結果

問題 No.922 東北きりきざむたん
ユーザー neterukun
提出日時 2021-01-14 14:51:58
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,156 ms / 2,000 ms
コード長 5,145 bytes
コンパイル時間 297 ms
コンパイル使用メモリ 82,436 KB
実行使用メモリ 183,004 KB
最終ジャッジ日時 2024-11-24 05:22:07
合計ジャッジ時間 17,857 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 26
権限があれば一括ダウンロードができます

ソースコード

diff # 

class DoublingLCA:
    def __init__(self, tree, root=None):
        self.n = len(tree)
        self.depth = [0] * self.n
        self.log_size = (self.n).bit_length()
        self.parent = [[-1] * self.n for i in range(self.log_size)]

        if root is None:
            for v in range(self.n):
                if self.parent[0][v] == -1:
                    self._dfs(v)
        else:
            self._dfs(root)

        for k in range(self.log_size - 1):
            for v in range(self.n):
                if self.parent[k][v] == -1:
                    self.parent[k + 1][v] = -1
                else:
                    self.parent[k + 1][v] = self.parent[k][self.parent[k][v]]

    def _dfs(self, rt):
        stack = [(rt, -1)]
        while stack:
            v, par = stack.pop()
            for chi_v in tree[v]:
                if chi_v == par:
                    continue
                self.parent[0][chi_v] = v
                self.depth[chi_v] = self.depth[v] + 1
                stack.append((chi_v, v))

    def lca(self, u, v):
        if self.depth[u] > self.depth[v]:
            u, v = v, u
        for k in range(self.log_size):
            if ((self.depth[v] - self.depth[u]) >> k) & 1:
                v = self.parent[k][v]
        if u == v:
            return u
        for k in reversed(range(self.log_size)):
            if self.parent[k][u] != self.parent[k][v]:
                u = self.parent[k][u]
                v = self.parent[k][v]
        return self.parent[0][u]

    def distance(self, u, v):
        lca_uv = self.lca(u, v)
        if lca_uv == -1:
            return -1
        else:
            return self.depth[u] + self.depth[v] - 2 * self.depth[lca_uv]


class UnionFind:
    def __init__(self, n):
        self.parent = [-1] * n
        self.n = n
        self.cnt = n

    def root(self, x):
        if self.parent[x] < 0:
            return x
        else:
            self.parent[x] = self.root(self.parent[x])
            return self.parent[x]

    def merge(self, x, y):
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return False
        if self.parent[x] > self.parent[y]:
            x, y = y, x
        self.parent[x] += self.parent[y]
        self.parent[y] = x
        self.cnt -= 1
        return True

    def same(self, x, y):
        return self.root(x) == self.root(y)

    def size(self, x):
        return -self.parent[self.root(x)]

    def count(self):
        return self.cnt

    def groups(self):
        res = [[] for _ in range(self.n)]
        for i in range(self.n):
            res[self.root(i)].append(i)
        return [group for group in res if group]


def rerooting(n, edges, unit, merge, addnode):
    tree = [[] for i in range(n)]
    idxs = [[] for i in range(n)]
    for u, v in edges:
        idxs[u].append(len(tree[v]))
        idxs[v].append(len(tree[u]))
        tree[u].append(v)
        tree[v].append(u)
    sub = [[unit] * len(tree[v]) for v in range(n)]
    noderes = [unit] * n

    # topological sort
    tp_order = []
    par = [-1] * n
    for root in range(n):
        if par[root] != -1:
            continue
        stack = [root]
        while stack:
            v = stack.pop()
            tp_order.append(v)
            for nxt_v in tree[v]:
                if nxt_v == par[v]:
                    continue
                par[nxt_v] = v
                stack.append(nxt_v)

    # tree DP
    for v in reversed(tp_order[1:]):
        res = unit
        par_idx = -1
        for idx, nxt_v in enumerate(tree[v]):
            if nxt_v == par[v]:
                par_idx = idx
                continue
            res = merge(res, sub[v][idx])
        if par_idx != -1:
            sub[par[v]][idxs[v][par_idx]] = addnode(res, v)

    # rerooting DP
    for v in tp_order:
        acc_back = [unit] * len(tree[v])
        for i in reversed(range(1, len(acc_back))):
            acc_back[i - 1] = merge(sub[v][i], acc_back[i])
        acc_front = unit
        for idx, nxt_v in enumerate(tree[v]):
            res = addnode(merge(acc_front, acc_back[idx]), v)
            sub[nxt_v][idxs[v][idx]] = res
            acc_front = merge(acc_front, sub[v][idx])
        noderes[v] = addnode(acc_front, v)
    return noderes


n, m, q = map(int, input().split())
edges = [list(map(int, input().split())) for i in range(m)]
queries = [list(map(int, input().split())) for i in range(q)]


tree = [[] for i in range(n)]
uf = UnionFind(n)
for i, (u, v) in enumerate(edges):
    u -= 1
    v -= 1
    tree[u].append(v)
    tree[v].append(u)
    uf.merge(u, v)
    edges[i] = (u, v)

ans = 0
weights = [0] * n
db = DoublingLCA(tree)
for u, v in queries:
    u -= 1
    v -= 1
    dist = db.distance(u, v)
    if dist == -1:
        weights[u] += 1
        weights[v] += 1
    else:
        ans += dist

unit = (0, 0)
merge = lambda x1, x2: (x1[0] + x2[0], x1[1] + x2[1])
addnode = lambda x1, v: (x1[0] + weights[v], x1[0] + x1[1])

res = rerooting(n, edges, unit, merge, addnode)
for gp in uf.groups():
    min_cost = 10 ** 9
    for i in gp:
        min_cost = min(res[i][1], min_cost)
    ans += min_cost
print(ans)
0