codeforce 455A—— DP—— Boredom

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 a_k) and delete it, at that all elements equal to a_k + 1 and a_k - 1 also must be deleted from the sequence. That step bringsa_k 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, ..., a_n (1 ≤ a_i ≤ 10⁵).

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

Consider the third test example. At first step we need to choose any element equal to 2. After that step our sequence looks like this [2, 2, 2, 2]. Then we do 4 steps, on each step we choose any element equals to 2. In total we earn 10 points.

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
long long  dp[100010][2];
int a[100010];
int temp[100010];
int n;
int main()
{
      while(~scanf("%d", &n)){
          memset(dp, 0, sizeof(dp));
        for(int i = 1; i <= n; i++){
            scanf("%d", &a[i]);
            temp[a[i]]++;
        }

        dp[1][1] = temp[1];
        dp[1][0] = 0;
        for(int i = 2; i <= 100000; i++){
            dp[i][1] = dp[i-1][0] + 1ll*temp[i]*i;
            dp[i][0] = max(dp[i-1][1], dp[i-1][0]);
        }

        printf("%lld\n", max(dp[100000][1], dp[100000][0]));
    }
    return 0;
}