Mock CCO '19 Contest 1 Problem 5 - A Tree Problem

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Points: 25 (partial)

Time limit: 0.6s

Memory limit: 162M

Problem types

Count the number of distinct spanning trees that exist on $N$ ~N~ labeled vertices, given that some of these vertices are restricted in their degree.

Constraints

$1 \le N \le 1000$ ~1 \le N \le 1000~

In test data worth 30% of marks, you may assume $N \le 300$ ~N \le 300~.

Input Specification

The first line contains a single positive integer, $N$ ~N~.

Each of the next $N$ ~N~ lines contains a single integer, $d_i$ ~d_i~. If $d_i$ ~d_i~ is -1, then there is no degree restriction on vertex $i$ ~i~. Otherwise, vertex $i$ ~i~ must have degree $d_i$ ~d_i~.

Output Specification

Output the number of distinct spanning trees.

Sample Input

3
-1
-1
1

Sample Output

Comments

14

bqi343 commented on May 19, 2019, 1:52 p.m.

Just read the formula at the end of this link.