結果

問題 No.1914 Directed by Two Sequences
ユーザー chineristACchineristAC
提出日時 2021-10-31 18:00:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,722 ms / 3,000 ms
コード長 5,794 bytes
コンパイル時間 1,032 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 156,920 KB
最終ジャッジ日時 2024-12-16 01:43:52
合計ジャッジ時間 59,428 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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 AC * 2
other AC * 38
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 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

def solve(N,A,B,M,E):
    A = [a-1 for a in A]
    B = [b-1 for b in B]
    res = set()

    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:]):
            res.add((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]]     
                res.add((v,nv))      
                memo_to[v] = N
            
            if memo_from[v]!=-1:
                pv = clique[target][memo_from[v]]
                res.add((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)
    
    print(len(res))
    for u,v in res:
        print(u+1,v+1)

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)
0