hihoCoder#1095(二分搜索)

时间限制:10000ms

单点时限:1000ms

内存限制:256MB

描述

Little Hi and Little Ho are playing a drinking game called HIHO. The game comprises N rounds. Each round, Little Hi pours T milliliter of water into Little Ho's cup then Little Ho rolls a K-faces dice to get a random number d among 1 to K. If the remaining water in Little Ho's cup is less than or equal to d milliliter Little Hi gets one score and Little Ho drinks up the remaining water, otherwise Little Ho gets one score and Little Ho drinks exactly d milliliter of water from his cup. After N rounds who has the most scores wins.

Here comes the problem. If Little Ho can predict the number d of N rounds in the game what is the minimum value of T that makes Little Ho the winner? You may assume that no matter how much water is added, Little Ho's cup would never be full.

输入

The first line contains N(1 <= N <= 100000, N is odd) and K(1 <= K <= 100000).
The second line contains N numbers, Little Ho's predicted number d of N rounds.

输出

Output the minimum value of T that makes Little Ho the winner.

样例输入

5 6
3 6 6 2 1

样例输出

4

思路：求最值时考虑使用二分搜索。

#include <iostream>
using namespace std;
const int MAXN=100005;
const int INF=0x3f3f3f3f;
int n,k;
int d[MAXN];
bool test(int T)
{
    int cup=0;
    int hi_score=0;
    int ho_score=0;
    for(int i=0;i<n;i++)
    {
        cup+=T;
        if(cup<=d[i])
        {
            hi_score++;
            cup=0;
        }
        else
        {
            ho_score++;
            cup-=d[i];
        }
    }
    return ho_score>hi_score;
}
int main()
{
    cin>>n>>k;
    for(int i=0;i<n;i++)
    {
        cin>>d[i];
    }
    int l=0,r=INF;
    while(r-l>1)
    {
        int mid=(l+r)>>1;
        if(test(mid))
        {
            r=mid;
        }
        else
        {
            l=mid;
        }
    }
    cout<<r<<endl;
    return 0;
}