模板 最长递增子序列

 

【模板】最长递增子序列

一般情况：

 

#include <stdio.h>
#include <algorithm>
#include <string.h>
using namespace std;

int a[1005],dp[1005],n;

int LIS()
{
    int i,j,ans,m;
    dp[1] = 1;
    ans = 1;
    for(i = 2;i<=n;i++)
    {
        m = 0;
        for(j = 1;j<i;j++)
        {
            if(dp[j]>m && a[j]<a[i])
            m = dp[j];
        }
        dp[i] = m+1;
        if(dp[i]>ans)
        ans = dp[i];
    }
    return ans;
}

 

 

二分优化：

 

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

int a[40005],dp[40005],n;

int bin(int size,int k)
{
    int l = 1,r = size;
    while(l<=r)
    {
        int mid = (l+r)/2;
        if(k>dp[mid])
            l = mid+1;
        else
            r = mid-1;
    }
    return l;
}

int LIS()
{
    int i,j,ans=1;
    dp[1] = a[1];
    for(i = 2; i<=n; i++)
    {
        if(a[i]<=dp[1])
            j = 1;
        else if(a[i]>dp[ans])
            j = ++ans;
        else
            j = bin(ans,a[i]);
        dp[j] = a[i];
    }
    return ans;
}