linear DP AcWing 895. Longest ascending subsequence

Original link

AcWing 895. Longest ascending subsequence

Algorithm tags

Dynamic programming linear DP Longest ascending subsequence

Ideas

Time complexity is represented by States * State calculation
State means One dimensional array N
State calculation Enumerate one-dimensional arrays N
Time complexity $O(N^2)$

Code

#include<bits/stdc++.h>
#define int long long
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>b;--i)
using namespace std;
const int N = 1005, INF = 0x3f3f3f3f;
int a[N], f[N];
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n=read();
    rep(i, 1, n+1){
        a[i]=read();
    }
    rep(i, 1, n+1){
    	//  initialization f[i] Only a[i] In itself   The length is 1
        f[i]=1;
        rep(j, 1, i){
            if(a[j]<a[i]){
                f[i]=max(f[j]+1, f[i]);
            }
        }
    }
    int ans=0;
    rep(i, 1, n+1){
        ans=max(ans, f[i]);
    }
    printf("%lld", ans);
    return 0;
}

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