D. Range and Partition
题意:给你一个长为n的数组,让你分成k段,满足每段在[x,y]内的严格大于在在[x,y]外的,请你最小化y − x并输出切割方案。
思路:若有cnt1个数在[x,y]内 cnt2个数在[x,y]外 则整个区间一定能分成cnt1-cnt2段(类似中位数分段:传送门)
cnt1+cnt2=n , cnt1-cnt2=k 则cnt1=(n+k+1)/2
可以用双指针求出 [x,y] 内有cnt1个数的最小区间
//#pragma GCC optimize(2)
//#pragma GCC optimize(3,"Ofast","inline")
#include<bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pb push_back
#define pii pair<int,int>
#define IOS ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
const int inf=8e18;
const int maxn=2e5+100;
int a[maxn],cnt[maxn];
signed main()
{
IOS
int tt;
cin>>tt;
while(tt--)
{
int n,k;
cin>>n>>k;
for(int i=1;i<=n;i++)
{
cin>>a[i];
cnt[a[i]]++;
}
int cnt1=(n+k+1)/2,l=1,r=n,mn=n,now=0;
for(int i=1,j=1;i<=n;i++)
{
while(j<=n&&now<cnt1)
{
now+=cnt[j];
j++;
}
if(now<cnt1)break;
if(j-i<mn)
{
mn=j-i;
l=i;
r=j-1;
}
now-=cnt[i];
}
cout<<l<<" "<<r<<"\n";
now=0;
int i,j;
for(i=1,j=1;i<=n;i=j)
{
if(k==1)break;
now=0;
while(j<=n&&now<1)
{
if(a[j]>=l&&a[j]<=r)now++;
else now--;
j++;
}
cout<<i<<" "<<j-1<<"\n";
k--;
}
cout<<j<<" "<<n<<"\n";
for(int i=1;i<=n;i++) cnt[i]=0;
}
}