Maximum Score of a Node Sequence

arraygraph theorysorting

Problem Statement

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

You are given a 0-indexed integer array scores of length n where scores[i] denotes the score of node i . You are also given a 2D integer array edges where edges[i] = [a _i , b _i ] denotes that there exists an undirected edge connecting nodes a _i and b _i .

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

There is an edge connecting every pair of adjacent nodes in the sequence.

No node appears more than once in the sequence.

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 4 . If no such sequence exists, return -1 .

Examples

Example 1

Input: scores = [5,2,9,8,4], edges = [[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]
Output: 24
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.

Example 2

Input: scores = [9,20,6,4,11,12], edges = [[0,3],[5,3],[2,4],[1,3]]
Output: -1
The figure above shows the graph.
There are no valid node sequences of length 4, so we return -1.

Constraints

n == scores.length

4 <= n <= 5 * 10 ^4

1 <= scores[i] <= 10 ^8

0 <= edges.length <= 5 * 10 ^4

edges[i].length == 2

0 <= a _i , b _i <= n - 1

a _i != b _i

There are no duplicate edges.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGraph Theory