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# Maximum Score of a Node Sequence LeetCode Solution

## Problem – Maximum Score of a Node Sequence LeetCode Solution

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] = [ai, bi]` denotes that there exists an undirected edge connecting nodes `ai` and `bi`.

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`.

Example 1:

``````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.
``````

Example 2:

``````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.
``````

Constraints:

• `n == scores.length`
• `4 <= n <= 5 * 104`
• `1 <= scores[i] <= 108`
• `0 <= edges.length <= 5 * 104`
• `edges[i].length == 2`
• `0 <= ai, bi <= n - 1`
• `ai != bi`
• There are no duplicate edges.

### Maximum Score of a Node Sequence LeetCode Solution in Java

``````    public int maximumScore(int[] A, int[][] edges) {
int n = A.length;
PriorityQueue<Integer>[] q = new PriorityQueue[n];
for (int i = 0; i < n; i++)
q[i] = new PriorityQueue<>((a, b) -> A[a] - A[b]);
for (int[] e : edges) {
q[e].offer(e);
q[e].offer(e);
if (q[e].size() > 3) q[e].poll();
if (q[e].size() > 3) q[e].poll();
}
int res = -1;
for (int[] edge : edges)
for (int i : q[edge])
for (int j : q[edge])
if (i != j && i != edge && j != edge)
res = Math.max(res, A[i] + A[j] + A[edge] + A[edge]);
return res;
}
``````

### Maximum Score of a Node Sequence LeetCode Solution in Python

``````    def maximumScore(self, A, edges):
n = len(A)
G = [[] for i in range(n)]
for i,j in edges:
G[i].append([A[j], j])
G[j].append([A[i], i])
for i in range(n):
G[i] = nlargest(3, G[i])

res = -1
for i,j  in edges:
for vii, ii in G[i]:
for vjj, jj in G[j]:
if ii != jj and ii != j and j != ii:
res = max(res, vii + vjj + A[i] + A[j])
return res
``````

### Maximum Score of a Node Sequence LeetCode Solution in C++

``````int maximumScore(vector<int>& sc, vector<vector<int>>& edges) {
int res = -1;
vector<vector<int>> al(sc.size());
for (auto &e : edges) {
al[e].push_back(e);
al[e].push_back(e);
}
for(auto &l : al) {
partial_sort(begin(l), begin(l) + min((int)l.size(), 3), end(l), [&](int i, int j){ return sc[i] > sc[j]; });
l.resize(min((int)l.size(), 3));
}
for (auto &e : edges)
for (int in : al[e])
for (int jn : al[e])
if (in != e && jn != e && in != jn)
res = max(res, sc[e] + sc[e] + sc[in] + sc[jn]);
return res;
}
``````

### Maximum Score of a Node Sequence LeetCode Solution in Python3

``````class Solution:
def maximumScore(self, scores: List[int], edges: List[List[int]]) -> int:
n = len(scores)
edge = [[] for _ in range(n)]
for u, v in edges:
edge[u].append(v)
edge[v].append(u)
for l in edge:
l.sort(key=lambda x:scores[x], reverse=True)
ans = -1
for u, v in edges:
for x1 in range(min(3, len(edge[u]))):
for y1 in range(min(3, len(edge[v]))):
x = edge[u][x1]
y = edge[v][y1]
if x != u and x != v and y != u and y != v and x != y:
ans = max(ans, scores[u] + scores[v] + scores[x] + scores[y])
return ans
``````
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