#856136 (PyPy3) No.391 CODING WAR

• 問題: No.391 CODING WAR
• ユーザー: 草苺奶昔
• 提出日時: 2023-04-02 20:49:00
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 149 ms / 2,000 ms
• コード長: 6,486 bytes
• コンパイル時間: 206 ms
• コンパイル使用メモリ: 82,312 KB
• 実行使用メモリ: 72,624 KB
• 最終ジャッジ日時: 2024-09-25 00:38:09
• 合計ジャッジ時間: 3,002 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 16

ソースコード

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
class 写像十二相:
    """https://qiita.com/drken/items/f2ea4b58b0d21621bd51"""
    __slots__ = ("_fac", "_ifac", "_inv", "_mod")
    def __init__(self, size: int, mod: int) -> None:
        self._mod = mod
        self._fac = [1]
        self._ifac = [1]
        self._inv = [1]
        self._expand(size)
    def query(
        self,
        n: int,
        k: int,
        *,
        isBallSame: bool,
        isBoxSame: bool,
        atMostOneBallPerBox=False,
        noLimitWithBox=False,
        atLeastOneBallPerBox=False,
    ) -> int:
        """n个球放入k个盒子的方案数.
        Args:
            isBallSame (bool): 球是否有区别.
            isBoxSame (bool): 盒子是否有区别.
            atMostOneBalPerBox (bool, optional): 每个盒子最多放一个球.
            noLimitWithBox (bool, optional): 每个盒子可以放任意个球.
            atLeastOneBallPerBox (bool, optional): 每个盒子至少放一个球.
        """
        limits = (atMostOneBallPerBox, noLimitWithBox, atLeastOneBallPerBox)
        assert limits.count(True) == 1, "Must have one limit and only one limit with box."
        if isBallSame and isBoxSame:
            if atMostOneBallPerBox:
                return self._solve1(n, k)
            if noLimitWithBox:
                return self._solve2(n, k)
            if atLeastOneBallPerBox:
                return self._solve3(n, k)
        if not isBallSame and isBoxSame:
            if atMostOneBallPerBox:
                return self._solve4(n, k)
            if noLimitWithBox:
                return self._solve5(n, k)
            if atLeastOneBallPerBox:
                return self._solve6(n, k)
        if isBallSame and not isBoxSame:
            if atMostOneBallPerBox:
                return self._solve7(n, k)
            if noLimitWithBox:
                return self._solve8(n, k)
            if atLeastOneBallPerBox:
                return self._solve9(n, k)
        if not isBallSame and not isBoxSame:
            if atMostOneBallPerBox:
                return self._solve10(n, k)
            if noLimitWithBox:
                return self._solve11(n, k)
            if atLeastOneBallPerBox:
                return self._solve12(n, k)
        raise Exception("Unreachable code.")
    def _solve1(self, n: int, k: int) -> int:
        """有区别的球放入有区别的盒子(每个盒子最多放一个球)."""
        return self.P(n, k)
    def _solve2(self, n: int, k: int) -> int:
        """有区别的球放入有区别的盒子(每个盒子可以放任意个球)."""
        return pow(k, n, self._mod)
    def _solve3(self, n: int, k: int) -> int:
        """有区别的球放入有区别的盒子(每个盒子至少放一个球).
        容斥原理:用总方案数减去不合法的方案数.
        O(k*logn)
        """
        mod = self._mod
        res = 0
        for i in range(k + 1):
            if (k - i) & 1:
                res -= self.C(k, i) * pow(i, n, mod)
            else:
                res += self.C(k, i) * pow(i, n, mod)
            res %= mod
        return res
    def _solve4(self, n: int, k: int) -> int:
        """无区别的球放入有区别的盒子(每个盒子最多放一个球)."""
        return self.C(n, k)
    def _solve5(self, n: int, k: int) -> int:
        """无区别的球放入有区别的盒子(每个盒子可以放任意个球)."""
        return self.C(n + k - 1, n)
    def _solve6(self, n: int, k: int) -> int:
        """无区别的球放入有区别的盒子(每个盒子至少放一个球)."""
        return self.C(n - 1, k - 1)
    def _solve7(self, n: int, k: int) -> int:
        """有区别的球放入无区别的盒子(每个盒子最多放一个球)."""
        return 0 if n > k else 1
    def _solve8(self, n: int, k: int) -> int:
        """有区别的球放入无区别的盒子(每个盒子可以放任意个球).
        贝尔数.
        """
        ...
    def _solve9(self, n: int, k: int) -> int:
        """有区别的球放入无区别的盒子(每个盒子至少放一个球).
        第二类斯特林数.
        """
        ...
    def _solve10(self, n: int, k: int) -> int:
        """无区别的球放入无区别的盒子(每个盒子最多放一个球)."""
        ...
    def _solve11(self, n: int, k: int) -> int:
        """无区别的球放入无区别的盒子(每个盒子可以放任意个球).
        分割数.
        """
        ...
    def _solve12(self, n: int, k: int) -> int:
        """无区别的球放入无区别的盒子(每个盒子至少放一个球).
        分割数.
        """
        ...
    def fac(self, k: int) -> int:
        self._expand(k)
        return self._fac[k]
    def ifac(self, k: int) -> int:
        self._expand(k)
        return self._ifac[k]
    def inv(self, k: int) -> int:
        self._expand(k)
        return self._inv[k]
    def C(self, n: int, k: int) -> int:
        if n < 0 or k < 0 or n < k:
            return 0
        mod = self._mod
        return self.fac(n) * self.ifac(k) % mod * self.ifac(n - k) % mod
    def P(self, n: int, k: int) -> int:
        if n < 0 or k < 0 or n < k:
            return 0
        mod = self._mod
        return self.fac(n) * self.ifac(n - k) % mod
    def H(self, n: int, k: int) -> int:
        """可重复选取元素的组合数"""
        return self.C(n + k - 1, k)
    def put(self, n: int, k: int) -> int:
        """n个相同的球放入k个不同的盒子(盒子可放任意个球)的方案数."""
        return self.C(n + k - 1, n)
    def _expand(self, size: int) -> None:
        if len(self._fac) < size + 1:
            mod = self._mod
            preSize = len(self._fac)
            diff = size + 1 - preSize
            self._fac += [1] * diff
            self._ifac += [1] * diff
            self._inv += [1] * diff
            for i in range(preSize, size + 1):
                self._fac[i] = self._fac[i - 1] * i % mod
            self._ifac[size] = pow(self._fac[size], mod - 2, mod)  # !modInv
            for i in range(size - 1, preSize - 1, -1):
                self._ifac[i] = self._ifac[i + 1] * (i + 1) % mod
            for i in range(preSize, size + 1):
                self._inv[i] = self._ifac[i] * self._fac[i - 1] % mod
MOD = int(1e9 + 7)
X = 写像十二相(int(1e5), MOD)
if __name__ == "__main__":
    n, k = map(int, input().split())
    print(X.query(n, k, isBallSame=True, isBoxSame=True, atLeastOneBallPerBox=True))
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX