2021-7-17 Boredom

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难度 1500

题目 CodeForces:

　　Alex doesn't like boredom. That's why whenever he gets bored, he comes up with games. One long winter evening he came up with a game and decided to play it.

　　Given a sequence a consisting of n integers. The player can make several steps. In a single step he can choose an element of the sequence (let's denote it ak) and delete it, at that all elements equal to ak + 1 and ak - 1 also must be deleted from the sequence. That step brings ak points to the player.

　　Alex is a perfectionist, so he decided to get as many points as possible. Help him.

The first line contains integer n (1 ≤ n ≤ 105) that shows how many numbers are in Alex's sequence.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105).

Print a single integer — the maximum number of points that Alex can earn.

KeyWord

boredom 无聊

perfectionist 完美主义者

题目解析

本题大意是对给出的n个数进行操作，使得最后得到的分数尽可能高，操作包括去掉一个元素，然后去掉数组内等于该元素-1和+1的所有元素，并使分数加上该元素的值。

这题是简单的dp，所以直接看代码

#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
ll x[100005] = { 0 }, y[100005] = { 0 };
ll n,ans;
int main()
{
    cin >> n;
    for (int i = 0; i < n; i++)
    {
        int t; cin >> t;
        x[t]++;
    }
    y[0] = 0;
    y[1] = x[1];
    for (int i = 2; i < 100005; i++)
    {
        y[i] = max(y[i - 1], y[i - 2] + x[i] * i);
        ans = max(ans, y[i]);
    }
    cout << ans<<endl;
    return 0;
}

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