hdu-6197 array array array(最长上升子序列(LIS)长度的O(nlogn)算法)

Problem Description
One day, Kaitou Kiddo had stolen a priceless diamond ring. But detective Conan blocked Kiddo’s path to escape from the museum. But Kiddo didn’t want to give it back. So, Kiddo asked Conan a question. If Conan could give a right answer, Kiddo would return the ring to the museum.
Kiddo: “I have an array A and a number k, if you can choose exactly k elements from A and erase them, then the remaining array is in non-increasing order or non-decreasing order, we say A is a magic array. Now I want you to tell me whether A is a magic array. ” Conan: “emmmmm…” Now, Conan seems to be in trouble, can you help him?

Input
The first line contains an integer T indicating the total number of test cases. Each test case starts with two integers n and k in one line, then one line with n integers: A1,A2…An.
1≤T≤20
1≤n≤105
0≤k≤n
1≤Ai≤105

Output
For each test case, please output “A is a magic array.” if it is a magic array. Otherwise, output “A is not a magic array.” (without quotes).

Sample Input
3
4 1
1 4 3 7
5 2
4 1 3 1 2
6 1
1 4 3 5 4 6

Sample Output
A is a magic array.
A is a magic array.
A is not a magic array.
最长上升子序列(LIS)长度的O(nlogn)算法：http://blog.csdn.net/shuangde800/article/details/7474903
求出最长上升或下降子序列长度为a，如果a>=n-k，则为magic array。

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#define N 100010#define LL long longusing namespace std;const LL mod=1000000007;int num[N],dp[N];int Search(int len, int key){    int l=0,r=len-1;    while (l<=r)    {        int mid=(l+r)/2;        if (dp[mid]>key)        {            r=mid-1;        }        else if (dp[mid]<key)        {            l=mid+1;        }        else        {            return mid;        }    }    return l;}int main(){    int t,n,k;    scanf("%d",&t);    while(t--)    {        scanf("%d%d",&n,&k);        for (int i=0;i<n;i++)        {            scanf("%d",&num[i]);        }        int len=1;        dp[0]=num[0];        for (int i=1;i<n;i++)        {            if (num[i]>dp[len-1])            {                dp[len]=num[i];                len++;            }            else            {                int pos=Search(len,num[i]);                dp[pos]=num[i];            }        }        int lena=len;        for (int i=0;i<n;i++)        {            num[i]=-num[i];        }        len=1;        dp[0]=num[0];        for (int i=1;i<n;i++)        {            if (num[i]>dp[len-1])            {                dp[len]=num[i];                len++;            }            else            {                int pos=Search(len,num[i]);                dp[pos]=num[i];            }        }        int lenb=len;        if (max(lena,lenb)>=n-k)        {            printf("A is a magic array.\n");        }        else        {            printf("A is not a magic array.\n");        }    }    return 0;}