POJ 2533 Longest Ordered Subsequence （LIS）

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最长上升子序列

O(n*logn)

//#pragma commmpnt(linkmpr, "/STACK:102400000,102400000")#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#include <cmath>#include <queue>using namespace std;typedef long long LL;const int M = 100010;const int INF =0x3f3f3f3f;const int MAXN=10010;int a[MAXN],b[MAXN];//用二分查找的方法找到一个位置，使得num>b[i-1] 并且num<b[i],并用num代替b[i]int Search(int num,int low,int high){    int mid;    while(low<=high)    {        mid=(low+high)/2;        if(num>=b[mid])  low=mid+1;        else   high=mid-1;    }    return low;}int DP(int n){    int i,len,pos;    b[1]=a[1];    len=1;    for(i=2; i<=n; i++)    {        if(a[i]>b[len])//如果a[i]比b[]数组中最大还大直接插入到后面即可        {            len=len+1;            b[len]=a[i];        }        else          //用二分的方法在b[]数组中找出第一个比a[i]大的位置并且让a[i]替代这个位置        {            pos=Search(a[i],1,len);            b[pos]=a[i];        }    }    return len;}int main(){    int n;    scanf("%d",&n);    memset(a,0,sizeof(a));    memset(b,0,sizeof(b));    for(int i=1;i<=n;++i)    {        cin>>a[i];    }    cout<<DP(n)<<endl;    return 0;}

O(n^2)

//#pragma commmpnt(linkmpr, "/STACK:102400000,102400000")#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#include <cmath>#include <queue>using namespace std;typedef long long LL;const int M = 100010;const int INF =0x3f3f3f3f;const int MAXN=10010;int a[MAXN],b[MAXN];int dp[MAXN];int main(){    int n;    scanf("%d",&n);    memset(a,0,sizeof(a));    memset(b,0,sizeof(b));    memset(dp,0,sizeof(dp));    for(int i=1; i<=n; ++i)    {        cin>>a[i];    }    int maxlen=0;    //dp[1]=0;    for(int i=1; i<=n; ++i)    {        dp[i]=1;        for(int j=1; j<=i; ++j)        {            if(a[j]<a[i] && dp[j]+1 >dp[i])            {                dp[i]=dp[j]+1;            }            if(dp[i]>maxlen)            {                maxlen=dp[i];            }        }    }    cout<<maxlen<<endl;    return 0;}

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