Even-Odd Game

题意翻译

Alice 和 Bob 玩游戏 给定含 $n$ 个数字的数列 $\{a\}$ 两人轮流进行游戏，Alice 先手 每一轮一人从数列中选取一个数字并将这个数字从数列中删掉 如果 Alice 选择的数字是偶数，那么 Alice 得分加上这个数字，否则 Alice 不加分 如果 Bob 选择的数字是奇数，那么 Bob 得分加上这个数字，否则 Bob 不加分 假设二人都采取最优策略，最后得分高的获胜，请输出胜者（Alice 或者 Bob），或者指明这是平局（Tie） ### 输入 多组测试数据 先输入 $T$ 表示有 $T$ 组测试数据（$1\le T \le 10^4$） 接下来 $T$ 组数据，每组数据先输入 $n$（$1\le n \le2\cdot10^5$），接下来 $n$ 个数字描述数列 $\{a\}$ 保证每个测试点 $T$ 组数据的 $n$ 之和不超过 $2\cdot10 ^5$ ### 输出 每组数据一行 - 如果 Alice 赢了，输出 `Alice` - 如果 Bob 赢了，输出 `Bob` - 如果二人得分相同，输出 `Tie` Translated By @_Leaving

题目描述

During their New Year holidays, Alice and Bob play the following game using an array $ a $ of $ n $ integers: - Players take turns, Alice moves first. - Each turn a player chooses any element and removes it from the array. - If Alice chooses even value, then she adds it to her score. If the chosen value is odd, Alice's score does not change. - Similarly, if Bob chooses odd value, then he adds it to his score. If the chosen value is even, then Bob's score does not change. If there are no numbers left in the array, then the game ends. The player with the highest score wins. If the scores of the players are equal, then a draw is declared. For example, if $ n = 4 $ and $ a = [5, 2, 7, 3] $ , then the game could go as follows (there are other options): - On the first move, Alice chooses $ 2 $ and get two points. Her score is now $ 2 $ . The array $ a $ is now $ [5, 7, 3] $ . - On the second move, Bob chooses $ 5 $ and get five points. His score is now $ 5 $ . The array $ a $ is now $ [7, 3] $ . - On the third move, Alice chooses $ 7 $ and get no points. Her score is now $ 2 $ . The array $ a $ is now $ [3] $ . - On the last move, Bob chooses $ 3 $ and get three points. His score is now $ 8 $ . The array $ a $ is empty now. - Since Bob has more points at the end of the game, he is the winner. You want to find out who will win if both players play optimally. Note that there may be duplicate numbers in the array.

输入输出格式

输入格式

The first line contains an integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. The first line of each test case contains an integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of elements in the array $ a $ . The next line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the array $ a $ used to play the game. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case, output on a separate line: - "Alice" if Alice wins with the optimal play; - "Bob" if Bob wins with the optimal play; - "Tie", if a tie is declared during the optimal play.

输入输出样例

输入样例 #1

4
4
5 2 7 3
3
3 2 1
4
2 2 2 2
2
7 8

输出样例 #1

Bob
Tie
Alice
Alice