b_i</code>

• There are no repeated edges.