結果

問題 No.1914 Directed by Two Sequences
ユーザー chineristAC
提出日時 2021-11-05 20:14:43
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 10,299 bytes
コンパイル時間 167 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 171,672 KB
最終ジャッジ日時 2024-12-16 01:35:34
合計ジャッジ時間 52,745 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample WA * 2
other AC * 1 WA * 37
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ソースコード

diff #
プレゼンテーションモードにする

"""
想定WA
"""
class SegmentTree:
    def __init__(self, init_val, segfunc, ide_ele):
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num
        self.size = n
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        for i in range(self.num - 1, 0, -1):
            self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
    def update(self, k, x):
        k += self.num
        self.tree[k] = x
        while k > 1:
            k >>= 1
            self.tree[k] = self.segfunc(self.tree[2*k], self.tree[2*k+1])
    def query(self, l, r):
        if r==self.size:
            r = self.num
        res = self.ide_ele
        l += self.num
        r += self.num
        right = []
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.tree[l])
                l += 1
            if r & 1:
                right.append(self.tree[r-1])
            l >>= 1
            r >>= 1
        for e in right[::-1]:
            res = self.segfunc(res,e)
        return res
class _csr:
    def __init__(self, n, edges):
        self.start = [0] * (n + 1)
        self.elist = [0] * len(edges)
        for v, _ in edges:
            self.start[v + 1] += 1
        for i in range(1, n + 1):
            self.start[i] += self.start[i - 1]
        counter = self.start.copy()
        for v, e in edges:
            self.elist[counter[v]] = e
            counter[v] += 1
class scc_graph:
    """It calculates the strongly connected components of directed graphs.
    """
    def __init__(self, n):
        """It creates a directed graph with n vertices and 0 edges.
        Constraints
        -----------
        >   0 <= n <= 10 ** 8
        Complexity
        ----------
        >   O(n)
        """
        self.n = n
        self.edges = []
    def add_edge(self, from_, to):
        """It adds a directed edge from the vertex `from_` to the vertex `to`.
        Constraints
        -----------
        >   0 <= from_ < n
        >   0 <= to < n
        Complexity
        ----------
        >   O(1) amortized
        """
        # assert 0 <= from_ < self.n
        # assert 0 <= to < self.n
        self.edges.append((from_, to))
    def _scc_ids(self):
        g = _csr(self.n, self.edges)
        now_ord = 0
        group_num = 0
        visited = []
        low = [0] * self.n
        order = [-1] * self.n
        ids = [0] * self.n
        parent = [-1] * self.n
        stack = []
        for i in range(self.n):
            if order[i] == -1:
                stack.append(i)
                stack.append(i)
                while stack:
                    v = stack.pop()
                    if order[v] == -1:
                        low[v] = order[v] = now_ord
                        now_ord += 1
                        visited.append(v)
                        for i in range(g.start[v], g.start[v + 1]):
                            to = g.elist[i]
                            if order[to] == -1:
                                stack.append(to)
                                stack.append(to)
                                parent[to] = v
                            else:
                                low[v] = min(low[v], order[to])
                    else:
                        if low[v] == order[v]:
                            while True:
                                u = visited.pop()
                                order[u] = self.n
                                ids[u] = group_num
                                if u == v:
                                    break
                            group_num += 1
                        if parent[v] != -1:
                            low[parent[v]] = min(low[parent[v]], low[v])
        for i, x in enumerate(ids):
            ids[i] = group_num - 1 - x
        return group_num, ids
    def scc(self):
        """It returns the list of the "list of the vertices" that satisfies the following.
        >   Each vertex is in exactly one "list of the vertices".
        >   Each "list of the vertices" corresponds to the vertex set of a strongly connected component.
        The order of the vertices in the list is undefined.
        >   The list of "list of the vertices" are sorted in topological order,
        i.e., for two vertices u, v in different strongly connected components,
        if there is a directed path from u to v,
        the list contains u appears earlier than the list contains v.
        Complexity
        ----------
        >   O(n + m), where m is the number of added edges.
        """
        group_num, ids = self._scc_ids()
        groups = [[] for _ in range(group_num)]
        for i, x in enumerate(ids):
            groups[x].append(i)
        return groups
def popcount(x):
    '''xの立っているビット数をカウントする関数
    (xは64bit整数)'''
    # 2bitごとの組に分け、立っているビット数を2bitで表現する
    x = x - ((x >> 1) & 0x5555555555555555)
    # 4bit整数に 上位2bit + 下位2bit を計算した値を入れる
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f # 8bitごと
    x = x + (x >> 8) # 16bitごと
    x = x + (x >> 16) # 32bitごと
    x = x + (x >> 32) # 64bitごと = 全部の合計
    return x & 0x0000007f
popcnt = [popcount(i) for i in range(2**20)]
def solve(N,A,B,M,E):
    A = [a-1 for a in A]
    B = [b-1 for b in B]
    G = scc_graph(N)
    edge = [[] for v in range(N)]
    for u,v in E:
        edge[u-1].append(v-1)
        edge[v-1].append(u-1)
    
    group = [-1 for v in range(N)]
    for v in range(N):
        mex = [False for i in range(len(edge[v])+1)]
        for nv in edge[v]:
            if nv < v and group[nv] < len(mex):
                mex[group[nv]] = True
        for i in range(len(mex)):
            if not mex[i]:
                group[v] = i
                break
    n = max(group) + 1
    clique = [[] for g in range(n)]
    for v in range(N):
        clique[group[v]].append(v)
    def direct(i,j):
        if i < j:
            return A[i] < B[j]
        else:
            return B[i] < A[j]
    def hamilton_path(V):
        n = len(V)
        if n <= 1:
            return V
        A = hamilton_path(V[:n//2])
        B = hamilton_path(V[n//2:])
        res = []
        bi = 0
        for ai in range(len(A)):
            while bi<len(B) and direct(B[bi],A[ai]):
                res.append(B[bi])
                bi += 1
            res.append(A[ai])
        res += B[bi:]
        return res
    idx = [-1 for v in range(N)]
    for g in range(n):
        clique[g] = hamilton_path(clique[g])
        for i in range(len(clique[g])):
            idx[clique[g][i]] = i
        for u,v in zip(clique[g],clique[g][1:]):
            G.add_edge(u,v)
    
    memo_to = [N for v in range(N)]
    memo_from = [-1 for v in range(N)]
    ci = [i for i in range(n)]
    ci.sort(lambda g:len(clique[g]))
    idx_on_ci = [-1 for i in range(n)]
    for i in range(n):
        idx_on_ci[ci[i]] = i
    ban = [[] for v in range(N)]
    Vs = []
    seg_to_large = SegmentTree([N]*2*N,min,N)
    seg_to_small = SegmentTree([N]*2*N,min,N)
    seg_from_large = SegmentTree([-1]*2*N,max,-1)
    seg_from_small = SegmentTree([-1]*2*N,max,-1)
    for i in range(n):
        target = ci[i]
        Vs += clique[target]
        Vs.sort()
        for nv in clique[target]:
            for v in edge[nv]:
                if idx_on_ci[group[v]] <= i:
                    ban[v].append(nv)
        for v in Vs[::-1]:
            for nv in ban[v]:
                if v < nv:
                    seg_to_large.update(B[nv],N)
            memo_to[v] = min(memo_to[v],seg_to_large.query(A[v],2*N))
            for nv in ban[v]:
                if v < nv:
                    seg_to_large.update(B[nv],idx[nv])
            if group[v]==target:
                seg_to_large.update(B[v],idx[v])
        
        for v in Vs:
            for nv in ban[v]:
                if nv < v:
                    seg_to_small.update(A[nv],N)
            memo_to[v] = min(memo_to[v],seg_to_small.query(B[v],2*N))
            for nv in ban[v]:
                if nv < v:
                    seg_to_small.update(A[nv],idx[nv])
            if group[v]==target:
                seg_to_small.update(A[v],idx[v])
        
        for v in Vs[::-1]:
            for nv in ban[v]:
                if v < nv:
                    seg_from_large.update(B[nv],-1)
            memo_from[v] = max(memo_from[v],seg_from_large.query(0,A[v]))
            for nv in ban[v]:
                if v < nv:
                    seg_from_large.update(B[nv],idx[nv])
            if group[v]==target:
                seg_from_large.update(B[v],idx[v])
        
        for v in Vs:
            for nv in ban[v]:
                if nv < v:
                    seg_from_small.update(A[nv],-1)
            memo_from[v] = max(memo_from[v],seg_from_small.query(0,B[v]))
            for nv in ban[v]:
                if nv < v:
                    seg_from_small.update(A[nv],idx[nv])
            if group[v]==target:
                seg_from_small.update(A[v],idx[v])
        
        for v in Vs:
            if memo_to[v]!=N:
                nv = clique[target][memo_to[v]]
                G.add_edge(v,nv)                
                memo_to[v] = N
            
            if memo_from[v]!=-1:
                pv = clique[target][memo_from[v]]
                G.add_edge(pv,v)
                memo_from[v] = -1
            
            ban[v] = []
            if group[v]==target:
                seg_to_large.update(B[v],N)
                seg_to_small.update(A[v],N)
                seg_from_large.update(B[v],-1)
                seg_from_small.update(A[v],-1)
    
    group_num,ids = G._scc_ids()
    res = [(i+1,i+2) for i in range(N-1)] + [(N,1)]
    
    
    print(len(res))
    for u,v in res:
        print(u,v)
    
    
    
    
import sys
input = lambda :sys.stdin.buffer.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
N,M = mi()
A = li()
B = li()
E = [tuple(mi()) for i in range(M)]
solve(N,A,B,M,E)
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