2016 Al-Baath University Training Camp Contest-1 I. March Rain —— 二分
题目链接:http://codeforces.com/problemset/gymProblem/101028/I
2 seconds
64 megabytes
standard input
standard output
It is raining again! Youssef really forgot that there is a chance of rain in March, so he didn't fix the roof of his house. Youssef's roof is 1-D, and it contains n holes
that make the water flow into the house, the position of hole i is denoted as xi where
(0 ≤ i < n). Youssef has to put strips at the bottoms of those holes in order to prevent the water from flowing. Let's say
there is a hole in position 4 and another hole in position 6, and Youssef decided to use a strip of length 3 to cover those two holes, then he places the strip from position 4 to 6 (it covers positions 4,5,6) and it covers the two holes. He can buy exactly k strips,
and he must pay a price equal to the longest strip he buys. What is the minimum length l he can choose as the longest strip in order
to keep his house safe?
The input consists of several test cases. The first line of the input contains a single integer T, the number of the test cases. Each
test case consists of two lines: the first line contains two space-separated integers, n and k (1 ≤ k < n ≤ 100000),
denoting the number of the holes in the roof, and the number of the strips he can buy respectively. The second line of the test case contains n integers (x0, x1, ..., xn - 1):
(0 ≤ xi ≤ 109),
denoting the positions of holes (these numbers are given in an increasing order).
For each test case print a single line containing a single integer denoting the minimum length l he can choose in order to buy k strips
(the longest of them is of length l) and cover all the holes in his house using them.
3
5 2
1 2 3 4 5
7 3
1 3 8 9 10 14 17
5 3
1 2 3 4 20
3
4
2
In the second test case the roof looks like this before and after putting the strips.
题解:
一开始以为是区间覆盖问题。后来想到可以用二分来寻找答案。由于付款金额依照最长长条的长度。所以就把每条长条都想成是最长的。二分长度,然后判断当前长度是否能覆盖完所有漏洞。
代码如下:
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<vector>
#include<map>
#include<string>
#include<set>
using namespace std;
#define pb push_back
#define ms(a, b) memset(a,b,sizeof(a));
typedef long long LL;
const int inf = 0x3f3f3f3f;
const int maxn = ; int a[], T, n,k; int test(int len)
{
int now= , cnt = ;
for(int i = ; i<n; i++)
{
if(a[i]>now)
{
cnt++;
now = a[i]+len-;
if(cnt==k)//如果用完了k条时,判断是否已经覆盖完
{
if(now>=a[n-])
return ;
else
return ;
}
if(now>=a[n-])//如果没用完k条,就覆盖完的话,肯定可以
return ;
}
}
return ;
} int main()
{
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&k);
for(int i = ; i<n; i++)
{
scanf("%d",&a[i]);
} int h = , t = a[n-];
while(t%k) t++;//注意这一步,将t自加到能整除k为止 int mid;
while(h<=t)
{
mid = (h+t)/;
if(test(mid))
t = mid-;
else
h = mid+;
} printf("%d\n",h);
}
return ;
}
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