結果
| 問題 |
No.738 平らな農地
|
| コンテスト | |
| ユーザー |
 terasa
|
| 提出日時 | 2023-01-07 17:10:27 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 943 ms / 2,000 ms |
| コード長 | 7,376 bytes |
| コンパイル時間 | 192 ms |
| コンパイル使用メモリ | 82,944 KB |
| 実行使用メモリ | 160,760 KB |
| 最終ジャッジ日時 | 2024-12-14 16:34:33 |
| 合計ジャッジ時間 | 39,956 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 87 |
ソースコード
from typing import List, Tuple, Callable, TypeVar, Optional
import sys
import itertools
import heapq
import bisect
import math
from collections import deque, defaultdict
from functools import lru_cache, cmp_to_key
input = sys.stdin.readline
if __file__ != 'prog.py':
sys.setrecursionlimit(10 ** 6)
def readints(): return map(int, input().split())
def readlist(): return list(readints())
def readstr(): return input()[:-1]
def readlist1(): return list(map(lambda x: int(x) - 1, input().split()))
class BitVector:
# reference: https://tiramister.net/blog/posts/bitvector/
# (reference implemention is succinct, but this implemention is not succinct.)
def __init__(self, N):
self.N = N
self.block_num = (N + 31) >> 5
self.bit = [0] * self.block_num
self.sum = [0] * self.block_num
self.built = False
def set(self, pos):
self.bit[pos >> 5] |= 1 << (pos & 31)
def build(self):
assert not self.built
for i in range(1, self.block_num):
self.sum[i] = self.sum[i - 1] + self.popcount(self.bit[i - 1])
self.built = True
def access(self, pos):
"""return pos-th bit"""
return self.bit[pos >> 5] >> (pos & 31) & 1
def rank(self, pos):
"""count 1's in [0, pos) range"""
assert self.built
i = pos >> 5
offset = pos & 31
return self.sum[i] + self.popcount(self.bit[i] & ((1 << offset) - 1))
def select(self, num):
"""return minimum i that satisfies rank(i) = num"""
assert self.built
if num == 0:
return 0
if self.rank(self.N) < num:
return -1
l = -1
r = self.N
while r - l > 1:
c = (l + r) >> 1
if self.rank(c) >= num:
r = c
else:
l = c
return r
def popcount(self, n):
c = (n & 0x5555555555555555) + ((n >> 1) & 0x5555555555555555)
c = (c & 0x3333333333333333) + ((c >> 2) & 0x3333333333333333)
c = (c & 0x0f0f0f0f0f0f0f0f) + ((c >> 4) & 0x0f0f0f0f0f0f0f0f)
c = (c & 0x00ff00ff00ff00ff) + ((c >> 8) & 0x00ff00ff00ff00ff)
c = (c & 0x0000ffff0000ffff) + ((c >> 16) & 0x0000ffff0000ffff)
return c
class WaveletMatrix:
# reference: https://miti-7.hatenablog.com/entry/2018/04/28/152259
def __init__(self, A):
self.nums = sorted(set(A))
self.idx = {a: i for i, a in enumerate(self.nums)}
self.A = [self.idx[a] for a in A]
self.digit = (len(self.nums) - 1).bit_length()
self.B = [None] * self.digit
self.offset = [None] * self.digit
self.start_index = {}
T = self.A
for k in range(self.digit)[::-1]:
self.B[k] = BitVector(len(T) + 1)
zeros = []
ones = []
for i, a in enumerate(T):
if a >> k & 1:
self.B[k].set(i)
ones.append(a)
else:
zeros.append(a)
self.B[k].build()
self.offset[k] = len(zeros)
T = zeros + ones
for i, a in enumerate(T):
self.start_index.setdefault(a, i)
def access(self, i):
"""return i-th value"""
ret = 0
cur = i
for k in range(self.digit)[::-1]:
if self.B[k].access(cur):
ret |= (1 << k)
cur = self.B[k].rank(cur) + self.offset[k]
else:
cur -= self.B[k].rank(cur)
return self.nums[ret]
def rank(self, i, x):
"""return the number of x's in [0, i) range"""
x = self.idx.get(x)
if x is None:
return 0
for k in range(self.digit)[::-1]:
if x >> k & 1:
i = self.B[k].rank(i) + self.offset[k]
else:
i -= self.B[k].rank(i)
return i - self.start_index[x]
def quantile(self, l, r, n):
"""return n-th (0-indexed) smallest value in [l, r) range"""
assert 0 <= n < r - l
ret = 0
for k in range(self.digit)[::-1]:
rank_l = self.B[k].rank(l)
rank_r = self.B[k].rank(r)
ones = rank_r - rank_l
zeros = r - l - ones
if zeros <= n:
ret |= 1 << k
l = rank_l + self.offset[k]
r = rank_r + self.offset[k]
n -= zeros
else:
l -= rank_l
r -= rank_r
return self.nums[ret]
def range_freq(self, l, r, lower, upper):
"""return the number of values s.t. lower <= x < upper"""
return self.range_freq_upper(l, r, upper) - self.range_freq_upper(l, r, lower)
def prev_value(self, l, r, upper):
"""return maximum x s.t. x < upper in [l, r) range if exist, otherwise None"""
cnt = self.range_freq_upper(l, r, upper)
if cnt == 0:
return None
return self.quantile(l, r, cnt - 1)
def next_value(self, l, r, lower):
"""return minimum x s.t. x >= lower in [l, r) range if exist, otherwise None"""
cnt = self.range_freq_upper(l, r, lower)
if cnt == r - l:
return None
return self.quantile(l, r, cnt)
def range_freq_upper(self, l, r, upper):
"""return the number of values s.t. x < upper in [l, r) range"""
if l >= r:
return 0
if upper > self.nums[-1]:
return r - l
if upper <= self.nums[0]:
return 0
upper = bisect.bisect_left(self.nums, upper)
ret = 0
for k in range(self.digit)[::-1]:
rank_l = self.B[k].rank(l)
rank_r = self.B[k].rank(r)
ones = rank_r - rank_l
zeros = r - l - ones
if upper >> k & 1:
ret += zeros
l = rank_l + self.offset[k]
r = rank_r + self.offset[k]
else:
l -= rank_l
r -= rank_r
return ret
class BIT:
def __init__(self, N):
self.N = N
self.A = [0] * (N + 1)
def add(self, i, x):
"""add x to i-th element (0-indexed)"""
assert 0 <= i < self.N
i += 1
while i <= self.N:
self.A[i] += x
i += i & -i
def sum(self, i):
"""return sum(A[:i])"""
assert 0 <= i <= self.N
s = 0
while i > 0:
s += self.A[i]
i -= i & -i
return s
def range_sum(self, l, r):
"""return sum(A[l:r])"""
return self.sum(r) - self.sum(l)
N, K = readints()
A = readlist()
WM = WaveletMatrix(A)
cands = [0] * (N - K + 1)
task = defaultdict(list)
for i in range(N - K + 1):
med = WM.quantile(i, i + K, K // 2)
task[med].append(i)
nums = WM.nums
idx = defaultdict(list)
for i, a in enumerate(A):
idx[a].append(i)
bit = BIT(N)
bit2 = BIT(N)
for k in nums:
for i in task[k]:
cands[i] += k * bit2.range_sum(i, i + K) - bit.range_sum(i, i + K)
for i in idx[k]:
bit.add(i, k)
bit2.add(i, 1)
bit = BIT(N)
bit2 = BIT(N)
for k in nums[::-1]:
for i in task[k]:
cands[i] += bit.range_sum(i, i + K) - k * bit2.range_sum(i, i + K)
for i in idx[k]:
bit.add(i, k)
bit2.add(i, 1)
print(min(cands))