ABC277 C — Ladder Takahashi

1# -*- coding: utf-8 -*-2 3 4class UnionFind:5    '''Represents a data structure that tracks a set of elements partitioned6       into a number of disjoint (non-overlapping) subsets.7    Landau notation: O(α(n)), where α(n) is the inverse Ackermann function.8    See:9    https://www.youtube.com/watch?v=zV3Ul2pA2Fw10    https://en.wikipedia.org/wiki/Disjoint-set_data_structure11    https://atcoder.jp/contests/abc120/submissions/444494212    '''13 14    def __init__(self, number_count: int):15        '''16        Args:17            number_count: The size of elements (greater than 2).18        '''19        self.parent_numbers = [-1 for _ in range(number_count)]20 21    def find_root(self, number: int) -> int:22        '''Follows the chain of parent pointers from number up the tree until23           it reaches a root element, whose parent is itself.24        Args:25            number: The trees id (0-index).26        Returns:27            The index of a root element.28        '''29        if self.parent_numbers[number] < 0:30            return number31 32        self.parent_numbers[number] = self.find_root(self.parent_numbers[number])33        return self.parent_numbers[number]34 35    def get_group_size(self, number: int) -> int:36        '''37        Args:38            number: The trees id (0-index).39        Returns:40            The size of group.41        '''42        return -self.parent_numbers[self.find_root(number)]43 44    def is_same_group(self, number_x: int, number_y: int) -> bool:45        '''Represents the roots of tree number_x and number_y are in the same46           group.47        Args:48            number_x: The trees x (0-index).49            number_y: The trees y (0-index).50        '''51        return self.find_root(number_x) == self.find_root(number_y)52 53    def merge_if_needs(self, number_x: int, number_y: int) -> bool:54        '''Uses find_root to determine the roots of the tree number_x and55           number_y belong to. If the roots are distinct, the trees are combined56           by attaching the roots of one to the root of the other.57        Args:58            number_x: The trees x (0-index).59            number_y: The trees y (0-index).60        '''61        x = self.find_root(number_x)62        y = self.find_root(number_y)63 64        if x == y:65            return False66 67        if self.get_group_size(x) >= self.get_group_size(y):68            self.parent_numbers[x] += self.parent_numbers[y]69            self.parent_numbers[y] = x70        else:71            self.parent_numbers[y] += self.parent_numbers[x]72            self.parent_numbers[x] = y73        return True74 75 76def compress_coordinate(elements: list) -> dict:77    ''' Means that reduce the numerical value while maintaining the magnitude78        relationship.79    Args:80        elements: list of integer numbers (greater than -1).81    Returns:82        A dictionary's items ((original number, compressed number) pairs).83    Landau notation: O(n log n)84    '''85 86    # See:87    # https://atcoder.jp/contests/abc036/submissions/5707999?lang=ja88    compressed_list = sorted(set(elements))89    return {element: index for index, element in enumerate(compressed_list)}90 91 92def main():93    import sys94 95    input = sys.stdin.readline96 97    n = int(input())98    ab = list()99    c = [1]100    uf = UnionFind(4 * 10 ** 5 + 10)101    102    for _ in range(n):103        ai, bi = map(int, input().split())104        ab.append((ai, bi))105        c.append(ai)106        c.append(bi)107    108    c = compress_coordinate(c)109 110    for ai, bi in ab:111        uf.merge_if_needs(c[ai], c[bi])112 113    ans = 1114 115    for key, value in c.items():116        if uf.is_same_group(0, value):117            ans = max(ans, key)118 119    print(ans)120    121 122if __name__ == "__main__":123    main()124