A Tree Problem

Points: 25 (partial)

Time limit: 0.6s

Memory limit: 162M

Problem types

Allowed languages

Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

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

10

bqi343 commented on May 19, 2019, 9:52 a.m.

Just read the formula at the end of this link.