P3131 [USACO16JAN]子共七Subsequences Summing to Sevens

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  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 前缀和 USACO 2016
  • 难度 普及-
  • 时空限制 1000ms / 128MB

题解

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    题目描述

    Farmer John's $N$ cows are standing in a row, as they have a tendency to do from time to time. Each cow is labeled with a distinct integer ID number so FJ can tell them apart. FJ would like to take a photo of a contiguous group of cows but, due to a traumatic childhood incident involving the numbers $1 \ldots 6$, he only wants to take a picture of a group of cows if their IDs add up to a multiple of 7.

    Please help FJ determine the size of the largest group he can photograph.

    给你n个数,分别是a[1],a[2],...,a[n]。求一个最长的区间[x,y],使得区间中的数(a[x],a[x+1],a[x+2],...,a[y-1],a[y])的和能被7整除。输出区间长度。若没有符合要求的区间,输出0。

    输入输出格式

    输入格式:

    The first line of input contains $N$ ($1 \leq N \leq 50,000$). The next $N$

    lines each contain the $N$ integer IDs of the cows (all are in the range

    $0 \ldots 1,000,000$).

    输出格式:

    Please output the number of cows in the largest consecutive group whose IDs sum

    to a multiple of 7. If no such group exists, output 0.

    输入输出样例

    输入样例#1: 复制
    7
    3
    5
    1
    6
    2
    14
    10
    输出样例#1: 复制
    5

    说明

    In this example, 5+1+6+2+14 = 28.

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