Valid Output for DSU Problems

AtCoder

IDagc074_d

Time2000ms

Memory256MB

Difficulty—

A sequence that can be obtained as $A$ by performing the following operations is called a **special sequence**: * Prepare an undirected graph consisting of $N$ vertices and $0$ edges, and a sequence $A$ of length $0$. * Prepare queries for integers $i,j$ satisfying $1 \leq i < j \leq N$ and $q \in {1,2}$: * When $q=1$, connect vertices $i$ and $j$ with an edge. * When $q=2$, append $1$ to the end of $A$ if vertices $i$ and $j$ are connected, and append $0$ otherwise. * There are $N(N-1)$ possible queries; rearrange them in any order and process them in that order. You are given a sequence $B$ of length $\frac{N(N-1)}{2}$ consisting of $0$ and $1$. You can perform the following operation on $B$ any number of times: * Choose an integer $i$ satisfying $1 \leq i \leq \frac{N(N-1)}{2}-1$, and swap $B_i$ and $B_{i+1}$. Determine whether it is possible to make $B$ a special sequence, and if possible, find the minimum number of operations required. Solve $T$ test cases per input. ## Constraints * $1 \leq T$ * $2 \leq N \leq 500$ * $|B| =\frac{N(N-1)}{2}$ * $0 \leq B_i \leq 1$ * The sum of $|B|$ over all test cases is at most $3 \times 10^5$. * The sum of $N^3$ over all test cases is at most $500^3$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each case is given in the following format: $N$ $B_1$ $B_2$ $\ldots$ $B_{\frac{N(N-1)}{2}}$ [samples]

Samples

Input #1

4
4
1 1 0 1 1 0
2
1
3
0 0 0
5
1 1 1 1 1 1 1 1 1 0

Output #1

1
0
0
3

In the first test case, if the queries are processed in the order $(q,i,j)=(1,1,4),$ $(2,1,4),$ $(1,2,4),$ $(2,1,2),$ $(1,1,2),$ $(2,2,3),$ $(2,2,4),$ $(2,3,4),$ $(1,3,4),$ $(1,1,3),$ $(2,1,3),$ $(1,2,3)$, the resulting sequence is $(1,1,0,1,0,1)$, and $B$ can be changed to this sequence by performing the operation once. Also, $(1,1,0,1,1,0)$ is not a special sequence, so the answer is $1$.

API Response (JSON)

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