Coloring Nodes — Coding Round Problem from Service Now !!

#	User	Rating
1	ecnerwala	3649
2	Benq	3581
3	jiangly	3578
4	orzdevinwang	3570
5	Geothermal	3569
5	cnnfls_csy	3569
7	tourist	3565
8	maroonrk	3531
9	Radewoosh	3521
10	Um_nik	3482

#	User	Contrib.
1	maomao90	174
2	awoo	164
3	adamant	161
4	TheScrasse	159
5	nor	158
6	maroonrk	156
7	-is-this-fft-	152
8	SecondThread	146
8	orz	146
10	pajenegod	145

Problem Statement

In this challenge, you are given a tree with nodes coloured as red or black and your goal is to change the colour of all the nodes as described.

Given a tree of tree_nodes vertices numbered from 1 to tree_nodes and rooted at vertex 1. Initially, all the vertices except 1 are coloured red. Vertex 1 is coloured black.

Select any red vertex adjacent to at least one of the black-coloured vertices and change the colour of that selected vertex to black. If there are multiple such vertices, choose any one of them.

Find the number of ways to change and colour all the tree vertices into black. Since this number can be large, return it modulo 10^9 + 7.

Note: Two ways are considered different if the nodes coloured in the ith step is different in the two ways.

For Example: Given tree_nodes = 4, tree_from[1, 1, 2], tree_to = [2, 3, 4]
1. Change the colour of vertex 3 to black(since vertex 1 is already black). Now, change the colour of vertex 2 to black (since vertex 1 is already coloured black). And finally, change the colour of vertex 4 to black(since vertex 2 is already coloured black).

2. Change the colour of vertex 2 to black(since vertex 1 is already black). Now, change the colour of vertex 3 to black (since vertex 1 is already coloured black). And finally, change the colour of vertex 4 to black(since vertex 2 is already coloured black).

3. Change the colour of vertex 2 to black(since vertex 1 is already black). Now, change the colour of vertex 4 to black (since vertex 2 is already coloured black). And finally, change the colour of vertex 3 to black(since vertex 1 is already coloured black).