def root(x): if F[x] != x: F[x] = root(F[x]) return F[x]

This is a Python function that finds the root of a given element in a disjoint set data structure.

The disjoint set data structure is a data structure that represents a collection of disjoint sets. Each set is represented by a root element, and each element in the set points to its root element. The root element is the representative of the set, and it is used to determine whether two elements belong to the same set.

The function takes an element x as input and checks whether x is its own root (i.e., it is the representative element of its set). If not, it recursively finds the root of the parent of x until it reaches the root of the set. Finally, it returns the root element.

The function assumes that the disjoint sets are represented using an array F, where F[i] is the parent of element i. Initially, each element is its own parent, so F[i] = i. The function updates the parent pointers in F to compress the path to the root element, which improves the efficiency of subsequent root() calls.

Example usage:

F = [0, 1, 2, 3, 4, 5]
print(root(3)) # Output: 3

In this example, the disjoint sets are {0}, {1}, {2}, {3}, {4}, and {5} initially. We call root(3), which returns the root element of element 3. Since 3 is its own root, the function returns 3.