uva1451 - Average（数形结合）

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4197

数形结合题，太过复杂请参考：《浅谈数形结合思想在信息学竞赛中的应用》

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<set>
#include<cassert>
#include<cmath>
#include<algorithm>
using namespace std;
const int maxn=100000+5;

int n,L;
char s[maxn];
int sum[maxn],p[maxn];

int compare_average(int x1,int x2,int x3,int x4)
{
    return (sum[x2]-sum[x1-1])*(x4-x3+1)-(sum[x4]-sum[x3-1])*(x2-x1+1);
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d%s",&n,&L,s+1);

        sum[0]=0;
        for(int i=1;i<=n;i++)
            sum[i]=sum[i-1]+s[i]-'0';
        int ansL=1,ansR=L;

        int i=0,j=0;
        for(int t=L;t<=n;t++)
        {
            while(j-i>1&&compare_average(p[j-2],t-L,p[j-1],t-L)>=0)
                j--;
            p[j++]=t-L+1;
            while(j-i>1&&compare_average(p[i],t,p[i+1],t)<=0)
                i++;
            int c=compare_average(p[i],t,ansL,ansR);
            if(c>0||c==0&&t-p[i]<ansR-ansL)
                ansL=p[i],ansR=t;
        }
        printf("%d %d\n",ansL,ansR);
    }
    return 0;
}