LeetCode 2836: Maximize Value of Function in a Ball Passing Game Solution

Master LeetCode problem 2836 (Maximize Value of Function in a Ball Passing Game), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2836. Maximize Value of Function in a Ball Passing Game

Hard

Array Dynamic Programming Bit Manipulation

Problem Explanation

Explanation

To maximize the score in this ball-passing game, we need to find the longest cycle in the graph where each player is a node and the ball passing sequence represents the edges. We can achieve this by iterating through each player, following the ball passing sequence for k times to create a cycle, and calculating the sum of indices in this cycle. The maximum score will be the maximum sum obtained from all cycles in the graph.

Create a function to calculate the score for a given starting player.
Iterate through each player as the starting player and find the maximum score.
Return the maximum score as the result.

Time complexity: O(n) where n is the number of players. Space complexity: O(n) for storing the visited status of players.

Solution Code

class Solution {
    public int maxGeneticDifference(int[] parents, int[][] queries) {
        Map<Integer, List<Integer>> graph = new HashMap<>();
        Map<Integer, Integer> queryToIndex = new HashMap<>();
        int index = 0;

        for (int i = 0; i < parents.length; i++) {
            graph.putIfAbsent(i, new ArrayList<>());
        }

        for (int i = 0; i < parents.length; i++) {
            if (parents[i] != -1) {
                graph.get(parents[i]).add(i);
            } else {
                queryToIndex.put(i, index++);
            }
        }

        TrieNode root = new TrieNode();
        int[] res = new int[queries.length];
        Arrays.fill(res, -1);

        for (int i = 0; i < parents.length; i++) {
            dfs(i, graph, root, res, queryToIndex);
        }

        return res;
    }

    private void dfs(int node, Map<Integer, List<Integer>> graph, TrieNode node, int[] res, Map<Integer, Integer> queryToIndex) {
        TrieNode cur = node;
        for (int query : queryToIndex.keySet()) {
            int xor = 0;
            int queryIndex = queryToIndex.get(query);
            for (int i = 17; i >= 0; i--) {
                int bit = (query >> i) & 1;
                if (cur.children[bit] != null) {
                    cur = cur.children[bit];
                } else {
                    cur = cur.children[1 - bit];
                }
                xor |= (bit ^ cur.val) << i;
            }
            res[queryIndex] = xor;
            cur = node;
        }

        for (int next : graph.getOrDefault(node, new ArrayList<>())) {
            dfs(next, graph, cur, res, queryToIndex);
        }
    }

    class TrieNode {
        TrieNode[] children;
        int val;

        public TrieNode() {
            children = new TrieNode[2];
            val = 0;
        }
    }
}

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