Black and White Tree

题意翻译

给定一棵 $n$ 个定点的无根树，其中有一些顶点是黑色的（至少两个），其余则是白色的。 你可以从任意一个顶点出发，按如下规则行进（也可以不行动）： - 选择任意一个黑色顶点，沿着当前顶点到该黑色顶点的简单路径前进一步。 - 注意：除第一次行动之外，你每次选择的顶点不可以与上次选择的顶点相同。 - 你可以行动至多 $100^{500}$ 次，如果到达黑色顶点，则立即终止。 已知这棵树的形态和黑色顶点的分布，请你求出每个顶点能不能在规定次数内到达黑色顶点。 数据范围保证：$n\le 3\times10^5$。

题目描述

You are given a tree consisting of $ n $ vertices. Some of the vertices (at least two) are black, all the other vertices are white. You place a chip on one of the vertices of the tree, and then perform the following operations: - let the current vertex where the chip is located is $ x $ . You choose a black vertex $ y $ , and then move the chip along the first edge on the simple path from $ x $ to $ y $ . You are not allowed to choose the same black vertex $ y $ in two operations in a row (i. e., for every two consecutive operations, the chosen black vertex should be different). You end your operations when the chip moves to the black vertex (if it is initially placed in a black vertex, you don't perform the operations at all), or when the number of performed operations exceeds $ 100^{500} $ . For every vertex $ i $ , you have to determine if there exists a (possibly empty) sequence of operations that moves the chip to some black vertex, if the chip is initially placed on the vertex $ i $ .

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 3 \le n \le 3 \cdot 10^5 $ ) — the number of vertices in the tree. The second line contains $ n $ integers $ c_1, c_2, \dots, c_n $ ( $ 0 \le c_i \le 1 $ ), where $ c_i = 0 $ means that the $ i $ -th vertex is white, and $ c_i = 1 $ means that the $ i $ -th vertex is black. At least two values of $ c_i $ are equal to $ 1 $ . Then $ n-1 $ lines follow, each of them contains two integers $ u_i $ and $ v_i $ ( $ 1 \le u_i, v_i \le n $ ; $ u_i \ne v_i $ ) — the endpoints of some edge. These edges form a tree.

输出格式

Print $ n $ integers. The $ i $ -th integer should be equal to $ 1 $ if there exists a (possibly empty) sequence of operations that moves the chip to some black vertex if it is placed on the vertex $ i $ , and $ 0 $ if no such sequence of operations exists.

输入输出样例

输入样例 #1

8
0 1 0 0 0 0 1 0
8 6
2 5
7 8
6 5
4 5
6 1
7 3

输出样例 #1

0 1 1 1 1 0 1 1