結果
| 問題 |
No.1479 Matrix Eraser
|
| コンテスト | |
| ユーザー |
 zkou
|
| 提出日時 | 2021-04-16 21:32:40 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,037 ms / 3,000 ms |
| コード長 | 7,532 bytes |
| コンパイル時間 | 237 ms |
| コンパイル使用メモリ | 82,520 KB |
| 実行使用メモリ | 153,536 KB |
| 最終ジャッジ日時 | 2024-07-03 00:56:04 |
| 合計ジャッジ時間 | 23,076 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 39 |
ソースコード
class mf_graph:
"""It solves maximum flow problem.
"""
def __init__(self, n):
"""It creates a graph of n vertices and 0 edges.
Constraints
-----------
> 0 <= n <= 10 ** 8
Complexity
----------
> O(n)
"""
self.n = n
self.g = [[] for _ in range(self.n)]
self.pos = []
def add_edge(self, from_, to, cap):
"""It adds an edge oriented from the vertex `from_` to the vertex `to`
with the capacity `cap` and the flow amount 0.
It returns an integer k such that this is the k-th edge that is added.
Constraints
-----------
> 0 <= from_, to < n
> 0 <= cap
Complexity
----------
> O(1) amortized
"""
# assert 0 <= from_ < self.n
# assert 0 <= to < self.n
# assert 0 <= cap
m = len(self.pos)
self.pos.append((from_, len(self.g[from_])))
from_id = len(self.g[from_])
to_id = len(self.g[to])
if from_ == to:
to_id += 1
self.g[from_].append(self.__class__._edge(to, to_id, cap))
self.g[to].append(self.__class__._edge(from_, from_id, 0))
return m
class edge:
def __init__(self, from_, to, cap, flow):
self.from_ = from_
self.to = to
self.cap = cap
self.flow = flow
def get_edge(self, i):
"""It returns the current internal state of the edges.
The edges are ordered in the same order as added by `add_edge`.
Constraints
-----------
> 0 <= i < m
Complexity
----------
> O(1)
"""
# assert 0 <= i < len(self.pos)
_e = self.g[self.pos[i][0]][self.pos[i][1]]
_re = self.g[_e.to][_e.rev]
return self.__class__.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap)
def edges(self):
"""It returns the current internal state of the edges.
The edges are ordered in the same order as added by `add_edge`.
Complexity
----------
> O(m), where m is the number of added edges.
"""
result = []
for i in range(len(self.pos)):
_e = self.g[self.pos[i][0]][self.pos[i][1]]
_re = self.g[_e.to][_e.rev]
result.append(self.__class__.edge(
self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap))
return result
def change_edge(self, i, new_cap, new_flow):
"""It changes the capacity and the flow amount of the i-th edge to `new_cap` and `new_flow`, respectively.
It doesn't change the capacity or the flow amount of other edges.
See Appendix in the document of AC Library for further details.
Constraints
-----------
> 0 <= i < m
> 0 <= new_flow <= new_cap
Complexity
----------
> O(1)
"""
# assert 0 <= i < len(self.pos)
# assert 0 <= new_flow <= new_cap
_e = self.g[self.pos[i][0]][self.pos[i][1]]
_re = self.g[_e.to][_e.rev]
_e.cap = new_cap - new_flow
_re.cap = new_flow
def _bfs(self, s, t):
self.level = [-1] * self.n
self.level[s] = 0
q = [s]
while q:
nq = []
for v in q:
for e in self.g[v]:
if e.cap and self.level[e.to] == -1:
self.level[e.to] = self.level[v] + 1
if e.to == t:
return True
nq.append(e.to)
q = nq
return False
def _dfs(self, s, t, up):
st = [t]
while st:
v = st[-1]
if v == s:
st.pop()
flow = up
for w in st:
e = self.g[w][self.it[w]]
flow = min(flow, self.g[e.to][e.rev].cap)
for w in st:
e = self.g[w][self.it[w]]
e.cap += flow
self.g[e.to][e.rev].cap -= flow
return flow
while self.it[v] < len(self.g[v]):
e = self.g[v][self.it[v]]
w = e.to
cap = self.g[e.to][e.rev].cap
if cap and self.level[v] > self.level[w]:
st.append(w)
break
self.it[v] += 1
else:
st.pop()
self.level[v] = self.n
return 0
def flow(self, s, t, flow_limit=float('inf')):
"""It augments the flow from s to t as much as possible.
It returns the amount of the flow augmented.
You may call it multiple times.
See Appendix in the document of AC Library for further details.
Constraints
-----------
> 0 <= s, t < n
> s != t
Complexity
----------
> O(min(n^(2/3)m, m^(3/2))) (if all the capacities are 1) or
> O(n^2 m) (general),
where m is the number of added edges.
"""
# assert 0 <= s < self.n
# assert 0 <= t < self.n
# assert s != t
flow = 0
while flow < flow_limit and self._bfs(s, t):
self.it = [0] * self.n
while flow < flow_limit:
f = self._dfs(s, t, flow_limit - flow)
if not f:
break
flow += f
return flow
def min_cut(self, s):
"""It returns a list of length n,
such that the i-th element is `True` if and only if there is a directed path from s to i in the residual network.
The returned list corresponds to a s−t minimum cut after calling flow(s, t) exactly once without flow_limit.
See Appendix in the document of AC Library for further details.
Constraints
-----------
> 0 <= s < n
Complexity
----------
> O(n + m), where m is the number of added edges.
"""
visited = [False] * self.n
q = [s]
while q:
nq = []
for p in q:
visited[p] = True
for e in self.g[p]:
if e.cap and not visited[e.to]:
visited[e.to] = True
nq.append(e.to)
q = nq
return visited
class _edge:
def __init__(self, to, rev, cap):
self.to = to
self.rev = rev
self.cap = cap
from collections import defaultdict
H, W = map(int, input().split())
As = [list(map(int, input().split())) for _ in range(H)]
vals = defaultdict(list)
for i in range(H):
for j in range(W):
vals[As[i][j]].append((i, j))
answer = 0
for key in sorted(vals.keys(), reverse=True):
if key == 0:
break
indices = vals[key]
i_set = set()
j_set = set()
for i, j in indices:
i_set.add(i)
j_set.add(j)
i_encode = {e: i for i, e in enumerate(i_set)}
j_encode = {e: j for j, e in enumerate(j_set)}
h = len(i_encode)
w = len(j_encode)
g = mf_graph(h + w + 2)
s = h + w
t = s + 1
for i, j in indices:
i = i_encode[i]
j = j_encode[j]
g.add_edge(i, j + h, 1)
for i in range(h):
g.add_edge(s, i, 1)
for j in range(w):
g.add_edge(h + j, t, 1)
answer += g.flow(s, t)
# print(answer)
print(answer)