最长上升子序列问题
状态表示: 集合：所有以第i个数结尾的上升子序列，属性:Max\
状态计算: 集合的划分：以i - 1个数结尾划分
f[i] = max(f[j] + 1),aj < ai(j = 0,1,2,3......i-1)

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;
const int N = 1010;
int n,res;
int a[N];
int 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){
        f[i] = 1;
        for(int j = 1;j < i;++j){
            if(a[j] < a[i]) f[i] = max(f[i],f[j] + 1);
        }
    }
    for(int i = 1;i <= n;++i)   res = max(res,f[i]);
    printf("%d\n",res);
    return 0;
}