POJ 3104 Drying

Drying

Time Limit: 2000ms

Memory Limit: 65536KB

This problem will be judged on PKU. Original ID: 3104
64-bit integer IO format: %lld      Java class name: Main

It is very hard to wash and especially to dry clothes in winter. But Jane is a very smart girl. She is not afraid of this boring process. Jane has decided to use a radiator to make drying faster. But the radiator is small, so it can hold only one thing at a time.

Jane wants to perform drying in the minimal possible time. She asked you to write a program that will calculate the minimal time for a given set of clothes.

There are n clothes Jane has just washed. Each of them took ai water during washing. Every minute the amount of water contained in each thing decreases by one (of course, only if the thing is not completely dry yet). When amount of water contained becomes zero the cloth becomes dry and is ready to be packed.

Every minute Jane can select one thing to dry on the radiator. The radiator is very hot, so the amount of water in this thing decreases by k this minute (but not less than zero — if the thing contains less than k water, the resulting amount of water will be zero).

The task is to minimize the total time of drying by means of using the radiator effectively. The drying process ends when all the clothes are dry.

 

Input

The first line contains a single integer n (1 ≤ n ≤ 100 000). The second line contains ai separated by spaces (1 ≤ ai ≤ 109). The third line contains k (1 ≤ k ≤ 109).

Output

Output a single integer — the minimal possible number of minutes required to dry all clothes.

 

Sample Input

sample input #1
3
2 3 9
5

sample input #2
3
2 3 6
5

Sample Output

sample output #1
3

sample output #2
2

Source

Northeastern Europe 2005

 

解题：二分，注意烘干需要减一，因为那个1是自然掉的，先把时间内可以自然掉的算出来，剩下的烘干

 

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <climits>
#include <cmath>
using namespace std;
typedef long long LL;
const int maxn = 1000010;
const int INF = 0x3f3f3f3f;
int n,d[maxn],k;
bool check(int mid){
    LL tmp = 0;
    for(int i = n-1; i >= 0 && d[i] > mid; --i){
         int p = (d[i] - mid)/(k - 1);
         if(p*(k - 1) < d[i] - mid) p++;
         tmp += p;
        if(tmp > mid) return false;
    }
    return true;
}
int main(){
    while(~scanf("%d",&n)){
        for(int i = 0; i < n; ++i)
            scanf("%d",d+i);
        scanf("%d",&k);
        sort(d,d+n);
        if(k <= 1){
            printf("%d
",d[n-1]);
            continue;
        }
        int low = 0,high = d[n-1],ret = 0;
        while(low <= high){
            int mid = (low + high)>>1;
            if(check(mid)){ret = mid;high = mid -1;}
            else low = mid + 1;
        }
        cout<<ret<<endl;
    }
    return 0;
}