2021 Niu Ke Winter Holiday Algorithm Basic Training Camp 3 I. The aesthetics of the sequence (dp)

I. The aesthetics of the sequence

Title link: https://ac.nowcoder.com/acm/contest/9983/I

Title description:

Suppose the aesthetics of a sequence S of length m is equal to how many integers i satisfy 1 ≤ i ≤ m−1 and S i = S i+1, where S i represents the i-th element of the sequence S.
Given a sequence a of length n, ask what is the maximum beauty of all its subsequences.
A subsequence of a sequence is a new sequence formed by removing some elements from the original sequence (or not removing, that is, the sequence itself is also a subsequence) but not destroying the relative position (before or after) of the remaining elements.

Enter a description:

The first line is a positive integer n.
Next line n positive integers ai separated by spaces.
2≤ n ≤10^6
1≤ ai ≤10^6

Output description:

Output an integer to represent the answer.

Example 1:

Input
5
1 1 2 3 2
Output
2
Description The most
beautiful subsequence is [1,1,2,2]

Example 2:

Input
7
1 1 2 2 2 1 1
Output
4

Problem-solving ideas:

dp
dp[i] represents the maximum aesthetics of the first i characters
①I don’t choose i/i is selected but i is different from the previous one dp[i] = dp[i-1]
②I is selected, and i is connected to the same as it (I is the same as the previous one) dp[i] = dp[pre[a[i]]] + 1 (pre[a[i]] is the position of the previous a[i].)

code show as below:

#include<iostream>
#include<cstdio>
using namespace std;

int dp[1000010],a[1000010],pre[1000010];
int main(){
    
    
	int n;
	cin>>n;
	for(int i=1;i<=n;i++){
    
    
		cin>>a[i];
	}
	for(int i=1;i<=n;i++){
    
    
		if(pre[a[i]] != 0)
			dp[i]=max(dp[i-1],dp[pre[a[i]]]+1);
		else
			dp[i] = dp[i-1];
		pre[a[i]] = i;
	}
	cout<<dp[n]<<endl;
	return 0;
}