POJ 2533 Longest Ordered Subsequence

题目链接：[kuangbin带你飞]专题十二 基础DP1 N - Longest Ordered Subsequence

题意

求最大递增子序列的长度

思路

两种方法
1. dp[i] = max(dp[j]+1) 1<=j<=i-1(n^2)
2. LIS(nlogn)

代码

#include<iostream>
#include<cstring>
#include<cmath>
#include<cstdio>
#include<algorithm>
#include<stack>
#include<queue>
using namespace std;

const int N = 1009;
int dp[N], a[N];

int main()
{
    int n;
    cin>>n;
    for(int i=0; i<n; i++)
        cin>>a[i];
    int ans = 0;
    for(int i=0; i<n; i++)
    {
        int mmax = 0;
        for(int j=0; j<i; j++)
            if(a[j]<a[i] && mmax<dp[j])
                mmax = dp[j];
        dp[i] = mmax+1;
        ans = max(ans, dp[i]);
    }
    cout<<ans<<endl;
    return 0;
}

#include<iostream>
#include<cstring>
#include<cmath>
#include<cstdio>
#include<algorithm>
#include<stack>
#include<queue>
using namespace std;

const int N = 1009;
int dp[N], a[N];

int binary_search(int len, int x)
{
    int start = 0;
    while(start < len)
    {
        int mid = (start + len)/2;
        if(dp[mid] == x)
            return mid;
        else if(dp[mid] > x)
            len = mid;
        else
            start = mid+1;
    }
    return len;
}

int main()
{
    int n;
    cin>>n;
    for(int i=0; i<n; i++)
        cin>>a[i];
    int len = 1;
    dp[0] = -1;
    for(int i=0; i<n; i++)
    {
        int pos = binary_search(len, a[i]);
        if(pos == len)
            len++;
        dp[pos] = a[i];
    }
    cout<<len-1<<endl;
    return 0;
}