結果
| 問題 | No.3423 Minimum Xor Query |
| コンテスト | |
| ユーザー |
 kidodesu
|
| 提出日時 | 2025-12-29 20:50:00 |
| 言語 | PyPy3 (7.3.17) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,462 bytes |
| 記録 | |
| コンパイル時間 | 213 ms |
| コンパイル使用メモリ | 82,540 KB |
| 実行使用メモリ | 101,568 KB |
| 最終ジャッジ日時 | 2026-01-11 13:05:10 |
| 合計ジャッジ時間 | 10,975 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 |
|---|---|
| other | AC * 5 WA * 13 |
ソースコード
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
import math
from bisect import bisect_left, bisect_right
import time
from heapq import *
def main(B_SIZE, n, q, A, Q):
time0 = time.time()
class SortedMultiset:
BUCKET_RATIO = 16
SPLIT_RATIO = 24
def __init__(self, a = []):
"Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
a = list(a)
n = self.size = len(a)
if any(a[i] > a[i + 1] for i in range(n - 1)):
a.sort()
num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))
self.a = [a[n * i // num_bucket : n * (i + 1) // num_bucket] for i in range(num_bucket)]
def __iter__(self):
for i in self.a:
for j in i: yield j
def __reversed__(self):
for i in reversed(self.a):
for j in reversed(i): yield j
def __eq__(self, other) -> bool:
return list(self) == list(other)
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedMultiset" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1 : len(s) - 1] + "}"
def _position(self, x):
"return the bucket, index of the bucket and position in which x should be. self must not be empty."
for i, a in enumerate(self.a):
if x <= a[-1]: break
return (a, i, bisect_left(a, x))
def __contains__(self, x) -> bool:
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def count(self, x) -> int:
"Count the number of x."
return self.index_right(x) - self.index(x)
def add(self, x) -> None:
"Add an element. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return
a, b, i = self._position(x)
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.SPLIT_RATIO:
mid = len(a) >> 1
self.a[b:b+1] = [a[:mid], a[mid:]]
def _pop(self, a, b: int, i: int):
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0: return False
a, b, i = self._position(x)
if i == len(a) or a[i] != x: return False
self._pop(a, b, i)
return True
def lt(self, x):
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x):
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x):
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x):
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, i: int):
"Return the i-th element."
if i < 0:
for a in reversed(self.a):
i += len(a)
if i >= 0: return a[i]
else:
for a in self.a:
if i < len(a): return a[i]
i -= len(a)
raise IndexError
def pop(self, i: int = -1):
"Pop and return the i-th element."
if i < 0:
for b, a in enumerate(reversed(self.a)):
i += len(a)
if i >= 0: return self._pop(a, ~b, i)
else:
for b, a in enumerate(self.a):
if i < len(a): return self._pop(a, b, i)
i -= len(a)
raise IndexError
def index(self, x) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
A_ = [A[i] for i in range(n)]
inf = 1 << 30
q0 = q1 = 0
Q_ = []
T = []
for i in range(q):
if Q[i][0] == 1:
T.append((Q[i][1], A_[Q[i][1]], Q[i][2]))
A_[Q[i][1]] = Q[i][2]
q0 += 1
else:
Q_.append((q0, Q[i][1], q1))
q1 += 1
Ans = [-1] * q1
b_siz = int((2*n*q0/q1) ** 0.5) + 1
b_siz = B_SIZE
b_cnt = n // b_siz + 1
D = [[] for _ in range(b_cnt)]
for i in range(q1):
t, r, idx = Q_[i]
D[r//b_siz].append((t, r, idx))
for i in range(b_cnt):
if i % 2:
D[i].sort(reverse = True)
else:
D[i].sort()
nt = nr = 0
S = SortedMultiset([inf])
hq0 = []
hq1 = []
cnt = 0
for x in range(b_cnt):
for now in range(max(0, (x-1)*b_siz), min(n, x*b_siz)):
a = A[now]
S.add(a)
idx = S.index(a)
if idx:
heappush(hq1, S[idx-1]^S[idx+1])
heappush(hq0, S[idx-1]^S[idx])
heappush(hq0, S[idx]^S[idx+1])
for t, r, ans_idx in D[x]:
if nt <= t:
for now in range(nt, t):
i, pa, a = T[now]
if i < nr:
idx = S.index(pa)
if idx:
heappush(hq0, S[idx-1]^S[idx+1])
heappush(hq1, S[idx-1]^S[idx])
heappush(hq1, S[idx]^S[idx+1])
S.discard(pa)
S.add(a)
idx = S.index(a)
if idx:
heappush(hq1, S[idx-1]^S[idx+1])
heappush(hq0, S[idx-1]^S[idx])
heappush(hq0, S[idx]^S[idx+1])
A[i] = a
else:
for now in range(nt-1, t-1, -1):
i, pa, a = T[now]
if i < nr:
idx = S.index(a)
if idx:
heappush(hq0, S[idx-1]^S[idx+1])
heappush(hq1, S[idx-1]^S[idx])
heappush(hq1, S[idx]^S[idx+1])
S.discard(a)
S.add(pa)
idx = S.index(pa)
if idx:
heappush(hq1, S[idx-1]^S[idx+1])
heappush(hq0, S[idx-1]^S[idx])
heappush(hq0, S[idx]^S[idx+1])
A[i] = pa
while hq0 and hq1 and hq0[0] == hq1[0]:
heappop(hq0)
heappop(hq1)
if hq0:
ans = hq0[0]
else:
ans = inf
B = A[x*b_siz : r]
nt = t
B.sort()
for i in range(len(B)-1):
ans = min(ans, B[i+1]^B[i])
for b in B:
idx = S.index(b)
if idx:
ans = min(ans, b^S[idx-1])
ans = min(ans, b^S[idx])
Ans[ans_idx] = ans
for ans in Ans:
print(ans)
#print(time.time()-time0)
#print()
n, q = map(int, input().split())
A = list(map(int, input().split()))
Q = [list(map(int, input().split())) for _ in range(q)]
for i in range(q):
if Q[i][0] == 1: Q[i][1] -= 1
main(10, n, q, A, Q)