Codeforces Round #263 (Div. 2)C. Appleman and Toastman

最新推荐文章于 2022-11-22 23:15:14 发布

原创最新推荐文章于 2022-11-22 23:15:14 发布 · 686 阅读

0 ·

CC 4.0 BY-SA版权

Codeforces 专栏收录该内容

23 篇文章

订阅专栏

本文介绍了一个涉及游戏策略的问题，玩家通过特定操作使游戏得分达到最大值。通过将一组数字进行拆分并求和的方式，利用贪心算法实现最优解。

Appleman and Toastman play a game. Initially Appleman gives one group of n numbers to the Toastman, then they start to complete the following tasks:

Each time Toastman gets a group of numbers, he sums up all the numbers and adds this sum to the score. Then he gives the group to the Appleman.
Each time Appleman gets a group consisting of a single number, he throws this group out. Each time Appleman gets a group consisting of more than one number, he splits the group into two non-empty groups (he can do it in any way) and gives each of them to Toastman.

After guys complete all the tasks they look at the score value. What is the maximum possible value of score they can get?

Input

The first line contains a single integer n (1 ≤ n ≤ 3·105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the initial group that is given to Toastman.

Output

Print a single integer — the largest possible score.

Sample test(s)

input
3
3 1 5

output
26

input
1
10

output
10

Note

Consider the following situation in the first example. Initially Toastman gets group [3, 1, 5] and adds 9 to the score, then he give the group to Appleman. Appleman splits group [3, 1, 5] into two groups: [3, 5] and [1]. Both of them should be given to Toastman. When Toastman receives group [1], he adds 1 to score and gives the group to Appleman (he will throw it out). When Toastman receives group [3, 5], he adds 8 to the score and gives the group to Appleman. Appleman splits [3, 5] in the only possible way: [5] and [3]. Then he gives both groups to Toastman. When Toastman receives [5], he adds 5 to the score and gives the group to Appleman (he will throws it out). When Toastman receives [3], he adds 3 to the score and gives the group to Appleman (he will throws it out). Finally Toastman have added 9 + 1 + 8 + 5 + 3 = 26 to the score. This is the optimal sequence of actions.

贪心的思想：

代码如下：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#define LL long long
using namespace std;

const int maxn = 300100;
LL a[maxn],sum,ans;
int n;
int main()
{
    while(~scanf("%d",&n))
    {
        for(int i = sum = 0; i < n; i++)
        {
            cin>>a[i];
            sum += a[i];
        }
        sort(a,a+n);
        ans = sum;
        for(int i = 0; i+1 < n; i++)
        {
            ans += sum;
            sum -= a[i];

        }
        cout<<ans<<endl;
    }
    return 0;
}