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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".
Each 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 $$$2 \cdot 10^5$$$.
For each test case, output a single integer — the maximum area of a rectangle consisting only of ones. If there is no such rectangle, output $$$0$$$.
501101011110101010
0 1 2 6 1
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.
Informação
Provedor Codeforces
Código CF1820B
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Datas 09/05/2023 10:38:50
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