LIS算法

LIS（Longest Increasing Subsequence）最长上升（不下降）子序列。

    1. O(n^2)

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

int n,ans;
int a[10005],d[10005];

int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&a[i]);
    for(int i=1;i<=n;++i){
        d[i]=1;
        for(int j=1;j<i;++j)
            if(a[i]>a[j]&&d[i]+1>d[j])d[i]=d[j]+1;
    }
    for(int i=1;i<=n;++i)ans=max(ans,d[i]);
    printf("%d",ans);
    return 0;
} 

    2. O(n logn)

#include<cstdio>
int n;
int a[10005];
int stack[10005],top;

int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&a[i]);
    stack[++top]=a[1];
    for(int i=2;i<=n;++i){
        if(a[i]>stack[top])stack[++top]=a[i];
        else {
            int l=1,r=top;
            while(l<=r){
                int mid=l+r>>1;
                if(stack[mid]<a[i])l=mid+1;
                else r=mid-1;
            }
            stack[r]=a[i];
        }
    }
    printf("%d",top);
    return 0;
}