結果

問題 No.2257 Swim and Sleep
ユーザー shobonvipshobonvip
提出日時 2023-03-24 06:32:18
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 484 ms / 2,000 ms
コード長 6,752 bytes
コンパイル時間 307 ms
コンパイル使用メモリ 81,628 KB
実行使用メモリ 80,636 KB
最終ジャッジ日時 2023-10-18 19:54:45
合計ジャッジ時間 7,377 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
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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 261 ms
77,892 KB
testcase_01 AC 273 ms
77,896 KB
testcase_02 AC 270 ms
77,896 KB
testcase_03 AC 483 ms
80,608 KB
testcase_04 AC 472 ms
79,652 KB
testcase_05 AC 472 ms
79,664 KB
testcase_06 AC 484 ms
80,636 KB
testcase_07 AC 342 ms
78,236 KB
testcase_08 AC 350 ms
78,240 KB
testcase_09 AC 364 ms
79,420 KB
testcase_10 AC 287 ms
77,900 KB
testcase_11 AC 275 ms
77,900 KB
testcase_12 AC 275 ms
77,908 KB
testcase_13 AC 275 ms
77,904 KB
testcase_14 AC 276 ms
77,900 KB
testcase_15 AC 272 ms
77,900 KB
testcase_16 AC 273 ms
77,904 KB
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ソースコード

diff # 

# コードを綺麗にした

from math import gcd
from collections import defaultdict
mod = 998244353

#  m ... 決まっている鯨の数
# rl ... 方向の個数 (長さ 4 の配列)
#  x ... 鯨の x 座標 (長さ m の配列)
#  y ... 鯨の y 座標 (長さ m の配列)
#  r ... 鯨の方向 (長さ m の配列)
#  w ... 盤面の x 軸の広さ
#  h ... 盤面の y 軸の広さ
#  g ... gcd(w, h)

# TYPE 1 縦・横のみ
def count_type1(m, rl, x, y, r, w, h, g):
	ret = 0

	# 横
	if rl[0] + rl[1] == 0:
		d = defaultdict(lambda: -1)
		mode = 1
		for i in range(m):
			if d[y[i]] == -1:
				d[y[i]] = r[i]
			elif d[y[i]] != r[i]:
				mode = 0
				break
		if mode:
			f = len(d)
			ret += pow(2, h-f, mod)
			ret %= mod
	
	# 縦
	if rl[2] + rl[3] == 0:
		d = defaultdict(lambda: -1)
		mode = 1
		for i in range(m):
			if d[x[i]] == -1:
				d[x[i]] = r[i]
			elif d[x[i]] != r[i]:
				mode = 0
				break
		if mode:
			f = len(d)
			ret += pow(2, w-f, mod)
			ret %= mod
	
	return ret

# TYPE 2 偶数自明 (g = 0 mod 2)
def count_type2(m, rl, x, y, r, w, h, g):
	ret = 0
	if g % 2 == 0:
		# パリティで場合分けする
		for parity in range(2):
			d1 = defaultdict(lambda: -1)
			d2 = defaultdict(lambda: -1)
			mode = 1
			for i in range(m):
				if r[i] == 0 or r[i] == 1:
					# 縦
					if (x[i] + y[i]) % 2 != parity:
						mode = 0
						break
					if d1[x[i]] == -1:
						d1[x[i]] = r[i]
					elif d1[x[i]] != r[i]:
						mode = 0
						break
				else:
					# 横
					if (x[i] + y[i]) % 2 != 1 ^ parity:
						mode = 0
						break
					if d2[y[i]] == -1:
						d2[y[i]] = r[i]
					elif d2[y[i]] != r[i]:
						mode = 0
						break
			if mode:
				ret += pow(2, w-len(d1) + h-len(d2), mod)
				ret %= mod	
	
	return ret

# TYPE 3 (x-y)%g で場合分け
def count_type3(m, rl, x, y, r, w, h, g):
	ret = 0
	for v in [(1, 3), (0, 2)]:
		if rl[v[0]] == rl[v[1]] == 0:
			mode = 1
			d = defaultdict(lambda:-1)	
			for i in range(m):
				t = (x[i] - y[i]) % g
				if d[t] == -1:
					d[t] = r[i]
				elif d[t] != r[i]:
					mode = 0
					break
			if mode:
				ret += pow(2, g-len(d), mod)
				ret %= mod
	
	return ret

# TYPE 4 (x+y)%g で場合分け
def count_type4(m, rl, x, y, r, w, h, g):
	ret = 0
	for v in [(1, 2), (0, 3)]:
		if rl[v[0]] == rl[v[1]] == 0:
			mode = 1
			d = defaultdict(lambda:-1)
			for i in range(m):
				t = (x[i] + y[i]) % g
				if d[t] == -1:
					d[t] = r[i]
				elif d[t] != r[i]:
					mode = 0
					break
			if mode:
				ret += pow(2, g-len(d), mod)
				ret %= mod
	return ret

# TYPE 4.5.1 
# TYPE 3, 4 のうち, TYPE 1 にあてはまるものを除く
def count_type451(m, rl, x, y, r, w, h, g):
	ret = 0
	for v in range(4):
		if rl[0] + rl[1] + rl[2] + rl[3] - rl[v] == 0:
			ret -= 2
			ret %= mod
	return ret

# TYPE 4.5.2
# TYPE 3, 4 のうち, TYPE 2 にあてはまるものを除く
def count_type452(m, rl, x, y, r, w, h, g):
	ret = 0
	if g % 2 == 0:
		for p in range(4):
			for q in range(4):
				if p//2 == q//2: continue
				mode = 1
				for i in range(m):
					t = (x[i] + y[i]) % 2
					if t == 0 and r[i] != p:
						mode = 0
						break
					if t == 1 and r[i] != q:
						mode = 0
						break
				if mode:
					ret -= 1
					ret %= mod
	return ret

# 非自明の 48 通りを作る
def make_hijimei():
	ret = []
	for num in range(4 ** 8):
		v = num
		a = [[0] * 4 for i in range(4)]
		rl = [0] * 4
		for i in range(8):
			t = v % 4
			v //= 4
			a[i//4][i%4] = t
			a[i//4 + 2][(i+2)%4] = t
			rl[t] += 2

		# 衝突するか否か
		mode = 1
		for i in range(4):
			md = -1
			for j in range(4):
				if a[i][j] == 0 or a[i][j] == 1:
					if md == -1:
						md = a[i][j]
					elif md != a[i][j]:
						mode = 0
						break
		
		for j in range(4):
			md = -1
			for i in range(4):
				if a[i][j] == 2 or a[i][j] == 3:
					if md == -1:
						md = a[i][j]
					elif md != a[i][j]:
						mode = 0
						break
		
		if mode == 0:
			continue

		b = [[0] * 4 for i in range(4)]
		for i in range(4):
			for j in range(4):
				b[i][j] = a[i][j]

		# 愚直にシミュレーションする
		for tyr in range(20):
			c = [[-1] * 4 for i in range(4)]
			for i in range(4):
				for j in range(4):
					if b[i][j] == 0:
						if c[i][(j+1)%4] != -1:
							mode = 0
							break
						c[i][(j+1)%4] = b[i][j]
					if b[i][j] == 1:
						if c[i][(j-1)%4] != -1:
							mode = 0
							break
						c[i][(j-1)%4] = b[i][j]
					if b[i][j] == 2:
						if c[(i-1)%4][j] != -1:
							mode = 0
							break
						c[(i-1)%4][j] = b[i][j]
					if b[i][j] == 3:
						if c[(i+1)%4][j] != -1:
							mode = 0
							break
						c[(i+1)%4][j] = b[i][j]
			if mode == 0:
				break
			b = c

		# 衝突しなかった場合, TYPE 1, 2, 3, 4 に当てはまるかを確認
		if mode:
			ans = 0
			m = 16
			x = [0] * m
			y = [0] * m
			r = [0] * m
			rl = [0] * 4
			for i in range(4):
				for j in range(4):
					x[i*4 + j] = i
					y[i*4 + j] = j
					r[i*4 + j] = a[i][j]
					rl[a[i][j]] += 1
			w = 4
			h = 4
			g = 4			
			ans += count_type1(m, rl, x, y, r, w, h, g)
			ans += count_type2(m, rl, x, y, r, w, h, g)
			ans += count_type3(m, rl, x, y, r, w, h, g)
			ans += count_type4(m, rl, x, y, r, w, h, g)
			ans += count_type451(m, rl, x, y, r, w, h, g)
			ans += count_type452(m, rl, x, y, r, w, h, g)
			# TYPE 1, 2, 3, 4 に当てはまらない場合, 非自明
			if ans == 0:
				ret.append(a)

	return ret

# 実行！
ar = make_hijimei()

# TYPE 5
# 非自明 48通りを全探索する
def count_type5(m, rl, x, y, r, w, h, g):
	ret = 0
	if g % 4 == 0:
		a = [[-1] * 4 for i in range(4)]
		mode = 1
		for i in range(m):
			if a[x[i]%4][y[i]%4] == -1:
				a[x[i]%4][y[i]%4] = r[i]
			elif a[x[i]%4][y[i]%4] != r[i]:
				mode = 0
				break
		if mode == 0:
			return 0
		for b in ar:
			mode = 1
			for i in range(4):
				for j in range(4):
					if a[i][j] != -1 and a[i][j] != b[i][j]:
						mode = 0
						break
			if mode:
				ret += 1
	return ret

# 解く
def solve():
	# 順番逆のほうが直感的なので逆にしてます（ごめんね）
	w, h, m = map(int,input().split())
	v = {"U":0, "D":1, "L":2, "R":3}
	g = gcd(w, h)

	rl = [0] * 4 # 方向のカウント
	x = [0] * m # X
	y = [0] * m # Y
	r = [0] * m # 方向

	# 入力
	for i in range(m):
		xs, ys, d = input().split()
		x[i] = int(xs)
		y[i] = int(ys)
		r[i] = v[d]
		rl[r[i]] += 1

	# 数え上げ
	ans = 0
	ans += count_type1(m, rl, x, y, r, w, h, g)
	ans += count_type2(m, rl, x, y, r, w, h, g)
	ans += count_type3(m, rl, x, y, r, w, h, g)
	ans += count_type4(m, rl, x, y, r, w, h, g)
	ans += count_type451(m, rl, x, y, r, w, h, g)
	ans += count_type452(m, rl, x, y, r, w, h, g)
	ans += count_type5(m, rl, x, y, r, w, h, g)
	ans %= mod

	return ans


T = int(input())
for _ in range(T):
	print(solve())
0