Little Monk and Flip Operations
Tag(s):

Algorithms, Bit manipulation, DFS, Easy-Medium, Graph Theory

Problem
Editorial
Analytics

Given a tree with $N$ nodes and one integer, $a$. Each node is numbered from $1$ to $N$. Each node $i$ has an integer, $A_i$, attached to it. You can perform only one type of operation, i.e.

1. Select a subtree of the given tree which includes the node $a$.

2. Select a non-negative integer $k$

3. Flip the $k^{th}$ least significant bit of the integers attached to each node in the selected subtree.

Note: A subtree of a tree $T$ is a tree with both nodes and edges as subsets of nodes and edges of $T$.

Calculate the minimum number of operations that is required to make all the integers attached to the nodes of the given tree equal to $0$.

Input format: :

First line contains two space separated integers, $N$ and $a$ $(1 \le N \le 10^5)$, $(1 \le a \le N)$. Next $N-1$ lines contains two space separated integers each, $x$ and $y$ $(1 \le x, y \le N)$, denoting that there is an edge between $x$ and $y$. Next line contains $N$ space separated integers, $A_i$ $(0 \le A_i \le 10^9)$, denoting the integers attached to the nodes.

Output format: :

Print the minimum number of operations that is required to make all the integers attached to the nodes of the given tree equal to $0$.

SAMPLE INPUT
3 1
1 2
1 3
1 2 1

SAMPLE OUTPUT
3

Explanation

Values on each node in binary notation are:

$A_1 = 01$
$A_2 = 10$
$A_3 = 01$

In first operation, we will select node $1$ and node $2$ as subtree and $k = 2$. So, after flipping the $k^{th}$ least significant bit of the integers attached to each node in the selected subtree the new values on each node in binary notation will be:

$A_1 = 11$
$A_2 = 00$
$A_3 = 01$

In second operation, we will select node $1$ as subtree and $k = 2$. So, after flipping the $k^{th}$ least significant bit of the integers attached to each node in the selected subtree the new values on each node in binary notation will be:

$A_1 = 01$
$A_2 = 00$
$A_3 = 01$

In third operation, we will select node $1$ and node $3$ as subtree and $k = 1$. So, after flipping the $k^{th}$ least significant bit of the integers attached to each node in the selected subtree the new values on each node in binary notation will be:

$A_1 = 00$
$A_2 = 00$
$A_3 = 00$

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Scala 2.11.8, Swift, Visual Basic

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This Problem was Asked in

Challenge Name

CodeMonk (Graph Theory Part I)

OTHER PROBLEMS OF THIS CHALLENGE
• Algorithms > Graphs
• Algorithms > Graphs
• Algorithms > Graphs
• Algorithms > Graphs