#701490 (Python3) No.463 魔法使いのすごろく🎲

提出ソース
結果

問題	No.463 魔法使いのすごろく🎲
ユーザー	vwxyz
提出日時	2021-09-22 18:27:53
言語	Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果	AC
実行時間	794 ms / 2,000 ms
コード長	25,735 bytes
コンパイル時間	94 ms
コンパイル使用メモリ	16,000 KB
実行使用メモリ	14,208 KB
最終ジャッジ日時	2024-07-05 09:18:39
合計ジャッジ時間	8,594 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
このコードへのチャレンジ
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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	79 ms 14,208 KB
testcase_01	AC	59 ms 14,208 KB
testcase_02	AC	59 ms 14,080 KB
testcase_03	AC	45 ms 14,080 KB
testcase_04	AC	64 ms 14,080 KB
testcase_05	AC	83 ms 14,080 KB
testcase_06	AC	46 ms 14,080 KB
testcase_07	AC	49 ms 14,208 KB
testcase_08	AC	55 ms 13,952 KB
testcase_09	AC	214 ms 14,080 KB
testcase_10	AC	52 ms 14,208 KB
testcase_11	AC	136 ms 13,952 KB
testcase_12	AC	84 ms 14,208 KB
testcase_13	AC	44 ms 14,080 KB
testcase_14	AC	251 ms 13,952 KB
testcase_15	AC	224 ms 14,080 KB
testcase_16	AC	47 ms 14,208 KB
testcase_17	AC	284 ms 14,080 KB
testcase_18	AC	46 ms 14,080 KB
testcase_19	AC	49 ms 13,952 KB
testcase_20	AC	45 ms 14,080 KB
testcase_21	AC	468 ms 14,208 KB
testcase_22	AC	792 ms 14,080 KB
testcase_23	AC	794 ms 14,080 KB
testcase_24	AC	163 ms 14,080 KB
testcase_25	AC	215 ms 13,952 KB
testcase_26	AC	258 ms 14,080 KB
testcase_27	AC	192 ms 14,080 KB
testcase_28	AC	541 ms 13,952 KB
testcase_29	AC	198 ms 14,080 KB
testcase_30	AC	328 ms 14,080 KB
testcase_31	AC	195 ms 14,080 KB
testcase_32	AC	313 ms 14,208 KB
testcase_33	AC	208 ms 14,080 KB
testcase_34	AC	162 ms 14,080 KB
testcase_35	AC	47 ms 14,080 KB
testcase_36	AC	46 ms 14,208 KB
testcase_37	AC	46 ms 13,952 KB
testcase_38	AC	45 ms 14,208 KB
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

raw source code
import sys
readline=sys.stdin.readline
import math

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

class MOD:
    def __init__(self,p,e=1):
        self.p=p
        self.e=e
        self.mod=self.p**self.e

    def Pow(self,a,n):
        a%=self.mod
        if n>=0:
            return pow(a,n,self.mod)
        else:
            assert math.gcd(a,self.mod)==1
            x=Extended_Euclid(a,self.mod)[0]
            return pow(x,-n,self.mod)

    def Build_Fact(self,N):
        assert N>=0
        self.factorial=[1]
        self.cnt=[0]*(N+1)
        for i in range(1,N+1):
            ii=i
            self.cnt[i]=self.cnt[i-1]
            while ii%self.p==0:
                ii//=self.p
                self.cnt[i]+=1
            self.factorial.append((self.factorial[-1]*ii)%self.mod)
        self.factorial_inve=[None]*(N+1)
        self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod

    def Fact(self,N):
        return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod

    def Fact_Inve(self,N):
        if self.cnt[N]:
            return None
        return self.factorial_inve[N]

    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.mod
        cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
        if divisible_count:
            return retu,cnt
        else:
            retu*=pow(self.p,cnt,self.mod)
            retu%=self.mod
            return retu

class Matrix:
    def __init__(self,H=0,W=0,matrix=False,eps=1e-12,mod=0,identity=0):
        if identity:
            if H:
                self.H=H
                self.W=H
            else:
                self.H=W
                self.W=W
            self.matrix=[[0]*self.W for i in range(self.H)]
            for i in range(self.H):
                self.matrix[i][i]=identity
        elif matrix:
            self.matrix=matrix
            self.H=len(self.matrix)
            self.W=len(self.matrix[0]) if self.matrix else 0
        else:
            self.H=H
            self.W=W
            self.matrix=[[0]*self.W for i in range(self.H)]
        self.mod=mod
        self.eps=eps

    def __eq__(self,other):
        if type(other)!=Matrix:
            return False
        if self.H!=other.H:
            return False
        if self.mod:
            for i in range(self.H):
                for j in range(self.W):
                    if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod:
                        return False
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if abs(self.matrix[i][j]-other.matrix[i][j])>self.eps:
                        return False
        return True

    def __ne__(self,other):
        if type(other)!=Matrix:
            return True
        if self.H!=other.H:
            return True
        if self.mod:
            for i in range(self.H):
                for j in range(self.W):
                    if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod:
                        return True
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if abs(self.matrix[i][j]-other.matrix[i][j])>self.eps:
                        return True
        return False

    def __add__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                summ=Matrix(matrix=[[(self.matrix[i][j]+other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                summ=Matrix(matrix=[[self.matrix[i][j]+other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                summ=Matrix(matrix=[[(self.matrix[i][j]+other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                summ=Matrix(matrix=[[self.matrix[i][j]+other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return summ

    def __sub__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                diff=Matrix(matrix=[[(self.matrix[i][j]-other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                diff=Matrix(matrix=[[self.matrix[i][j]-other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                diff=Matrix(matrix=[[(self.matrix[i][j]-other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                diff=Matrix(matrix=[[self.matrix[i][j]-other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return diff

    def __mul__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                prod=Matrix(matrix=[[(self.matrix[i][j]*other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(matrix=[[self.matrix[i][j]*other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                prod=Matrix(matrix=[[(self.matrix[i][j]*other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(matrix=[[self.matrix[i][j]*other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return prod

    def __matmul__(self,other):
        if type(other)==Matrix:
            assert self.W==other.H
            prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod)
            for i in range(self.H):
                for j in range(other.W):
                    for k in range(self.W):
                        prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j]
                        if self.mod:
                            prod.matrix[i][j]%=self.mod
        elif type(other)==int:
            assert self.H==self.W
            if other==0:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
            elif other==1:
                prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
                doub=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
                while other>=2:
                    if other&1:
                        prod@=doub
                    doub@=doub
                    other>>=1
                prod@=doub
        return prod

    def __truediv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                quot=Matrix(matrix=[[(self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1))%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                quot=Matrix(matrix=[[self.matrix[i][j]/other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                inve=MOD(self.mod).Pow(other,-1)
                quot=Matrix(matrix=[[(self.matrix[i][j]*inve)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                quot=Matrix(matrix=[[self.matrix[i][j]/other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return quot

    def __floordiv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            quot=Matrix(matrix=[[self.matrix[i][j]//other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            quot=Matrix(matrix=[[self.matrix[i][j]//other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return quot

    def __mod__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            rema=Matrix(matrix=[[self.matrix[i][j]%other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            rema=Matrix(matrix=[[self.matrix[i][j]%other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return rema

    def __pow__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j],self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other,self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return powe

    def __lshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            lshi=Matrix(matrix=[[self.matrix[i][j]<<other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            lshi=Matrix(matrix=[[self.matrix[i][j]<<other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return lshi

    def __rshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            rshi=Matrix(matrix=[[self.matrix[i][j]>>other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            rshi=Matrix(matrix=[[self.matrix[i][j]>>other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return rshi

    def __and__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            conj=Matrix(matrix=[[self.matrix[i][j]&other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            conj=Matrix(matrix=[[self.matrix[i][j]&other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return conj

    def __or__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            disj=Matrix(matrix=[[self.matrix[i][j]|other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            disj=Matrix(matrix=[[self.matrix[i][j]|other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return disj

    def __xor__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            excl=Matrix(matrix=[[self.matrix[i][j]^other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            excl=Matrix(matrix=[[self.matrix[i][j]^other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return excl

    def __iadd__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]+=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]+=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __isub__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]-=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]-=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __imul__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]*=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]*=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __imatmul__(self,other):
        if type(other)==Matrix:
            assert self.W==other.H
            prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod)
            for i in range(self.H):
                for j in range(other.W):
                    for k in range(self.W):
                        prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j]
                        if self.mod:
                            prod.matrix[i][j]%=self.mod
        elif type(other)==int:
            assert self.H==self.W
            if other==0:
                return Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
            elif other==1:
                prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
                doub=self
                while other>=2:
                    if other&1:
                        prod@=doub
                    doub@=doub
                    other>>=1
                prod@=doub
        return prod

    def __itruediv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1)%self.mod
                    else:
                        self.matrix[i][j]/=other.matrix[i][j]
        else:
            if self.mod:
                inve=MOD(self.mod).Pow(other,-1)
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=self.matrix[i][j]*inve%self.mod
                    else:
                        self.matrix[i][j]/=other
        return self

    def __ifloordiv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]//=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]//=other
        return self

    def __imod__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]%=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]%=other
        return self

    def __ipow__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j],self.mod)
                    else:
                        self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j])
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=pow(self.matrix[i][j],other,self.mod)
                    else:
                        self.matrix[i][j]=pow(self.matrix[i][j],other)
        return self

    def __ilshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]<<=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]<<=other
        return self

    def __irshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]>>=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]>>=other
        return self

    def __iand__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]&=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]&=other
        return self

    def __ior__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]|=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]|=other
        return self

    def __ixor__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]^=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]^=other
        return self

    def __neg__(self):
        if self.mod:
            nega=Matrix(matrix=[[(-self.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            nega=Matrix(matrix=[[-self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return nega

    def __pos__(self):
        posi=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return posi

    def __invert__(self):
        inve=Matrix(matrix=[[~self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return inve

    def __abs__(self):
        abso=Matrix(matrix=[[abs(self.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return abso

    def __getitem__(self,i):
        if type(i)==int:
            return self.matrix[i]
        elif type(i)==tuple:
            i,j=i
            if type(i)==int:
                i=slice(i,i+1)
            if type(j)==int:
                j=slice(j,j+1)
            return Matrix(matrix=[lst[j] for lst in self.matrix[i]],eps=self.eps,mod=self.mod)

    def __contains__(self,x):
        for i in range(self.H):
            if x in self.matrix[i]:
                return True
        return False

    def __str__(self):
        digit=[max(len(str(self.matrix[i][j])) for i in range(self.H)) for j in range(self.W)]
        return "\n".join([(" [" if i else "[[")+", ".join([str(self.matrix[i][j]).rjust(digit[j]," ") for j in range(self.W)])+"]" for i in range(self.H)])+"]"

    def __bool__(self):
        return True

    def Transpose(self):
        return Matrix(matrix=[[self.matrix[i][j] for i in range(self.H)] for j in range(self.W)])

    def Trace(self):
        assert self.H==self.W
        trace=sum(self.matrix[i][i] for i in range(self.H))
        if self.mod:
            trace%=self.mod
        return trace

    def Elem_Raw_Operate_1(self,i1,i2):
        self.matrix[i1],self.matrix[i2]=self.matrix[i2],self.matrix[i1]

    def Elem_Raw_Operate_2(self,i,c):
        if self.mod:
            self.matrix[i]=[self.matrix[i][j]*c%self.mod for j in range(self.W)]
        else:
            self.matrix[i]=[self.matrix[i][j]*c for j in range(self.W)]

    def Elem_Raw_Operate_3(self,i1,i2,c):
        if self.mod:
            self.matrix[i1]=[(self.matrix[i1][j]+c*self.matrix[i2][j])%self.mod for j in range(self.W)]
        else:
            self.matrix[i1]=[self.matrix[i1][j]+c*self.matrix[i2][j] for j in range(self.W)]

    def Elimination(self,determinant=False,inverse_matrix=False,linear_equation=False,rank=False,upper_triangular=False):
        h=0
        ut=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        if determinant or inverse_matrix:
            assert self.H==self.W
            det=1
        if inverse_matrix:
            assert self.H==self.W
            im=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
        if linear_equation:
            assert self.H==linear_equation.H
            le=Matrix(matrix=[[linear_equation.matrix[i][j] for j in range(linear_equation.W)] for i in range(linear_equation.H)],eps=self.eps,mod=self.mod)
        for j in range(ut.W):
            for i in range(h,ut.H):
                if abs(ut.matrix[i][j])>ut.eps:
                    if ut.mod:
                        inve=MOD(ut.mod).Pow(ut.matrix[i][j],-1)
                    else:
                        inve=1/ut.matrix[i][j]

                    ut.Elem_Raw_Operate_1(i,h)
                    if determinant and h%2!=i%2:
                        det=(-det)%self.mod
                    if inverse_matrix:
                        im.Elem_Raw_Operate_1(i,h)
                    if linear_equation:
                        le.Elem_Raw_Operate_1(i,h)
                    
                    ut.Elem_Raw_Operate_2(h,inve)
                    if determinant or inverse_matrix:
                        det*=inve
                        if ut.mod:
                            det%=ut.mod
                    if inverse_matrix:
                        im.Elem_Raw_Operate_2(h,inve)
                    if linear_equation:
                        le.Elem_Raw_Operate_2(h,inve)
                    
                    for ii in range(ut.H):
                        if ii==h:
                            continue
                        x=-ut.matrix[ii][j]
                        ut.Elem_Raw_Operate_3(ii,h,x)
                        if inverse_matrix:
                            im.Elem_Raw_Operate_3(ii,h,x)
                        if linear_equation:
                            le.Elem_Raw_Operate_3(ii,h,x)
                    h+=1
                    break
            else:
                det=0
        tpl=()
        if determinant:
            tpl+=(det,)
        if inverse_matrix:
            if det<=0:
                im=False
            tpl+=(im,)
        if linear_equation:
            tpl+=(le,)
        if rank:
            tpl+=(h,)
        if upper_triangular:
            tpl+=(ut,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

N,M=map(int,readline().split())
C=list(map(int,readline().split()))+[0]
Mat=Matrix(H=N,W=N)
A_Mat=Matrix(H=N,W=1)
for i in range(N-1):
    Mat[i][i]=1
    for j in range(i+1,i+M+1):
        j=min(j,2*(N-1)-j)
        Mat[i][j]-=1/M
        A_Mat[i][0]+=C[j-1]/M
Mat[N-1][N-1]=1
A_Mat=Mat.Elimination(linear_equation=A_Mat)
inf=1<<60
dp=[inf]*N
dp[N-1]=0
for i in range(N-1):
    for j in range(i+1,i+M+1):
        j=min(j,2*(N-1)-j)
        dp[i]=min(dp[i],A_Mat[j][0]+C[j-1])
for _ in range(N):
    for i in range(N-2,-1,-1):
        s=0
        for j in range(i+1,i+M+1):
            j=min(j,2*(N-1)-j)
            s+=dp[j]+C[j-1]
        s/=M
        dp[i]=min(dp[i],s)
ans=dp[0]
print(ans)
yukicoder

結果

テストケース

ソースコード
