array array array
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 459 Accepted Submission(s): 282
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
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
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.
A is a magic array.
A is not a magic array.
Source
这道题转换之后就是求最长上升子序列长度，此外，发现了一种二分求LIS方法。
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
#include<cmath>
#include<string>
#define LL long long
const int maxn=1e5+5;
using namespace std;
int a[maxn],b[maxn],c[maxn];
int n;
int LIS(int *d){
memset(c,0,sizeof(c));
c[1]=d[1];
int l,r,mid,len=1;
for(int i=2;i<=n;i++){
l=1;
r=len;
while(l<=r){
mid=(l+r)/2;
if(c[mid]<=d[i]) l=mid+1;
else r=mid-1;
}
c[l]=d[i];
if(l>len) len++; }
return len;
}
int main()
{
int T;
scanf("%d",&T);
int k;
while(T--)
{
scanf("%d%d",&n,&k);
for(int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
b[i]=-a[i];
}
int maxn=max(LIS(a),LIS(b)); if(n-maxn>k)
printf("A is not a magic array.\n");
else
printf("A is a magic array.\n");
}
return 0;
}