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Java-based LeetCode algorithm problem solutions, regularly updated
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package g1401_1500.s1406_stone_game_iii;

// #Hard #Array #Dynamic_Programming #Math #Game_Theory
// #2022_03_26_Time_14_ms_(82.02%)_Space_117_MB_(71.71%)

import java.util.Arrays;

/**
 * 1406 - Stone Game III\.
 *
 * Hard
 *
 * Alice and Bob continue their games with piles of stones. There are several stones **arranged in a row** , and each stone has an associated value which is an integer given in the array `stoneValue`.
 *
 * Alice and Bob take turns, with Alice starting first. On each player's turn, that player can take `1`, `2`, or `3` stones from the **first** remaining stones in the row.
 *
 * The score of each player is the sum of the values of the stones taken. The score of each player is `0` initially.
 *
 * The objective of the game is to end with the highest score, and the winner is the player with the highest score and there could be a tie. The game continues until all the stones have been taken.
 *
 * Assume Alice and Bob **play optimally**.
 *
 * Return `"Alice"` _if Alice will win,_ `"Bob"` _if Bob will win, or_ `"Tie"` _if they will end the game with the same score_.
 *
 * **Example 1:**
 *
 * **Input:** values = [1,2,3,7]
 *
 * **Output:** "Bob"
 *
 * **Explanation:** Alice will always lose. Her best move will be to take three piles and the score become 6. Now the score of Bob is 7 and Bob wins.
 *
 * **Example 2:**
 *
 * **Input:** values = [1,2,3,-9]
 *
 * **Output:** "Alice"
 *
 * **Explanation:** Alice must choose all the three piles at the first move to win and leave Bob with negative score. If Alice chooses one pile her score will be 1 and the next move Bob's score becomes 5. In the next move, Alice will take the pile with value = -9 and lose. If Alice chooses two piles her score will be 3 and the next move Bob's score becomes 3. In the next move, Alice will take the pile with value = -9 and also lose. Remember that both play optimally so here Alice will choose the scenario that makes her win.
 *
 * **Example 3:**
 *
 * **Input:** values = [1,2,3,6]
 *
 * **Output:** "Tie"
 *
 * **Explanation:** Alice cannot win this game. She can end the game in a draw if she decided to choose all the first three piles, otherwise she will lose.
 *
 * **Constraints:**
 *
 * *   1 <= stoneValue.length <= 5 * 10⁴
 * *   `-1000 <= stoneValue[i] <= 1000`
**/
public class Solution {
    public String stoneGameIII(int[] stoneValue) {
        int[] dp = new int[stoneValue.length + 1];
        Arrays.fill(dp, 0);
        int i = stoneValue.length - 1;
        while (i >= 0) {
            int ans = Integer.MIN_VALUE;
            ans = Math.max(ans, stoneValue[i] - dp[i + 1]);
            if (i + 1 < stoneValue.length) {
                ans = Math.max(ans, stoneValue[i] + stoneValue[i + 1] - dp[i + 2]);
            }
            if (i + 2 < stoneValue.length) {
                ans =
                        Math.max(
                                ans,
                                stoneValue[i] + stoneValue[i + 1] + stoneValue[i + 2] - dp[i + 3]);
            }
            dp[i] = ans;
            i--;
        }
        int value = dp[0];
        if (value > 0) {
            return "Alice";
        }
        return value == 0 ? "Tie" : "Bob";
    }
}