maximum-score-of-a-node-sequence

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Algorithms

There is an undirected graph with <code>n</code> nodes, numbered from <code>0</code> to <code>n - 1</code>.

You are given a 0-indexed integer array <code>scores</code> of length <code>n</code> where <code>scores[i]</code> denotes the score of node <code>i</code>. You are also 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>.

A node sequence is valid if it meets the following conditions:

<ul>
	<li>There is an edge connecting every pair of adjacent nodes in the sequence.</li>
	<li>No node appears more than once in the sequence.</li>
</ul>

The score of a node sequence is defined as the sum of the scores of the nodes in the sequence.

Return the maximum score of a valid node sequence with a length of <code>4</code>. If no such sequence exists, return <code>-1</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2022/04/15/ex1new3.png" style="width: 290px; height: 215px;" />
<pre>
Input: scores = [5,2,9,8,4], edges = [[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]
Output: 24
Explanation: The figure above shows the graph and the chosen node sequence [0,1,2,3].
The score of the node sequence is 5 + 2 + 9 + 8 = 24.
It can be shown that no other node sequence has a score of more than 24.
Note that the sequences [3,1,2,0] and [1,0,2,3] are also valid and have a score of 24.
The sequence [0,3,2,4] is not valid since no edge connects nodes 0 and 3.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/17/ex2.png" style="width: 333px; height: 151px;" />
<pre>
Input: scores = [9,20,6,4,11,12], edges = [[0,3],[5,3],[2,4],[1,3]]
Output: -1
Explanation: The figure above shows the graph.
There are no valid node sequences of length 4, so we return -1.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == scores.length</code></li>
	<li><code>4 &lt;= n &lt;= 5 * 104</code></li>
	<li><code>1 &lt;= scores[i] &lt;= 108</code></li>
	<li><code>0 &lt;= edges.length &lt;= 5 * 104</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= ai, bi &lt;= n - 1</code></li>
	<li><code>ai != bi</code></li>
	<li>There are no duplicate edges.</li>
</ul>