A15394 | Sending a Sequence Over the Network
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题目描述
The sequence $a$ is sent over the network as follows:
1. sequence $a$ is split into segments (each element of the sequence belongs to exactly one segment, each segment is a group of consecutive elements of sequence);
2. for each segment, its length is written next to it, either to the left of it or to the right of it;
3. the resulting sequence $b$ is sent over the network.
For example, we needed to send the sequence $a = [1, 2, 3, 1, 2, 3]$ . Suppose it was split into segments as follows: $[\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}]$ . Then we could have the following sequences:
- $b = [1, \color{red}{1}, 3, \color{blue}{2, 3, 1}, \color{green}{2, 3}, 2]$ ,
- $b = [\color{red}{1}, 1, 3, \color{blue}{2, 3, 1}, 2, \color{green}{2, 3}]$ ,
- $b = [\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}]$ ,
- $b = [\color{red}{1}, 1,\color{blue}{2, 3, 1}, 3, \color{green}{2, 3}, 2]$ .
If a different segmentation had been used, the sent sequence might have been different.
The sequence $b$ is given. Could the sequence $b$ be sent over the network? In other words, is there such a sequence $a$ that converting $a$ to send it over the network could result in a sequence $b$ ?
1. sequence $a$ is split into segments (each element of the sequence belongs to exactly one segment, each segment is a group of consecutive elements of sequence);
2. for each segment, its length is written next to it, either to the left of it or to the right of it;
3. the resulting sequence $b$ is sent over the network.
For example, we needed to send the sequence $a = [1, 2, 3, 1, 2, 3]$ . Suppose it was split into segments as follows: $[\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}]$ . Then we could have the following sequences:
- $b = [1, \color{red}{1}, 3, \color{blue}{2, 3, 1}, \color{green}{2, 3}, 2]$ ,
- $b = [\color{red}{1}, 1, 3, \color{blue}{2, 3, 1}, 2, \color{green}{2, 3}]$ ,
- $b = [\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}]$ ,
- $b = [\color{red}{1}, 1,\color{blue}{2, 3, 1}, 3, \color{green}{2, 3}, 2]$ .
If a different segmentation had been used, the sent sequence might have been different.
The sequence $b$ is given. Could the sequence $b$ be sent over the network? In other words, is there such a sequence $a$ that converting $a$ to send it over the network could result in a sequence $b$ ?
输入格式
The first line of input data contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.
Each test case consists of two lines.
The first line of the test case contains an integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the size of the sequence $b$ .
The second line of test case contains $n$ integers $b_1, b_2, \dots, b_n$ ( $1 \le b_i \le 10^9$ ) — the sequence $b$ itself.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .
Each test case consists of two lines.
The first line of the test case contains an integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the size of the sequence $b$ .
The second line of test case contains $n$ integers $b_1, b_2, \dots, b_n$ ( $1 \le b_i \le 10^9$ ) — the sequence $b$ itself.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .
输出格式
For each test case print on a separate line:
- YES if sequence $b$ could be sent over the network, that is, if sequence $b$ could be obtained from some sequence $a$ to send $a$ over the network.
- NO otherwise.
You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).
- YES if sequence $b$ could be sent over the network, that is, if sequence $b$ could be obtained from some sequence $a$ to send $a$ over the network.
- NO otherwise.
You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).
输入输出样例
输入 #1
7 9 1 1 2 3 1 3 2 2 3 5 12 1 2 7 5 6 5 7 8 9 10 3 4 4 8 6 2 2 3 1 10 4 6 2 1 9 4 9 3 4 2 1 1
输出 #1
YES YES YES NO YES YES NO
In the first case, the sequence $b$ could be obtained from the sequence $a = [1, 2, 3, 1, 2, 3]$ with the following partition: $[\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}]$ . The sequence $b$ : $[\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}]$ .
In the second case, the sequence $b$ could be obtained from the sequence $a = [12, 7, 5]$ with the following partition: $[\color{red}{12}] + [\color{green}{7, 5}]$ . The sequence $b$ : $[\color{red}{12}, 1, 2, \color{green}{7, 5}]$ .
In the third case, the sequence $b$ could be obtained from the sequence $a = [7, 8, 9, 10, 3]$ with the following partition: $[\color{red}{7, 8, 9, 10, 3}]$ . The sequence $b$ : $[5, \color{red}{7, 8, 9, 10, 3}]$ .
In the fourth case, there is no sequence $a$ such that changing $a$ for transmission over the network could produce a sequence $b$ .
In the second case, the sequence $b$ could be obtained from the sequence $a = [12, 7, 5]$ with the following partition: $[\color{red}{12}] + [\color{green}{7, 5}]$ . The sequence $b$ : $[\color{red}{12}, 1, 2, \color{green}{7, 5}]$ .
In the third case, the sequence $b$ could be obtained from the sequence $a = [7, 8, 9, 10, 3]$ with the following partition: $[\color{red}{7, 8, 9, 10, 3}]$ . The sequence $b$ : $[5, \color{red}{7, 8, 9, 10, 3}]$ .
In the fourth case, there is no sequence $a$ such that changing $a$ for transmission over the network could produce a sequence $b$ .
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评测结果：Accepted