CentroidDecomposition
(expansion/tree/CentroidDecomposition.py)

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• Last update: 2023-07-08 15:30:30+09:00

概要

重心分解 です．

使い方

• __init__(n, edges=None) := 頂点数 n で初期化します．辺情報を与える場合は，$ edges[from] = [to1, to2, …]$の形式で与えてください．
• add_edge(u, v) := u -> v の有向辺を追加します．
• read_edges(indexed=1) := n - 1 辺の情報を標準入力として受け取ります．
• build(root) := 根を root として構築します

• cent_ind_dist(u) := 頂点 u + 重心分解木における u の各先祖の [頂点番号, u からの距離] を返します．

• self.par := 重心分解木における各頂点の親です．
• self.centroids[i] := 重心分解木における深さがiの頂点の一覧です

Code

class CentroidDecomposition:
    def __init__(self, n, edges=None):
        self.n = n
        self.par = [-1] * n  # 重心分解木の親
        self.depth = [-1] * n  # 重心分解木の深さ
        self.size = [-1] * n  # 重心分解木の部分木のサイズ
        self.childcnt = [0] * n  # 重心分解木の子の数
        if edges is None:
            self.edges = [[] for _ in range(n)]
        else:
            self.edges = edges
            # コピーしてないので注意

        self.centroids = []  # centroids[i] := 深さが i の重心のリスト
        self.treeind = []  # treeind[j * logn + i] := 頂点 j が深さ i の重心の何番目の部分木か
        self.cent_dist = []  # cent_dist[j * logn + i] := 頂点 j が深さ i の重心からの距離

    def add_edge(self, u, v):
        self.edges[u].append(v)
        self.edges[v].append(u)

    def read_edges(self, indexed=1):
        for _ in range(self.n - 1):
            u, v = map(int, input().split())
            u -= indexed
            v -= indexed
            self.add_edge(u, v)

    def build(self):
        stack = [(0, -1, 0, -1)]
        while stack:
            pos, bpos, d, c = stack.pop()
            st = [pos]
            route = []
            sz = 0

            if len(self.treeind) == d * self.n:
                self.treeind += [-1] * self.n
                self.cent_dist += [-1] * self.n
                self.centroids.append([])
            if d >= 1:
                self.cent_dist[(d - 1) * self.n + pos] = 1

            while st:
                pos = st.pop()
                self.depth[pos] = -2
                route.append(pos)
                sz += 1
                if d >= 1:
                    self.treeind[(d - 1) * self.n + pos] = c

                for npos in self.edges[pos]:
                    if self.depth[npos] == -1:
                        st.append(npos)
                        if d >= 1:
                            self.cent_dist[(d - 1) * self.n + npos] = (
                                self.cent_dist[(d - 1) * self.n + pos] + 1
                            )

            g = -1
            for pos in route[::-1]:
                self.size[pos] = 1
                self.depth[pos] = -1
                if g != -1:
                    continue
                isg = True
                for npos in self.edges[pos]:
                    if self.depth[npos] == -1:
                        self.size[pos] += self.size[npos]
                        if self.size[npos] * 2 > sz:
                            isg = False
                            break

                if isg and 2 * self.size[pos] >= sz:
                    g = pos

            self.centroids[d].append(g)

            self.size[g] = sz
            self.par[g] = bpos
            self.depth[g] = d
            self.cent_dist[d * self.n + g] = 0

            if sz != 1:
                c = 0
                for npos in self.edges[g]:
                    if self.depth[npos] == -1:
                        stack.append((npos, g, d + 1, c))
                        c += 1
                self.childcnt[g] = c

        self.logn = len(self.centroids)
        nex = [0] * (self.n * self.logn)
        for i in range(self.n):
            for j in range(self.logn):
                nex[i * self.logn + j] = self.cent_dist[j * self.n + i]

        self.cent_dist, nex = nex, self.cent_dist

        for i in range(self.n):
            for j in range(self.logn):
                nex[i * self.logn + j] = self.treeind[j * self.n + i]

        self.treeind = nex

    def cent_ind_dist(self, u):
        """
        u + u の各先祖の {頂点番号, 距離} を返す
        """

        ret = [(u, 0)]
        v = u
        p = u * self.logn + self.depth[u] - 1
        for d in range(self.depth[u] - 1, -1, -1):
            v = self.par[v]
            ret.append((v, self.cent_dist[p]))
            p -= 1

        return ret

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/documentation/build.py", line 81, in _render_source_code_stat
    bundled_code = language.bundle(
                   ^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/languages/python.py", line 108, in bundle
    raise NotImplementedError
NotImplementedError

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