Kattis 2019 ICPC Mid-Central Regional C convoy

You and your friends have gathered at your house to prepare for the Big Game, which you all plan to attend in the afternoon at the football stadium across town. The problem: you only have kk cars between you, with each car seating five people (including the driver), so you might have to take multiple trips to get all nn people to the stadium. In addition, some of your friends know the city better than others, and so take different amounts of time to drive to the stadium from your house. You’d like to procrastinate as long as possible before hitting the road: can you concoct a transportation plan that gets all people to the stadium in the shortest amount of time possible?
More specifically, each person ii currently at your house can drive to the stadium in titi minutes. All kk cars are currently parked at your house. Any person can drive any car (so the cars are interchangeable). After a car arrives at the stadium, any person currently at the stadium can immediately start driving back to your house (and it takes person ii the same amount of time titi to drive back as to drive to the stadium), or alternatively, cars can be temporarily or permanently parked at the stadium. Drivers driving to the stadium can take up to four passengers with them, but drivers driving back can NOT take any passenger. You care only about getting all nn people from your house to the stadium—you do NOT need to park all kk cars at the stadium, if doing so would require more time than an alternative plan that leaves some cars at your house.
Input
The first line of input contains two space-separated integers nn and kk (1≤n,k≤20000)(1≤n,k≤20000), the number of people at your house and the number of available cars. Then follow nn lines containing a single integer each; the iith such integer is the number of seconds titi (1≤ti≤1000000)(1≤ti≤1000000) that it takes person ii to drive from your house to the stadium, or vice-versa.
Output
Print the minimum number of seconds it takes to move all nn people from your house to the stadium, if all people coordinate and drive optimally.

Sample Input 1
11 2
12000
9000
4500
10000
12000
11000
12000
18000
10000
9000
12000
Sample Output 1
13500
Sample Input 2
6 2
1000
2000
3000
4000
5000
6000
Sample Output 2
2000

题解

二分答案（最初想用优先队列没有成功）
对时间T二分
下界为0
上界为1e12（大概）
每次判断为该时间能否运完
最优为O（1）
最差为O（k）
总时间复杂的O（klog（1e12））
可以接受

AC代码

#include
using namespace std;
const long long N=20001;
long long a[N];
long long n,mid,k;
long long l,r;
long long ans;
inline bool ch (long long now){
 long long l=1,r=n+1,c=0;
 while(1){
  if(c==k) return 0;
  if(now<a[l]) return 0;
  long long rou=(now-a[l])/(2*a[l])+1;
  r-=rou*4;
  if(r-l<=1) return 1;
  l++;
  c++;
 }
}
int main(){
 cin>>n>>k;
 for(long long i=1;i<=n;i++)
  scanf("%lld",&a[i]);
 sort(a+1,a+n+1);
 l=0;r=1e12+3;
 while(l!=r){
  mid=(long long)((l+r)>>1);
  if(ch(mid)) r=mid;
  else l=mid+1;
  //cout<
 }
 cout<<l<<endl;
}
``