結果

問題 No.541 3 x N グリッド上のサイクルの個数
コンテスト
ユーザー maspy
提出日時 2020-05-06 18:08:01
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 538 ms / 2,000 ms
コード長 2,647 bytes
コンパイル時間 87 ms
コンパイル使用メモリ 12,928 KB
実行使用メモリ 44,912 KB
最終ジャッジ日時 2024-07-03 09:03:41
合計ジャッジ時間 33,868 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 62
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
import numpy as np

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

MOD = 10**9 + 7

def compute_next_status(status, vertical):
    status = list(status)
    deg = [0] * 4
    for i, x in enumerate(status):
        if x != 0:
            deg[i] = 1

    loop = False
    for i in range(3):
        if vertical & (1 << i):
            deg[i] += 1
            deg[i+1] += 1
            if status[i] == status[i+1] != 0:
                if loop:
                    return None
                loop = True
                status[i] = status[i+1] = 0
                continue
            if status[i] == status[i+1] == 0:
                status[i] = status[i+1] = max(status) + 1
            elif status[i] != 0 and status[i+1] == 0:
                status[i+1] = status[i]
            elif status[i+1] != 0 and status[i] == 0:
                status[i] = status[i+1]
            else:
                n, m = status[i:i+2]
                n, m = max(n, m), min(n, m)
                for v in range(4):
                    if status[v] == m:
                        status[v] = n
    if loop:
        if any(x in [1,3] for x in deg):
            return None
        return (0,0,0,0)
    if any(x >= 3 for x in deg):
        return None
    for v in range(4):
        if deg[v] != 1:
            status[v] = 0
    for n, k in enumerate(set(status + [0])):
        if k == 0:
            continue
        for v in range(4):
            if status[v] == k:
                status[v] = n
    return tuple(status)

visited = set([(0,0,0,0)])
q = [(0,0,0,0)]
edges = []
while q:
    v = q.pop()
    for i in range(8):
        w = compute_next_status(v, i)
        if w is None:
            continue
        edges.append((v,w))
        if w in visited:
            continue
        visited.add(w)
        q.append(w)

visited

L = len(visited) + 1
A = np.zeros((L,L), dtype=object)
v_to_i = {v:i for i,v in enumerate(visited)}
i0 = v_to_i[(0,0,0,0)]
i_end = L - 1
for v,w in edges:
    iv, iw = v_to_i[v], v_to_i[w]
    if iv != i0 and iw == i0:
        iw = i_end
    A[iw, iv] = 1
A[i_end, i_end] += 1

def mult_mod(A, B, MOD=MOD):
    mask = (1<<15) - 1
    A1, A2 = A>>15, A & mask
    B1, B2 = B>>15, B&mask
    X = np.dot(A1, B1) % MOD
    Z = np.dot(A2, B2) % MOD
    Y = (np.dot(A1+A2,B1+B2)-X-Z)%MOD
    return ((X<<30)+(Y<<15)+Z)%MOD

def matrix_power(A, n, MOD=MOD):
    if n == 1:
        return A
    B = matrix_power(A, n//2)
    B = mult_mod(B, B)
    if n & 1:
        B = mult_mod(A, B)
    return B

MOD = 10**9 + 7
N = int(read())

print(matrix_power(A, N + 1)[i_end, i0])
0