[LIS]Longest Increasing Sequence:nlogn算法和两种普通DP的实现

//最长单调上升子序列 nlogn算法

#include<iostream>
using namespace std;
#define MAXN 40002
int a[MAXN],d[MAXN];
int main()
{
int n;
cin>>n;
for(int i=1; i<=n; i++)
cin>>a[i];
int len=1;
d[1] = a[1];
for(int i=2; i<=n; i++)
{
if(d[len]<a[i])
{
d[++len] = a[i];
continue;
}
int l=1,r=len,mid;
while(l<=r)
{
mid = (l+r)/2;
if(d[mid]<a[i])
l = mid+1;
else
r = mid-1;
}
d[l] = a[i];//相等的时候 r左移 故退出时可选l或mid
}
cout<<len<<endl;

return 0;
}
//那么DP应该怎么写呢?
//这样写是找都哪些可以接在a[i]后面,可以的话,取max更新;不可以的话不变

#include<iostream>
#include<cstring>
using namespace std;
#define MAXN 1005
int a[MAXN],dp[MAXN];
int main()
{
int n;
cin>>n;
for(int i=1; i<=n; i++)
cin>>a[i];
int i,j;
memset(dp,0,sizeof(dp));
for(int i=1;i<=n;i++)
dp[i] = 1;
for(i=1; i<=n; i++)
for(j=i+1; j<=n; j++)//j铺路,i断后;j
{
if(a[j]>a[i])
{
dp[j] = max(dp[i] + 1,dp[j]);
//cout<<"dp["<<j<<"] = "<<dp[j]<<endl;
}
}
int m = dp[1];
for(i=2;i<=n;i++)
if(dp[i]>m) m = dp[i];
cout<<m<<endl;
return 0;
}

//还有一种是看前面那些可以插入a[j]

#include<iostream>
#include<cstring>
using namespace std;
#define MAXN 1005
int a[MAXN],dp[MAXN];
int main()
{
int n;
cin>>n;
for(int i=1; i<=n; i++)
cin>>a[i];
memset(dp,0,sizeof(dp));
for(int i=1;i<=n;i++)
dp[i] = 1;
for(int i=1;i<=n;i++)
for(int j=1;j<i;j++)
{
if(a[j]<a[i]) dp[i] = max(dp[i],dp[j]+1);
}
int m = 1;
for(int i=1;i<=n;i++)
if(dp[i]>m) m = dp[i];
cout<<m<<endl;
return 0;
}