310338: CF1820B. JoJo's Incredible Adventures
Description
Did you think there was going to be a JoJo legend here? But no, that was me, Dio!
Given a binary string $s$ of length $n$, consisting of characters 0 and 1. Let's build a square table of size $n \times n$, consisting of 0 and 1 characters as follows.
In the first row of the table write the original string $s$. In the second row of the table write cyclic shift of the string $s$ by one to the right. In the third row of the table, write the cyclic shift of line $s$ by two to the right. And so on. Thus, the row with number $k$ will contain a cyclic shift of string $s$ by $k$ to the right. The rows are numbered from $0$ to $n - 1$ top-to-bottom.
In the resulting table we need to find the rectangle consisting only of ones that has the largest area.
We call a rectangle the set of all cells $(i, j)$ in the table, such that $x_1 \le i \le x_2$ and $y_1 \le j \le y_2$ for some integers $0 \le x_1 \le x_2 < n$ and $0 \le y_1 \le y_2 < n$.
Recall that the cyclic shift of string $s$ by $k$ to the right is the string $s_{n-k+1} \ldots s_n s_1 s_2 \ldots s_{n-k}$. For example, the cyclic shift of the string "01011" by $0$ to the right is the string itself "01011", its cyclic shift by $3$ to the right is the string "01101".
InputEach test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. The description of test cases follows.
The first and the only line of each test case contains a single binary string $s$ ($1 \le \lvert s \rvert \le 2 \cdot 10^5$), consisting of characters 0 and 1.
It is guaranteed that the sum of string lengths $|s|$ over all test cases does not exceed $2 \cdot 10^5$.
OutputFor each test case, output a single integer — the maximum area of a rectangle consisting only of ones. If there is no such rectangle, output $0$.
ExampleInput5 0 1 101 011110 101010Output
0 1 2 6 1Note
In the first test case, there is a table $1 \times 1$ consisting of a single character 0, so there are no rectangles consisting of ones, and the answer is $0$.
In the second test case, there is a table $1 \times 1$, consisting of a single character 1, so the answer is $1$.
In the third test case, there is a table:
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| 0 | 1 | 1 |
In the fourth test case, there is a table:
| 0 | 1 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 |
In the fifth test case, there is a table:
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
Rectangles with maximum area are shown in bold.
Input
题意翻译
#### 题目描述 给定一个长度为 $n$ 的二进制字符串 $s$，构建一个 $n \times n$ 的方格表。首行写下原始字符串 $s$，次行右移一个字符的循环移位字符串 $s$，第三行右移两个字符的循环移位字符串 $s$，以此类推。因此，第 $k$ 行包含一个从 $s$ 右移 $k$ 个字符的循环移位字符串。行从上到下编号 $0$ 至 $n-1$。 在生成的表中，需要找到只由数字 $1$ 构成的矩形并计算其面积，返回最大的面积。 注意：字符串 $s$ 向右循环移动 $k$ 位是指将其最后 $k$ 个字符移动到前面，即字符串 $s_{n-k+1} \cdots s_n \; s_1 \cdots s_{n-k}$。 #### 输入格式 第一行的正整数 $t$ ($1\leq t\leq 2\times10^4$) 是测试用例的数量。 对于每个测试用例，只有一行，是一个只由零和一组成的二进制字符串。 保证所有测试用例中字符总数之和不超过 $2\times 10^5$。 #### 输出格式 对于每个测试用例，输出一个整数：只由数字 $1$ 构成的矩形的最大面积。如果不存在这样的矩形，则输出 $0$。Output
输入数据格式：每个测试用例包含多个测试案例。第一行包含一个整数t（1≤t≤2×10^4）——测试案例的数量。接下来是每个测试案例的描述。每个测试案例的第一行（也是唯一一行）包含一个二进制字符串s（1≤|s|≤2×10^5），由字符'0'和'1'组成。
输出数据格式：对于每个测试案例，输出一个整数——只由'1'组成的最大矩形的面积。如果没有这样的矩形，输出0。
示例输入输出已在题目中给出，这里不再重复。题目大意：给定一个长度为n的二进制字符串s，由字符'0'和'1'组成。根据s构建一个n×n的方形表，表的第一行是原始字符串s，第二行是s向右循环移动一次的结果，第三行是s向右循环移动两次的结果，以此类推。在得到的表中，需要找到只由'1'组成的面积最大的矩形。 输入数据格式：每个测试用例包含多个测试案例。第一行包含一个整数t（1≤t≤2×10^4）——测试案例的数量。接下来是每个测试案例的描述。每个测试案例的第一行（也是唯一一行）包含一个二进制字符串s（1≤|s|≤2×10^5），由字符'0'和'1'组成。 输出数据格式：对于每个测试案例，输出一个整数——只由'1'组成的最大矩形的面积。如果没有这样的矩形，输出0。 示例输入输出已在题目中给出，这里不再重复。