LIS 最长上升子序列

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$O(n^2)写法$

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#define debug(x) cout<<#x<<" = "<<x<<endl;
#define INF 0x3f3f3f3f
using namespace std;

const int maxn = 100010;
int s[maxn], dp[maxn];

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

$O(nlog_n)写法$

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <vector>
#define debug(x) cout<<#x<<" = "<<x<<endl;
#define INF 0x3f3f3f3f
using namespace std;

const int maxn = 100010;
int s[maxn];
vector<int> vcii;

int main(void) {
    int n;
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> s[i];
    vcii.push_back(s[0]);
    for(int i=1;i<n;i++){
        if(s[i]>vcii.back())
            vcii.push_back(s[i]);
        else
            *(lower_bound(vcii.begin(),vcii.end(),s[i]))=s[i];
    }
    cout<<vcii.size()<<endl;
    return 0;
}