結果

問題 No.1745 Selfish Spies 2 (à la Princess' Perfectionism)
ユーザー vwxyzvwxyz
提出日時 2023-08-09 03:38:18
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 3,992 ms / 5,000 ms
コード長 8,638 bytes
コンパイル時間 388 ms
コンパイル使用メモリ 82,224 KB
実行使用メモリ 397,044 KB
最終ジャッジ日時 2024-11-14 09:11:52
合計ジャッジ時間 55,185 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 66 ms
70,172 KB
testcase_01 AC 66 ms
70,840 KB
testcase_02 AC 66 ms
70,468 KB
testcase_03 AC 66 ms
69,472 KB
testcase_04 AC 65 ms
70,964 KB
testcase_05 AC 67 ms
69,848 KB
testcase_06 AC 67 ms
69,108 KB
testcase_07 AC 67 ms
69,892 KB
testcase_08 AC 67 ms
69,524 KB
testcase_09 AC 70 ms
72,076 KB
testcase_10 AC 75 ms
71,288 KB
testcase_11 AC 80 ms
74,328 KB
testcase_12 AC 100 ms
78,344 KB
testcase_13 AC 102 ms
78,240 KB
testcase_14 AC 134 ms
79,552 KB
testcase_15 AC 144 ms
79,516 KB
testcase_16 AC 162 ms
80,476 KB
testcase_17 AC 201 ms
82,064 KB
testcase_18 AC 195 ms
82,304 KB
testcase_19 AC 75 ms
72,332 KB
testcase_20 AC 79 ms
73,404 KB
testcase_21 AC 124 ms
78,736 KB
testcase_22 AC 100 ms
78,140 KB
testcase_23 AC 102 ms
78,816 KB
testcase_24 AC 229 ms
89,968 KB
testcase_25 AC 160 ms
80,832 KB
testcase_26 AC 163 ms
80,852 KB
testcase_27 AC 209 ms
82,000 KB
testcase_28 AC 652 ms
151,116 KB
testcase_29 AC 214 ms
82,544 KB
testcase_30 AC 207 ms
82,900 KB
testcase_31 AC 222 ms
83,548 KB
testcase_32 AC 223 ms
83,696 KB
testcase_33 AC 624 ms
150,836 KB
testcase_34 AC 579 ms
151,856 KB
testcase_35 AC 852 ms
151,792 KB
testcase_36 AC 822 ms
151,608 KB
testcase_37 AC 796 ms
151,852 KB
testcase_38 AC 579 ms
151,768 KB
testcase_39 AC 431 ms
103,512 KB
testcase_40 AC 488 ms
125,464 KB
testcase_41 AC 429 ms
120,652 KB
testcase_42 AC 766 ms
173,172 KB
testcase_43 AC 980 ms
215,848 KB
testcase_44 AC 1,229 ms
260,664 KB
testcase_45 AC 3,668 ms
304,672 KB
testcase_46 AC 3,538 ms
305,204 KB
testcase_47 AC 3,952 ms
388,032 KB
testcase_48 AC 3,752 ms
395,796 KB
testcase_49 AC 2,955 ms
240,436 KB
testcase_50 AC 2,559 ms
221,992 KB
testcase_51 AC 723 ms
121,936 KB
testcase_52 AC 529 ms
141,104 KB
testcase_53 AC 660 ms
142,392 KB
testcase_54 AC 1,515 ms
267,400 KB
testcase_55 AC 1,368 ms
240,256 KB
testcase_56 AC 3,992 ms
268,524 KB
testcase_57 AC 3,694 ms
391,520 KB
testcase_58 AC 3,414 ms
397,044 KB
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 # 

import sys
readline=sys.stdin.readline
from typing import NamedTuple, Optional, List, cast

class MFGraph:
    class Edge(NamedTuple):
        src: int
        dst: int
        cap: int
        flow: int

    class _Edge:
        def __init__(self, dst: int, cap: int) -> None:
            self.dst = dst
            self.cap = cap
            self.rev: Optional[MFGraph._Edge] = None

    def __init__(self, n: int) -> None:
        self._n = n
        self._g: List[List[MFGraph._Edge]] = [[] for _ in range(n)]
        self._edges: List[MFGraph._Edge] = []

    def add_edge(self, src: int, dst: int, cap: int) -> int:
        assert 0 <= src < self._n
        assert 0 <= dst < self._n
        assert 0 <= cap
        m = len(self._edges)
        e = MFGraph._Edge(dst, cap)
        re = MFGraph._Edge(src, 0)
        e.rev = re
        re.rev = e
        self._g[src].append(e)
        self._g[dst].append(re)
        self._edges.append(e)
        return m

    def get_edge(self, i: int) -> Edge:
        assert 0 <= i < len(self._edges)
        e = self._edges[i]
        re = cast(MFGraph._Edge, e.rev)
        return MFGraph.Edge(
            re.dst,
            e.dst,
            e.cap + re.cap,
            re.cap
        )

    def edges(self) -> List[Edge]:
        return [self.get_edge(i) for i in range(len(self._edges))]

    def change_edge(self, i: int, new_cap: int, new_flow: int) -> None:
        assert 0 <= i < len(self._edges)
        assert 0 <= new_flow <= new_cap
        e = self._edges[i]
        e.cap = new_cap - new_flow
        assert e.rev is not None
        e.rev.cap = new_flow

    def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> int:
        assert 0 <= s < self._n
        assert 0 <= t < self._n
        assert s != t
        if flow_limit is None:
            flow_limit = cast(int, sum(e.cap for e in self._g[s]))

        current_edge = [0] * self._n
        level = [0] * self._n

        def fill(arr: List[int], value: int) -> None:
            for i in range(len(arr)):
                arr[i] = value

        def bfs() -> bool:
            fill(level, self._n)
            queue = []
            q_front = 0
            queue.append(s)
            level[s] = 0
            while q_front < len(queue):
                v = queue[q_front]
                q_front += 1
                next_level = level[v] + 1
                for e in self._g[v]:
                    if e.cap == 0 or level[e.dst] <= next_level:
                        continue
                    level[e.dst] = next_level
                    if e.dst == t:
                        return True
                    queue.append(e.dst)
            return False

        def dfs(lim: int) -> int:
            stack = []
            edge_stack: List[MFGraph._Edge] = []
            stack.append(t)
            while stack:
                v = stack[-1]
                if v == s:
                    flow = min(lim, min(e.cap for e in edge_stack))
                    for e in edge_stack:
                        e.cap -= flow
                        assert e.rev is not None
                        e.rev.cap += flow
                    return flow
                next_level = level[v] - 1
                while current_edge[v] < len(self._g[v]):
                    e = self._g[v][current_edge[v]]
                    re = cast(MFGraph._Edge, e.rev)
                    if level[e.dst] != next_level or re.cap == 0:
                        current_edge[v] += 1
                        continue
                    stack.append(e.dst)
                    edge_stack.append(re)
                    break
                else:
                    stack.pop()
                    if edge_stack:
                        edge_stack.pop()
                    level[v] = self._n
            return 0

        flow = 0
        while flow < flow_limit:
            if not bfs():
                break
            fill(current_edge, 0)
            while flow < flow_limit:
                f = dfs(flow_limit - flow)
                flow += f
                if f == 0:
                    break
        return flow

    def min_cut(self, s: int) -> List[bool]:
        visited = [False] * self._n
        stack = [s]
        visited[s] = True
        while stack:
            v = stack.pop()
            for e in self._g[v]:
                if e.cap > 0 and not visited[e.dst]:
                    visited[e.dst] = True
                    stack.append(e.dst)
        return visited
  
def SCC(N,edges):
    start = [0] * (N + 1)
    elist = [0] * len(edges)
    for e in edges:
        start[e[0] + 1] += 1
    for i in range(1, N + 1):
        start[i] += start[i - 1]
    counter = start[:]
    for e in edges:
        elist[counter[e[0]]] = e[1]
        counter[e[0]] += 1
    N = N
    now_ord = group_num = 0
    visited = []
    low = [0] * N
    order = [-1] * N
    ids = [0] * N
    parent = [-1] * N
    stack = []
    for i in range(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(start[v], start[v + 1]):
                        to = 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] = 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
    groups = [[] for _ in range(group_num)]
    for i, x in enumerate(ids):
        groups[x].append(i)
    return groups

def DM_Decomposition(N,M,edges):
    s=0
    t=N+M+1
    MFG=MFGraph(N+M+2)
    for n,m in edges:
        assert 0<=n<N and N<=m<N+M
        MFG.add_edge(1+n,1+m,1)
    for n in range(N):
        MFG.add_edge(s,1+n,1)
    for m in range(M):
        MFG.add_edge(1+N+m,t,1)
    MFG.flow(s,t)
    graph=[[] for x in range(N+M)]
    graph_rev=[[] for x in range(N+M)]
    covering=[False]*(N+M)
    for e in MFG.edges():
        if 1<=e.src<1+N and 1+N<=e.dst<1+N+M:
            x=e.src-1
            y=e.dst-1
            if e.flow:
                graph[x].append(y)
                graph[y].append(x)
                graph_rev[x].append(y)
                graph_rev[y].append(x)
                covering[x]=True
                covering[y]=True
            else:
                graph[x].append(y)
                graph_rev[y].append(x)
    retu=[[]]
    seen=[False]*(N+M)
    stack=[]
    for m in range(M):
        if not covering[m+N]:
            stack.append(m+N)
            seen[m+N]=True
    while stack:
        x=stack.pop()
        retu[0].append(x)
        for y in graph_rev[x]:
            if not seen[y]:
                stack.append(y)
                seen[y]=True
    stack=[]
    V_inf=[]
    for n in range(N):
        if not covering[n]:
            seen[n]=True
            stack.append(n)
    while stack:
        x=stack.pop()
        V_inf.append(x)
        for y in graph[x]:
            if not seen[y]:
                stack.append(y)
                seen[y]=True
    scc_edges=[]
    for e in MFG.edges():
        if 1<=e.src<1+N and 1+N<=e.dst<1+N+M:
            x=e.src-1
            y=e.dst-1
            if not seen[x] and not seen[y]:
                if e.flow:
                    scc_edges.append((x,y))
                    scc_edges.append((y,x))
                else:
                    scc_edges.append((x,y))
    scc=SCC(N+M,scc_edges)
    for lst in scc:
        if seen[lst[0]]:
            continue
        retu.append(lst)
    retu.append(V_inf)
    return retu

N,M,L=map(int,readline().split())
edges=[]
for l in range(L):
    x,y=map(int,readline().split())
    x-=1;y-=1
    edges.append((x,y+N))
dm=DM_Decomposition(N,M,edges)
idx=[None]*(N+M)
for i,lst in enumerate(dm):
    for x in lst:
        idx[x]=i
for x,y in edges:
    if idx[x]==idx[y]:
        ans="Yes"
    else:
        ans="No"
    print(ans)
0