시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
2 초 | 256 MB | 16 | 13 | 13 | 81.250% |
You are given a tree with $N$ vertices. The vertices are numbered $0$ through $N-1$, and the edges are numbered $1$ through $N-1$. Edge $i$ connects vertex $x_i$ and $y_i$, and has a value $a_i$. You can perform the following operation any number of times: choose a simple path and a non-negative integer $x$, then for each edge $e$ that belongs to the path, change $a_e$ by executing $a_e := a_e \oplus x$ ($\oplus$ denotes $XOR$).
Your objective is to have $a_e = 0$ for all edges $e$. Find the minimum number of operations required to achieve it.
Input is given in the following format:
$N$
$x_1$ $y_1$ $a_1$
$x_2$ $y_2$ $a_2$
$\ldots$
$x_{N-1}$ $y_{N-1}$ $a_{N-1}$
Find the minimum number of operations required to achieve the objective.
$2 \le N \le 10^5$, $0 \le x_i,y_i \le N-1$, $0 \le a_i \le 15$. The given graph is a tree, all input values are integers.
5 0 1 1 0 2 3 0 3 6 3 4 4
3
2 1 0 0
0
In Sample 1, the objective can be achieved in three operations, as follows: first, choose the path connecting Vertex $1, 2$, and $x = 1$, then, choose the path connecting Vertex $2, 3$, and $x = 2$; lastly, choose the path connecting Vertex $0, 4$, and $x = 4$.