Source code for algorithms.data_structures.union_find_with_path_compression

    Union Find with path compression
    A disjoint-set data structure, also called union-find data structure
    implements two functions:

    union(A, B) - merge A's set with B's set

    find(A) - finds what set A belongs to

    Union with path compression approach:

    Each node visited on the way to a root node may as well be attached
    directly to the root node.
    attach the smaller tree to the root of the larger tree

    Time Complexity  :  O(a(n)), where a(n) is the inverse of the function
    n=f(x)=A(x,x) and A is the extremely fast-growing Ackermann function.

    Psuedo Code:

[docs]class UnionFindWithPathCompression: def __init__(self, N): if type(N) != int: raise TypeError("size must be integer") if N < 0: raise ValueError("N cannot be a negative integer") self.__parent = [] self.__rank = [] self.__N = N for i in range(0, N): self.__parent.append(i) self.__rank.append(0)
[docs] def make_set(self, x): if type(x) != int: raise TypeError("x must be integer") if x != self.__N: raise ValueError( "a new element must have index {0}".format(self.__N)) self.__parent.append(x) self.__rank.append(0) self.__N = self.__N + 1
[docs] def union(self, x, y): self.__validate_ele(x) self.__validate_ele(y) x_root = self.__find(x) y_root = self.__find(y) if x_root == y_root: return # x and y are not already in same set. Merge them if self.__rank[x_root] < self.__rank[y_root]: self.__parent[x_root] = y_root elif self.__rank[x_root] > self.__rank[y_root]: self.__parent[y_root] = x_root else: self.__parent[y_root] = x_root self.__rank[x_root] = self.__rank[x_root] + 1
def __find(self, x): if self.__parent[x] != x: self.__parent[x] = self.__find(self.__parent[x]) return self.__parent[x]
[docs] def find(self, x): self.__validate_ele(x) if self.__parent[x] == x: return x else: return self.find(self.__parent[x])
[docs] def is_connected(self, x, y): self.__validate_ele(x) self.__validate_ele(y) return self.find(x) == self.find(y) # use for unit testing check if the path is compressed
[docs] def parent(self, x): return self.__parent[x]
def __validate_ele(self, x): if type(x) != int: raise TypeError("{0} is not an integer".format(x)) if x < 0 or x >= self.__N: raise ValueError("{0} is not in [0,{1})".format(x, self.__N))