斜率优化

Average UVALive - 4726 

http://www.docin.com/p-881778722.html

这个论文说的很清楚

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<queue>
#include<map>
#include<set>
#include<list>
#include<ctime>
#include<ctype.h>
#include<bitset>
#include<algorithm>
#include<numeric> //accumulate
#define endl "
"
#define fi first
#define se second
#define FOR(i,s,t) for(int i=(s);i<=(t);++i)
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
const int maxn=100000+5;
int n,k;
string s;
int pre[maxn];
int q[maxn];
inline double cal(int i,int j)
{
    return 1.0*(pre[j]-pre[i])/(j-i);
}
int main()
{

    //cout<<mid(25,5)<<endl;
    //cin.tie(0);
    //cout.tie(0);
    //ios_base::sync_with_stdio(false);
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int T;
    cin>>T;
    while(T--)
    {
        cin>>n>>k;
        cin>>s;
        //cout<<s<<endl;
        for(int i=1;i<=n;i++)
        {
            pre[i]=pre[i-1]+(s[i-1]=='1');
            //cout<<pre[i]<<endl;
        }
        int l=1,r=1;
        q[l]=0;
        int ans_l=0,ans_r=k;
        for(int i=k+1;i<=n;i++)
        {
            int t=i-k;
            while(l<r&&cal(q[r],t)<=cal(q[r-1],q[r]))
                r--;
            q[++r]=t;
            while(l<r&&cal(q[l],i)<=cal(q[l+1],i))
            {
                l++;
            }
            if(cal(ans_l,ans_r)<cal(q[l],i))
            {
                ans_l=q[l];
                ans_r=i;
            }
            else if(cal(ans_l,ans_r)==cal(q[l],i))
            {
                if(i-q[l]<ans_r-ans_l)
                {
                    ans_l=q[l];
                    ans_r=i;
                }
            }
        }
        cout<<ans_l+1<<' '<<ans_r<<endl;
    }
}



/*
void read()
{

    char c = getchar();
    int x = 0;
    for (; (c < 48 || c>57); c = getchar());
    for (; c > 47 && c < 58; c = getchar())
    {
        x = (x << 1) + (x << 3) + c - 48;
    }
    return x;
}
*/