UVALive - 4726 Average （斜率优化+单调队列）

题意：求连续的子序列使得平均数最大

思路：一切尽在

《浅谈数形结合思想在信息学竞赛中的应用》

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXN = 1000005;

char str[MAXN];
int q[MAXN],sum[MAXN];
int n,m;

double dis(int a,int b){
    return (sum[b]-sum[a])*1.0/(b-a);
}

int main(){
    int t;
    scanf("%d",&t);
    while (t--){
        scanf("%d%d",&n,&m);
        scanf("%s",str+1);
        sum[0] = 0;
        for (int i = 1; i <= n; i++)
            sum[i] = sum[i-1] + str[i] - '0';
        int ansl = 0,ansr = m;
        double ans = dis(0,m);
        int front = 0,rear = -1,len = m;
        for (int i = m; i <= n; i++){
            int ita = i - m;
            while (front < rear && dis(q[rear],ita) <= dis(q[rear-1],ita))
                rear--;
            q[++rear] = ita;
            while (front < rear && dis(q[front],i) <= dis(q[front+1],i))
                front++;
            double itb = dis(q[front],i);
            if (itb > ans){
                ans = itb;
                ansl = q[front];
                ansr = i;
                len = i - q[front];
            }
            else if (itb == ans && len > i - q[front]){
                ansl = q[front];
                ansr = i;
                len = i - q[front];
            }
        }
        printf("%d %d\n",ansl+1,ansr); //注意sum[]的定义，所以+1
    }
    return 0;
}