結果

問題 No.2770 Coupon Optimization
ユーザー nikoro256nikoro256
提出日時 2024-06-01 01:36:11
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,217 ms / 3,000 ms
コード長 7,930 bytes
コンパイル時間 432 ms
コンパイル使用メモリ 82,356 KB
実行使用メモリ 149,520 KB
最終ジャッジ日時 2024-06-01 01:36:45
合計ジャッジ時間 16,000 ms
ジャッジサーバーID
(参考情報)
judge1 / judge2
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 45 ms
54,016 KB
testcase_01 AC 43 ms
54,016 KB
testcase_02 AC 45 ms
53,888 KB
testcase_03 AC 312 ms
107,424 KB
testcase_04 AC 1,115 ms
147,992 KB
testcase_05 AC 94 ms
103,296 KB
testcase_06 AC 1,155 ms
146,596 KB
testcase_07 AC 1,131 ms
125,296 KB
testcase_08 AC 1,206 ms
149,520 KB
testcase_09 AC 589 ms
105,984 KB
testcase_10 AC 607 ms
98,116 KB
testcase_11 AC 390 ms
92,416 KB
testcase_12 AC 1,057 ms
123,876 KB
testcase_13 AC 644 ms
101,684 KB
testcase_14 AC 1,217 ms
149,000 KB
testcase_15 AC 1,210 ms
149,364 KB
testcase_16 AC 1,203 ms
149,088 KB
testcase_17 AC 1,207 ms
149,000 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

diff #

# https://github.com/shakayami/ACL-for-python/blob/master/convolution.py
class FFT:
    def primitive_root_constexpr(self, m):
        if m == 2:
            return 1
        if m == 167772161:
            return 3
        if m == 469762049:
            return 3
        if m == 754974721:
            return 11
        if m == 998244353:
            return 3
        if m == 46039102721957560334603910272195756033:
            return 5
        divs = [0] * 20
        divs[0] = 2
        cnt = 1
        x = (m - 1) // 2
        while x % 2 == 0:
            x //= 2
        i = 3
        while i * i <= x:
            if x % i == 0:
                divs[cnt] = i
                cnt += 1
                while x % i == 0:
                    x //= i
            i += 2
        if x > 1:
            divs[cnt] = x
            cnt += 1
        g = 2
        while 1:
            ok = True
            for i in range(cnt):
                if pow(g, (m - 1) // divs[i], m) == 1:
                    ok = False
                    break
            if ok:
                return g
            g += 1

    def bsf(self, x):
        res = 0
        while x % 2 == 0:
            res += 1
            x //= 2
        return res

    rank2 = 0
    root = []
    iroot = []
    rate2 = []
    irate2 = []
    rate3 = []
    irate3 = []

    def __init__(self, MOD):
        self.mod = MOD
        self.g = self.primitive_root_constexpr(self.mod)
        self.rank2 = self.bsf(self.mod - 1)
        self.root = [0 for i in range(self.rank2 + 1)]
        self.iroot = [0 for i in range(self.rank2 + 1)]
        self.rate2 = [0 for i in range(self.rank2)]
        self.irate2 = [0 for i in range(self.rank2)]
        self.rate3 = [0 for i in range(self.rank2 - 1)]
        self.irate3 = [0 for i in range(self.rank2 - 1)]
        self.root[self.rank2] = pow(self.g, (self.mod - 1) >> self.rank2, self.mod)
        self.iroot[self.rank2] = pow(self.root[self.rank2], self.mod - 2, self.mod)
        for i in range(self.rank2 - 1, -1, -1):
            self.root[i] = (self.root[i + 1] ** 2) % self.mod
            self.iroot[i] = (self.iroot[i + 1] ** 2) % self.mod
        prod = 1
        iprod = 1
        for i in range(self.rank2 - 1):
            self.rate2[i] = (self.root[i + 2] * prod) % self.mod
            self.irate2[i] = (self.iroot[i + 2] * iprod) % self.mod
            prod = (prod * self.iroot[i + 2]) % self.mod
            iprod = (iprod * self.root[i + 2]) % self.mod
        prod = 1
        iprod = 1
        for i in range(self.rank2 - 2):
            self.rate3[i] = (self.root[i + 3] * prod) % self.mod
            self.irate3[i] = (self.iroot[i + 3] * iprod) % self.mod
            prod = (prod * self.iroot[i + 3]) % self.mod
            iprod = (iprod * self.root[i + 3]) % self.mod

    def butterfly(self, a):
        n = len(a)
        h = (n - 1).bit_length()

        LEN = 0
        while LEN < h:
            if h - LEN == 1:
                p = 1 << (h - LEN - 1)
                rot = 1
                for s in range(1 << LEN):
                    offset = s << (h - LEN)
                    for i in range(p):
                        l = a[i + offset]
                        r = a[i + offset + p] * rot
                        a[i + offset] = (l + r) % self.mod
                        a[i + offset + p] = (l - r) % self.mod
                    rot *= self.rate2[(~s & -~s).bit_length() - 1]
                    rot %= self.mod
                LEN += 1
            else:
                p = 1 << (h - LEN - 2)
                rot = 1
                imag = self.root[2]
                for s in range(1 << LEN):
                    rot2 = (rot * rot) % self.mod
                    rot3 = (rot2 * rot) % self.mod
                    offset = s << (h - LEN)
                    for i in range(p):
                        a0 = a[i + offset]
                        a1 = a[i + offset + p] * rot
                        a2 = a[i + offset + 2 * p] * rot2
                        a3 = a[i + offset + 3 * p] * rot3
                        a1na3imag = (a1 - a3) % self.mod * imag
                        a[i + offset] = (a0 + a2 + a1 + a3) % self.mod
                        a[i + offset + p] = (a0 + a2 - a1 - a3) % self.mod
                        a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % self.mod
                        a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % self.mod
                    rot *= self.rate3[(~s & -~s).bit_length() - 1]
                    rot %= self.mod
                LEN += 2

    def butterfly_inv(self, a):
        n = len(a)
        h = (n - 1).bit_length()
        LEN = h
        while LEN:
            if LEN == 1:
                p = 1 << (h - LEN)
                irot = 1
                for s in range(1 << (LEN - 1)):
                    offset = s << (h - LEN + 1)
                    for i in range(p):
                        l = a[i + offset]
                        r = a[i + offset + p]
                        a[i + offset] = (l + r) % self.mod
                        a[i + offset + p] = (l - r) * irot % self.mod
                    irot *= self.irate2[(~s & -~s).bit_length() - 1]
                    irot %= self.mod
                LEN -= 1
            else:
                p = 1 << (h - LEN)
                irot = 1
                iimag = self.iroot[2]
                for s in range(1 << (LEN - 2)):
                    irot2 = (irot * irot) % self.mod
                    irot3 = (irot * irot2) % self.mod
                    offset = s << (h - LEN + 2)
                    for i in range(p):
                        a0 = a[i + offset]
                        a1 = a[i + offset + p]
                        a2 = a[i + offset + 2 * p]
                        a3 = a[i + offset + 3 * p]
                        a2na3iimag = (a2 - a3) * iimag % self.mod
                        a[i + offset] = (a0 + a1 + a2 + a3) % self.mod
                        a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % self.mod
                        a[i + offset + 2 * p] = (a0 + a1 - a2 - a3) * irot2 % self.mod
                        a[i + offset + 3 * p] = (
                            (a0 - a1 - a2na3iimag) * irot3 % self.mod
                        )
                    irot *= self.irate3[(~s & -~s).bit_length() - 1]
                    irot %= self.mod
                LEN -= 2

    def convolution(self, a, b):
        n = len(a)
        m = len(b)
        if not (a) or not (b):
            return []
        if min(n, m) <= 40:
            res = [0] * (n + m - 1)
            for i in range(n):
                for j in range(m):
                    res[i + j] += a[i] * b[j]
                    res[i + j] %= self.mod
            return res
        z = 1 << ((n + m - 2).bit_length())
        a = a + [0] * (z - n)
        b = b + [0] * (z - m)
        self.butterfly(a)
        self.butterfly(b)
        c = [(a[i] * b[i]) % self.mod for i in range(z)]
        self.butterfly_inv(c)
        iz = pow(z, self.mod - 2, self.mod)
        for i in range(n + m - 1):
            c[i] = (c[i] * iz) % self.mod
        return c[: n + m - 1]


def extgcd(a, b):
    if b:
        d, y, x = extgcd(b, a % b)
        y -= (a // b) * x
        return d, x, y
    return a, 1, 0


# V = [(X_i, Y_i), ...]: X_i (mod Y_i)
def remainder(V):
    x = 0
    d = 1
    for X, Y in V:
        g, a, b = extgcd(d, Y)
        if x % g != X % g:
            return 0, 0
        x, d = (Y * b * x + d * a * X) // g, d * (Y // g)
        x %= d
    return x, d


N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
A = [a // 100 for a in A]
A.sort()
B.sort(reverse=True)
fft = FFT(998244353)
fft2 = FFT(469762049)
ans = fft.convolution(A, B)
ans2 = fft2.convolution(A, B)
left = 0
for i in range(N):
    ans_, d = remainder([(ans[i], 998244353), (ans2[i], 469762049)])
    left += A[i] * 100
    print(left - ans_)
0