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.youkuaiyun.com/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 long
using 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;
}