Codeforces Hello2015第一题Cursed Query

Posted 2020-09-29 lytwajue

英文题面：

De Prezer loves movies and series. He has watched the Troy for like 100 times and also he is a big fan of Supernatural series.So, he did some researches and found a cursed object which had n lights on it and initially all of them were turned off.Because of his love to the Troy, he called that object Troy.

He looked and saw a note on it in Khikulish (language of people of Khikuland): "Ma in hame rah umadim, hala migi ... ? ... Mage man De Prezer am k mikhay mano ... ? .... Man se sale ... To boro .... beshur manam miram ... o mishuram".

He doesn‘t know Khikulish, so just ignored the note and tested the Troy.

He realized that the light number i stays turned on for exactly a_i seconds, and then it turns itself off (if it is turned on, in time t, in time t?+?a_i?-?1 it will be turned on, but on time t?+?a_i it won‘t be) and the next light will be turned on (if i?<?n, next light is the light number i?+?1, otherwise it is light with number 1).

For example if n?=?2 and we turn on the first light in time 0, it will be turned on in hole interval [0,?a₁) and in hole interval [a₁,?a₁?+?a₂) the second light will be turned on and so on.

In time 0 he turns on the light number 1.

De Prezer also loves query.So he gives you q queries.In each query he will give you integer t (the time a revengeful ghost attacked him) and you should print the number of the light that is turned on, in time t.

Input

The first line of input contains two integers n and q.

The second line contains n space separated integers, a₁,?a₂,?...,?a_n .

The next q lines, each line contains a single integer t .

1?≤?n,?q?≤?10⁵

1?≤?a_i?≤?10⁹

1?≤?t?≤?10¹⁸

Output

For each query, print the answer in one line.

 

        就是说有n盏灯，然后给出每盏灯亮的时间（第一盏从时刻0開始亮直到时刻0+a1-1，第二盏在a1时刻亮起，以此类推），然后题目给出q组询问，询问内容是一个t,要你给出t时刻亮的时哪盏灯。

我的做法是每次询问就来一次二分查找，log2n的复杂度再盛上10^5次询问能够接受。

Sample test(s)：

Input

5 7
1 2 3 4 5
1
2
3
7
14
15
16

 

Output

2
2
3
4
5
1
2

 

        这组測试数据还是业界良心的。爆出了可能出错的坑，这一串灯是循环的首尾相接地亮。所以那个t是10^18这么大，要取模。

 

代码：

 

#include <iostream>
#include<stdio.h>
using namespace std;

long long int start[100005];//每盏灯開始亮时刻
long long int End[100005];//每盏灯亮完时刻
int n,q,a;
long long int t;

int work(long long int ask)//每次二分查找函数
{
    int p=1;
    int p1=1;
    int p2=n;
    while(ask<start[p]||ask>End[p])
    {
        p=(p1+p2)/2;
        if(ask>=start[p]&&ask<=End[p])
        {
            break;
        }else if(ask>=start[p1]&&ask<=End[p1])
        {
            p=p1;
            break;
        }else if(ask>=start[p2]&&ask<=End[p2])
        {
            p=p2;
            break;
        }else if(ask<start[p]&&ask>End[p1])
        {
            p2=p;
        }else if(ask>End[p]&&ask<start[p2])
        {
            p1=p;
        }
    }

    return p;//p就是那盏灯
}

int main()
{
    scanf("%d%d",&n,&q);
    start[1]=0;
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&a);
        End[i]=start[i]+a-1;
        start[i+1]=start[i]+a;
    }
    while(q--)
    {
        scanf("%I64d",&t);
        printf("%d\n",work(t%start[n+1]));
    }
    return 0;
}