poj 3104 Drying（二分）

Drying Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 13600 Accepted: 3499

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

Source

Northeastern Europe 2005, Northern Subregion

思路：对时间二分

注意三点：

1. 计算每件衣服需要吹风机的时间：x = (a[i]-mid)/(k-1)向上取整， 而不是(a[i]-mid)/k,  因为k*x+(mid-x) >= a[i]

2. k = 1时，除数为0，要特别处理

3. 吹风机的总耗时要用long long

代码：

#include<iostream> #include<cstdio> using namespace std; const int maxn = 1e5+5; const int INF = 0x3f3f3f3f; int a[maxn]; int main(void) { int n, k; while(cin >> n) { int l = 0, r = -INF; for(int i = 0; i < n; i++) { scanf("%d", &a[i]); if(a[i] > r) r = a[i]; } scanf("%d", &k); if(k <= 1) { printf("%d\n", r); continue; } int ans = - 1, mid; while(l <= r) { mid = (l+r)/2; long long t = 0; for(int i = 0; i < n; i++) if(a[i] > mid) { t += (a[i]-mid)/(k-1); //一定要用long long if((a[i]-mid)%(k-1)) t++; } if(t <= mid) ans = mid, r = mid-1; else l = mid+1; } printf("%d\n", ans); } return 0; }