結果

問題 No.3231 2×2行列相似判定 〜hard〜
ユーザー lif4635
提出日時 2025-08-08 22:26:14
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 49 ms / 2,000 ms
コード長 4,225 bytes
コンパイル時間 288 ms
コンパイル使用メモリ 82,468 KB
実行使用メモリ 57,368 KB
最終ジャッジ日時 2025-08-08 22:26:56
合計ジャッジ時間 3,198 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 * 3
other AC * 37
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 # 

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]

def graph(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[int]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b = map(int, input().split())
        a += index
        b += index
        edge[a].add(b)
        if not dir:
            edge[b].add(a)
    return edge

def graph_w(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[tuple]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b,c = map(int, input().split())
        a += index
        b += index
        edge[a].add((b,c))
        if not dir:
            edge[b].add((a,c))
    return edge

mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
def acc(a:list[int]):
    sa = [0]*(len(a)+1)
    for i in range(len(a)):
        sa[i+1] = a[i] + sa[i]
    return sa

prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')

from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right

mod = 67

def mat_add(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] + b[i][j])%mod
    return res

def mat_sub(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] - b[i][j])%mod
    return res

def mat_mul(a, b):
    # assert len(a[0]) == len(b)
    n = len(a)
    m = len(b[0])
    res = [[0]*m for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,b_kj in enumerate(b[k]):
                r_i[j] = (r_i[j] + a_ik*b_kj)%mod
    return res

def mat_pow2(a):
    n = len(a)
    res = [[0]*n for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,a_kj in enumerate(a[k]):
                r_i[j] = (r_i[j] + a_ik*a_kj)%mod
    return res

def mat_inv(a, mod = mod):
    """いつか実装します"""
    pass

def mat_pow(a, exp):
    n = len(a)
    res = [[int(i == j) for j in range(n)] for i in range(n)]
    
    d = exp.bit_length()
    for i in range(d, -1, -1):
        if (exp >> i) & 1: res = mat_mul(res, a)
        if i == 0: return res
        res = mat_pow2(res)



mod = 10 ** 9 + 7
m = LLI(2)
k = LLI(2)

def calc(m):
    tr = (m[0][0] + m[1][1]) % mod
    det = (m[0][0] * m[1][1] - m[1][0] * m[0][1]) % mod
    # print(r, s)
    return tr, det

def jordan(m):
    # λI かどうか 
    return m[0][1] == 0 and m[1][0] == 0

inv2 = mod + 1 >> 1
# print(calc(m))
# print(calc(k))
if calc(m) == calc(k):
    r, s = calc(m)
    t = (r * inv2 % mod) ** 2 % mod
    # print(r, t, s)
    if t == s:
        # 重解のとき
        if jordan(m) == jordan(k):
            yes()
        else:
            no()
    else:
        yes()
else:
    no()
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