Longest ascending subsequence

subject

Given a length of N Sequence of numbers , Find the longest length of a strictly monotonically increasing subsequence .

Input format
The first line contains integers N.

The second line contains N It's an integer , Represents a complete sequence .

Output format
Output an integer , Represents the maximum length .

Data range

1≤N≤1000,
−109≤ The number in a sequence ≤109

sample input ：

7
3 1 2 1 8 5 6

sample output ：

4

Thought analysis

Answer key

#include<iostream>

using namespace std;

const int N = 1010;
int n;
int a[N] , f[N];

int main(){
    
    scanf("%d",&n);
    
    for(int i = 1; i <= n; i ++){
    
        scanf("%d",&a[i]);
    }
    
    for(int i = 1; i <= n ; i++){
    
        // When empty set , That is, there is only one number 
        f[i] = 1;
        
        for(int j = 1;j <= i; j++){
    
            if(a[j] < a[i]){
    
                f[i] = max(f[i] , f[j] + 1);
            }
        }
    }
    
    int res = 0;
    for(int i = 1; i <= n; i++){
    
        res = max(res , f[i]);
    }
    printf("%d\n",res);
    return 0;
}