Educational DP Contest AtCoder P - Independent Set

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Points: 12
Time limit: 1.0s
Memory limit: 1G
Problem types

There is a tree with N vertices, numbered 1, 2, \dots, N. For each i (1 \le i \le N-1), the i-th edge connects Vertex x_i and y_i.

Taro has decided to paint each vertex in white or black. Here, it is not allowed to paint two adjacent vertices both in black.

Find the number of ways in which the vertices can be painted, modulo 10^9+7.

Constraints

  • All values in input are integers.
  • 1 \le N \le 10^5
  • 1 \le x_i, y_i \le N
  • The given graph is a tree.

Input Specification

The first line will contain the integer N.

The next N-1 lines will each contain 2 space separated integers x_i, y_i.

Output Specification

Print the number of ways in which the vertices can be painted, modulo 10^9+7.

Sample Input 1

3
1 2
2 3

Sample Output 1

5

Explanation For Sample 1

There are five ways to paint the vertices, as follows:

Sample Input 2

4
1 2
1 3
1 4

Sample Output 2

9

Explanation For Sample 2

There are nine ways to paint the vertices, as follows:

Sample Input 3

1

Sample Output 3

2

Sample Input 4

10
8 5
10 8
6 5
1 5
4 8
2 10
3 6
9 2
1 7

Sample Output 4

157

Comments


  • 0
    ExoskeletalPhosphors  commented on Dec. 12, 2020, 1:27 a.m.

    Can we assume the edge goes from x_i to y_i? (As in, can we assume that the tree functions if you assume all the edges are directed?)


    • 0
      julian33  commented on Dec. 12, 2020, 3:49 p.m.

      The graph is bidirectional.


  • 2
    Medi  commented on Jan. 18, 2019, 5:36 p.m.

    Since it's a single tree, all the vertices will be part of the graph, right?


    • 2
      Kirito  commented on Jan. 18, 2019, 8:29 p.m.

      Yes.