CF1043A Elections

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  • 题目来源 CodeForces 1043A
  • 评测方式 RemoteJudge
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  • 难度 普及-
  • 时空限制 1000ms / 256MB

题解

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    题意翻译

    有两个人小A和小B参加选举,共有n个人参与投票,每人可以投k票。小A通过暗箱操作知道了每个人一定会投ai票给小B。 他很想赢,所以决定通过操作来改变每个人可以投的票数k。问k最小为多少时,小A能获胜。

    输入:第一行,包含一个整数n,投票的人数。 第二行,n个整数ai,ai为第i个人投给小B的票数。

    输出:仅一行,包含一个整数k,每个人可投的票数。

    题目描述

    Awruk is taking part in elections in his school. It is the final round. He has only one opponent — Elodreip. The are $ n $ students in the school. Each student has exactly $ k $ votes and is obligated to use all of them. So Awruk knows that if a person gives $ a_i $ votes for Elodreip, than he will get exactly $ k - a_i $ votes from this person. Of course $ 0 \le k - a_i $ holds.

    Awruk knows that if he loses his life is over. He has been speaking a lot with his friends and now he knows $ a_1, a_2, \dots, a_n $ — how many votes for Elodreip each student wants to give. Now he wants to change the number $ k $ to win the elections. Of course he knows that bigger $ k $ means bigger chance that somebody may notice that he has changed something and then he will be disqualified.

    So, Awruk knows $ a_1, a_2, \dots, a_n $ — how many votes each student will give to his opponent. Help him select the smallest winning number $ k $ . In order to win, Awruk needs to get strictly more votes than Elodreip.

    输入输出格式

    输入格式:

    The first line contains integer $ n $ ( $ 1 \le n \le 100 $ ) — the number of students in the school.

    The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 100 $ ) — the number of votes each student gives to Elodreip.

    输出格式:

    Output the smallest integer $ k $ ( $ k \ge \max a_i $ ) which gives Awruk the victory. In order to win, Awruk needs to get strictly more votes than Elodreip.

    输入输出样例

    输入样例#1: 复制
    5
    1 1 1 5 1
    
    输出样例#1: 复制
    5
    输入样例#2: 复制
    5
    2 2 3 2 2
    
    输出样例#2: 复制
    5

    说明

    In the first example, Elodreip gets $ 1 + 1 + 1 + 5 + 1 = 9 $ votes. The smallest possible $ k $ is $ 5 $ (it surely can't be less due to the fourth person), and it leads to $ 4 + 4 + 4 + 0 + 4 = 16 $ votes for Awruk, which is enough to win.

    In the second example, Elodreip gets $ 11 $ votes. If $ k = 4 $ , Awruk gets $ 9 $ votes and loses to Elodreip.

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