array array array-- 2017 ACM/ICPC Asia Regional Shenyang Online

本文链接：https://blog.youkuaiyun.com/Joe19310/article/details/77936667

Kaitou Kiddo 向侦探 Conan 提出了一个数学谜题：如何通过删除最多 k 个元素使得数组变为单调递增或递减。本文提供了一个高效算法解决方案，使用改进的二分查找来确定是否可以实现这一目标。

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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.

解析：此题换位思考就是要求给定的数组的最长递增序列或者是最长递减序列，倘若要是用线性DP的话绝对会超时，所以这题运用了改进的二分查找的办法，这样就会使时间复杂度在O(nlogn)；


#include"iostream"
using namespace std;

int ai[101100];
int ci[101100];
int bi[101100];
int n;

int lis1(int ai[101100])
{
    bi[0]=-10000;//把B[0]设为最小，假设任何输入都大于-10000；
    bi[1]=ai[0];//初始时，最大递增子序列长度为1的最末元素为a1
    int Len = 1;//Len为当前最大递增子序列长度，初始化为1；
    int p,r,m;//p,r,m分别为二分查找的上界，下界和中点；
    for(int i = 1;i<n;i++)
    {
        p=0;r=Len;
        while(p<=r)
        //二分查找最末元素小于ai+1的长度最大的最大递增子序列；
        {
        m = (p+r)/2;
        if(bi[m]<ai[i]) p = m+1;
        else r = m-1;
        }
        bi[p] = ai[i];//将长度为p的最大递增子序列的当前最末元素置为ai+1;
        if(p>Len) Len++;//更新当前最大递增子序列长度；
    }
    return Len;
}

int main()
{
    int T;
    cin>>T;
    while(T--)
    {
        int k;
        cin>>n>>k;
        for(int i=0;i<n;i++)
        {
            cin>>ai[i];
        }
        for(int i=0;i<n;i++)
        {
            ci[i]=ai[n-i-1];
        }
        int num=lis1(ai);
        int num1=lis1(ci);
        if(max(num,num1)+k>=n) 
            cout<<"A is a magic array."<<endl;
        else
            cout<<"A is not a magic array."<<endl; 
    }
    return 0;
}