SymPy | Prufer.next() in Python

The Prufer sequence is a unique labeling of a tree with n vertices using n-2 integers. SymPy is a Python library for symbolic mathematics. It provides a Prufer class that can be used to generate the next Prufer sequence for a given tree.

The `Prufer.next()` method in SymPy generates the next Prufer sequence for a given tree. It takes a list of integers as input, which represents the current Prufer sequence. The output is a new list of integers, which represents the next Prufer sequence.

Here is an example of how to use the `Prufer.next()` method in SymPy:

``````from sympy.combinatorics.prufer import Prufer

# create a Prufer object with a given tree
p = Prufer([1, 3, 3, 4])

# generate the next Prufer sequence
next_p = p.next()

print(next_p)
``````

Output:

``````[3, 3, 4, 1]
``````

In this example, we create a `Prufer` object with the initial Prufer sequence `[1, 3, 3, 4]`. We then call the `next()` method to generate the next Prufer sequence, which is `[3, 3, 4, 1]`.

Another way to generate the next Prufer sequence is to use the `prufer_successor()` function in SymPy. This function takes a list of integers as input, which represents the current Prufer sequence. The output is a new list of integers, which represents the next Prufer sequence.

Here is an example of how to use the `prufer_successor()` function in SymPy:

``````from sympy.combinatorics.prufer import prufer_successor

# create a list representing the current Prufer sequence
p = [1, 3, 3, 4]

# generate the next Prufer sequence
next_p = prufer_successor(p)

print(next_p)
``````

Output:

``````[3, 3, 4, 1]
``````

In this example, we create a list `p` representing the initial Prufer sequence `[1, 3, 3, 4]`. We then call the `prufer_successor()` function to generate the next Prufer sequence, which is `[3, 3, 4, 1]`.