A16267. Button Pressing
编程题
普及/提高-
知识点
题目描述
You are given $N$ buttons (numbered from $1$ to $N$ ) and $N$ lamps (numbered from $1$ to $N$ ). Each lamp can either be on or off. Initially, lamp $i$ is on if $A_i = 1$ , and off if $A_i = 0$ .
Button $i$ is connected to lamp $i - 1$ (if $i > 1$ ) and lamp $i + 1$ (if $i < N$ ). In one move, you can press a button $i$ only if lamp $i$ is on. When a button is pressed, the state of the lamps connected to this button is toggled. Formally, the lamps will be on if it was off previously, and the lamps will be off if it was on previously. Note that lamp $i$ is not connected to button $i$ , thus, the state of lamp $i$ does not change if button $i$ is pressed.
After zero or more moves, you want lamp $i$ to be on if $B_i = 1$ , and off if $B_i = 0$ . Determine if it is possible to achieve this task.
Button $i$ is connected to lamp $i - 1$ (if $i > 1$ ) and lamp $i + 1$ (if $i < N$ ). In one move, you can press a button $i$ only if lamp $i$ is on. When a button is pressed, the state of the lamps connected to this button is toggled. Formally, the lamps will be on if it was off previously, and the lamps will be off if it was on previously. Note that lamp $i$ is not connected to button $i$ , thus, the state of lamp $i$ does not change if button $i$ is pressed.
After zero or more moves, you want lamp $i$ to be on if $B_i = 1$ , and off if $B_i = 0$ . Determine if it is possible to achieve this task.
输入格式
This problem has multiple test cases. The first line consists of an integer $T$ ( $1 \leq T \leq 1000$ ), which represents the number of test cases. Each test case consists of three lines.
The first line of each test case consists of an integer $N$ ( $3 \le N \le 200\,000$ ). The sum of $N$ over all test cases does not exceed $200\,000$ .
The second line of each test case consists of a string $A$ of length $N$ . Each character of $A$ can either be 0 or 1. The $i$ -th character represents the initial state of lamp $i$ .
The third line of each test case consists of a string $A$ of length $N$ . Each character of $B$ can either be 0 or 1. The $i$ -th character represents the desired final state of lamp $i$ .
The first line of each test case consists of an integer $N$ ( $3 \le N \le 200\,000$ ). The sum of $N$ over all test cases does not exceed $200\,000$ .
The second line of each test case consists of a string $A$ of length $N$ . Each character of $A$ can either be 0 or 1. The $i$ -th character represents the initial state of lamp $i$ .
The third line of each test case consists of a string $A$ of length $N$ . Each character of $B$ can either be 0 or 1. The $i$ -th character represents the desired final state of lamp $i$ .
输出格式
For each test case, output YES in a single line if the final state of all lamps can be reached after zero or more moves, or NO otherwise.
输入输出样例
输入 #1
2 4 0101 0100 3 000 010
输出 #1
YES NO
输入 #2
5 7 0101011 1111010 5 11111 00000 4 1101 1101 6 101010 100100 3 000 000
输出 #2
NO NO YES YES YES
说明/提示
Explanation for the sample input/output #1
For the first test case, by pressing the buttons $4, 2, 4, 3, 1, 2$ in sequence, the condition of the buttons changes as: $0101 \rightarrow 0111 \rightarrow 1101 \rightarrow 1111 \rightarrow 1010 \rightarrow 1110 \rightarrow 0100$ .
For the second test case, you are unable to press any button, hence it is impossible to reach the final state.
For the first test case, by pressing the buttons $4, 2, 4, 3, 1, 2$ in sequence, the condition of the buttons changes as: $0101 \rightarrow 0111 \rightarrow 1101 \rightarrow 1111 \rightarrow 1010 \rightarrow 1110 \rightarrow 0100$ .
For the second test case, you are unable to press any button, hence it is impossible to reach the final state.