Poj 3104 (二分)

Drying

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 7104 Accepted: 1823

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 byk this minute (but not less than zero — if the thing contains less thank 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 containsa_i separated by spaces (1 ≤a_i ≤ 10⁹). The third line containsk (1 ≤ k ≤ 10⁹).

Output

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

Sample Input

sample input #132 3 95sample input #232 3 65

Sample Output

sample output #13sample output #22

Source

Northeastern Europe 2005, Northern Subregion

贪心的去模拟会超时，这里关键是要想到二分。然后注意几个细节。1 注意可能超int。 2在每次烘干时，自然风干是没有的。 3 当k为1的情况。 4一个小技巧，整数运算中，a/b的上取整可以用（a+b-1）/b。

#include<cstdio>#include<algorithm>#include<vector>#include<set>#include<map>#include<iostream>#include<string>#include<cstring>#include<queue>#include<cmath>using namespace std;typedef long long LL;const int maxn = 100000 + 5;const int INF = 1000000000;int a[maxn];int n,k;bool can(int x){    int cnt = 0;    for(int i = 0;i < n;i++){        if(a[i] > x){            cnt += (a[i] - x + k - 2) / (k - 1);            if(cnt > x) return false;        }    }    return true;}int main(){    while(scanf("%d",&n) != EOF){        for(int i = 0;i < n;i++) scanf("%d",&a[i]);        sort(a,a+n);        scanf("%d",&k);        if(k == 1){            printf("%d\n",a[n-1]);            continue;        }        int l = 1,r = a[n-1];        int ans;        while(l <= r){            int mid = l+(r-l)/2;            if(can(mid)){                ans = mid;                r = mid-1;            }            else l = mid+1;        }        printf("%d\n",ans);    }    return 0;}