AtCoder Regular Contest 150
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Problem Statement
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We have a connected undirected graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$. The $i$-th edge connects vertices $U_i$ and $V_i$.
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Additionally, we are given an integer sequence of length $N$, $A=(A_1,\ A_2, \dots,\ A_N)$, and an integer sequence of length $K$, $B=(B_1,\ B_2,\ \dots,\ B_K)$.
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Determine whether $G$, $A$, and $B$ satisfy the following condition.
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- For every simple path from vertex
$1$to$N$in$G$,$v=(v_1,\ v_2, \dots,\ v_k)\ (v_1=1,\ v_k=N)$,$B$is a (not necessarily contiguous) subsequence of$(A_{v_1},\ A_{v_2},\ \dots,\ A_{v_k})$.
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Constraints
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$2 \leq N \leq 10^5$$1 \leq K \leq N$$N-1 \leq M \leq 2 \times 10^5$$1 \leq U_i < V_i \leq N$$(U_i,\ V_i) \neq (U_j,\ V_j)$if$i \neq j$.$1 \leq A_i,\ B_i \leq N$- All values in the input are integers.
- The given graph
$G$is connected.
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Input
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The input is given from Standard Input in the following format:
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N M K
U_1 V_1
U_2 V_2
\vdots
U_M V_M
A_1 A_2 \dots A_N
B_1 B_2 \dots B_K翻译中…
Output
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If the condition is satisfied, print Yes; otherwise, print No.
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样例
Input #1
6 6 3
1 2
1 3
2 4
3 5
4 6
5 6
1 2 4 5 2 6
1 2 6
Output #1
Yes
There are two simple paths from vertex $1$ to vertex $6$: $(1,\ 2,\ 4,\ 6)$ and $(1,\ 3,\ 5,\ 6)$. The $(A_{v_1},\ A_{v_2},\ \dots,\ A_{v_k})$ corresponding to these paths are $(1,\ 2,\ 5,\ 6)$ and $(1,\ 4,\ 2,\ 6)$. Both of them have $B=(1,\ 2,\ 6)$ as a subsequence, so the answer is `Yes`.
Input #2
5 5 3
1 2
2 3
3 4
4 5
2 5
1 2 3 5 2
1 3 2
Output #2
No
For a simple path $(1,\ 2,\ 5)$ from vertex $1$ to vertex $5$, the $(A_{v_1},\ A_{v_2},\ \dots,\ A_{v_k})$ is $(1,\ 2,\ 2)$, which does not have $B=(1,\ 3,\ 2)$ as a subsequence.
Input #3
10 20 3
5 6
5 10
5 7
3 5
3 7
2 6
3 8
4 5
5 8
7 10
1 6
1 9
4 6
1 2
1 4
6 7
4 8
2 5
3 10
6 9
2 5 8 5 1 5 1 1 5 10
2 5 1
Output #3
Yes
题目信息
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