#yukicoder 650 行列木クエリ #Heavy-Light decomposition 分解するだけ class HL_decomposition: def __init__(self, N, G, root = 0): #pos[v] = i, order[i] = v 頂点vのDFS順がi番目 #leader[i]: 深さdepth[i]の代表のDFS順 parent[i]: ひとつ根側のDFS順 self._N = N; self._G = G = [[v for v,*_ in S] for S in G] if N > 1 and not isinstance(G[0][0], int) else G; self.pos = pos = [-1] * N; self.order = order = [-1] * N; self.leader = leader = [-1] * N; self.depth = depth = [-1] * N; self.parent = parent = [-1] * N; size = [1] * N; Q = [(root, -1)] for now,back in Q: for nxt in G[now]: if nxt != back: Q.append((nxt, now)) while Q: now,back = Q.pop(); size[back] += size[now] if back != -1 else 0 Q.append((root, -1, 0, -1)) for i in range(N): now, back, d, t = Q.pop(); pos[now], order[i], parent[i], depth[i] = i, now, pos[back], d; leader[i] = t = t if t != -1 else i if size[now] > 1: s, v = 0, now for nxt in G[now]: if nxt == back: continue if s < size[nxt]: if s > 0: Q.append((v, now, d + 1, -1)) s, v = size[nxt], nxt else: Q.append((nxt, now, d + 1, -1)) Q.append((v, now, d, t)) def LCA(self, u, v): i, j = self.pos[u], self.pos[v]; c, d = self.depth[i], self.depth[j]; s, t = self.leader[i], self.leader[j] for c in range(c - 1, d - 1, -1): i = self.parent[s]; s = self.leader[i] for d in range(d - 1, c - 1, -1): j = self.parent[t]; t = self.leader[j] while s != t: i, j = self.parent[s], self.parent[t]; s, t = self.leader[i], self.leader[j] return self.order[ min(i, j) ] def find(self, index_u, v = None): #対応する列の添字を返す return self.pos[index_u] if v == None else max( self.pos[index_u], self.pos[v] ) def rev(self, Lt, Rt = None): #B = A[::-1] A[i], A[Lt,Rt)の対応添字を返す return self._N - 1 - Lt if Rt == None else (self._N - Rt, self._N - Lt) def fold(self, u, v): #u→vパスの作用値順を(to, go, LCA)の順に返す #to, goともに下から区間作用を行い、最後にf( f(to, A[LCA]), go )を行う #to: LCA ← uの作用区間[Lt,Rt) x ← f( x, fold(Lt, Rt) ) の順 反転列を使う #go: LCA → vの作用区間[Lt,Rt) y ← f( fold(Lt, Rt), y ) の順 i, j = self.pos[u], self.pos[v]; c, d = self.depth[i], self.depth[j]; s, t = self.leader[i], self.leader[j]; to, go = [], [] for c in range(c - 1, d - 1, -1): to.append((s, i + 1)); i = self.parent[s]; s = self.leader[i] for d in range(d - 1, c - 1, -1): go.append((t, j + 1)); j = self.parent[t]; t = self.leader[j] while s != t: to.append((s, i + 1)); i = self.parent[s]; s = self.leader[i]; go.append((t, j + 1)); j = self.parent[t]; t = self.leader[j] if i > j: to.append((j + 1, i + 1)) if i < j: go.append((i + 1, j + 1)) return to, go, min(i, j) #Segment Tree: O(logN) class SegmentTree: def __init__(self, n, identity_e, combine_f): self._n = n; self._size = 1 << (n-1).bit_length(); self._identity_e = identity_e; self._combine_f = combine_f; self._node = [self._identity_e] * 2 * self._size def build(self, array): assert len(array) == self._n, 'array too large' for i,v in enumerate(array, start = self._size): self._node[i] = v for i in range(self._size - 1, 0, -1): self._node[i] = self._combine_f(self._node[i<<1|0], self._node[i<<1|1]) def update(self, index, value): #一点更新 i = self._size + index; self._node[i] = value while i - 1: i >>= 1; self._node[i] = self._combine_f(self._node[i<<1|0], self._node[i<<1|1]) def fold(self, L, R): #区間取得: [L,R)の区間値を得る L += self._size; R += self._size; vL = vR = self._identity_e while L < R: if L & 1: vL = self._combine_f(vL, self._node[L]); L += 1 if R & 1: R -= 1; vR = self._combine_f(self._node[R], vR) L >>= 1; R >>= 1 return self._combine_f(vL, vR) #down: Falseなら単調増加、Trueなら単調減少を仮定する。 #[Lt:Rt]の作用値がX以上/以下 となる、最小のRtを返す。閉区間なので扱い注意。 def bisect(self, Lt, X, down = False): if Lt >= self._n: return self._n now = Lt + self._size; cnt = self._identity_e while 1: #nodeの上昇 f = now & 3; now = now >> 2 if f == 0 else now >> 1 if f == 2 else now; t = self._combine_f(cnt, self._node[now]) if not down and t >= X: break elif down and t <= X: break else: cnt = t; now += 1 if now & (now - 1) == 0: return self._n while now < self._size: #下降 Lt, Rt = self._node[now<<1|0], self._node[now<<1|1] if not down and self._combine_f(cnt, Lt) >= X: now = now<<1|0 elif down and self._combine_f(cnt, Lt) <= X: now = now<<1|0 else: cnt = self._combine_f(cnt, Lt); now = now<<1|1 return now - self._size #行列累乗 1行N列の行列は[[1, 2, ...]] と2重括弧に自動変換するので注意 class matrix_pow: def __init__(self,MOD=998244353): self._MOD=MOD def eye(self,N): #単位行列の作成 return [[1 if i==j else 0 for j in range(N)] for i in range(N)] def add(self,A,B): #行列の加算 if isinstance(A[0],int): A=[A] if isinstance(B[0],int): B=[B] assert len(A) ==len(B), 'not same size' assert len(A[0])==len(B[0]), 'not same size' nG=[[0]*max(len(A[i]) for i in range(len(A))) for _ in range(len(A))] for h in range(len(nG)): for w in range(len(nG[h])): if len(A[h])