POj3104 Drying(二分)

Drying

Time Limit: 2000MS Memory Limit: 65536K

Description

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 a_i 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 a_i separated by spaces (1 ≤ a_i ≤ 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

：：二分时间，找满足题意的结果

//本代码用cin,cout输入输出时间慢，改为scanf，printf会快很多
#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
const int maxn=100100;
int a[maxn];

int is_ok(int m,int k,int n)//时间为m时是否能够把衣服弄干
{
    int sum=0;
    for(int i=0;i<n;i++)
    {                 //如果含水量小于等于m，自然晾干就好
        if(a[i]>m)//当含水量大于m
        {
            sum+=(a[i]-m)/k;//
            if((a[i]-m)%k)
              sum++;
        }
        if(sum>m) return 0;
    }
   return 1;
}

int run()
{
    int n,i,k;
    while(cin>>n)
    {
        int big=0;
        for(i=0;i<n;i++)
        {
            cin>>a[i];
            if(a[i]>big) big=a[i];
        }
        cin>>k;
        if(k==1)
        {
            cout<<big<<endl;
            continue;
        }
        int l=0,r=big,ans=big;

        while(l<=r)
        {
            int m=(l+r)>>1;
            if(is_ok(m,k-1,n))  //k-1是为了处理当含水a[i]大于m时，
                r=m-1,ans=m;      //可以处理为a[i]-m;(m点水相当于自然晾干)
            else
               l=m+1;
        }
        cout<<ans<<endl;
    }
    return 0;
}

int main()
{
    ios::sync_with_stdio(0);
    return run();
}