AtCoder problem 015

C++ solution:


Python solution: # でつoO(YOU PLAY WITH THE CARDS YOU'RE DEALT..)
N = int(input())

MOD = 10**9 + 7
class Mint:
    __slots__ = ('value')

    def __init__(self, value=0):
        self.value = int(value) % MOD
        if self.value < 0: self.value += MOD

    def inverse(self):
        a, b = self.value, MOD
        u, v = 1, 0
        while b:
            t = a // b
            b, a = a - t * b, b
            v, u = u - t * v, v
        if u < 0: u += MOD
        return u

    def __repr__(self): return str(self.value)
    def __int__(self): return self.value
    def __eq__(self, other): return self.value == other.value
    def __neg__(self): return Mint(-self.value)
    def __hash__(self): return hash(self.value)
    def __bool__(self): return self.value != 0

    def __iadd__(self, other):
        self.value = (self.value + int(other)) % MOD
        return self

    def __add__(self, other):
        new_obj = Mint(self.value)
        new_obj += other
        return new_obj
    __radd__ = __add__

    def __isub__(self, other):
        self.value = (self.value - int(other)) % MOD
        if self.value < 0: self.value += MOD
        return self

    def __sub__(self, other):
        new_obj = Mint(self.value)
        new_obj -= other
        return new_obj

    def __rsub__(self, other):
        new_obj = Mint(int(other))
        new_obj -= self
        return new_obj

    def __imul__(self, other):
        self.value = self.value * int(other) % MOD
        return self

    def __mul__(self, other):
        new_obj = Mint(self.value)
        new_obj *= other
        return new_obj
    __rmul__ = __mul__

    def __ifloordiv__(self, other):
        other = other if isinstance(other, Mint) else Mint(other)
        self *= other.inverse()
        return self

    def __floordiv__(self, other):
        new_obj = Mint(self.value)
        new_obj //= other
        return new_obj

    def __rfloordiv__(self, other):
        new_obj = Mint(int(other))
        new_obj //= self
        return new_obj

class FactorialUtils:
    __slots__ = ('fac', 'ifac')

    def __init__(self, n):
        self.fac = [1] * (n + 1)
        self.ifac = [1] * (n + 1)
        for i in range(2, n + 1): self.fac[i] = self.fac[i - 1] * i % MOD
        self.ifac[n] = pow(self.fac[n], MOD - 2, MOD)
        for i in range(n, 1, -1): self.ifac[i - 1] = self.ifac[i] * i % MOD

    def choose(self, n, r):
        if r < 0 or r > n: return 0
        return (self.fac[n] * self.ifac[n - r] % MOD) * self.ifac[r] % MOD

    def multichoose(self, u, k):
        return (self.fac[u + k - 1] * self.ifac[u - 1] % MOD) * self.ifac[k] % MOD

    def permutation(self, n, r):
        if r < 0 or r > n: return 0
        return self.fac[n] * self.ifac[n - r] % MOD

fu = FactorialUtils(N)
for k in range(1, N + 1):
    ans = Mint()
    for i in range(N // k + 1):
        ans += fu.choose(N - (k - 1) * i, i + 1)
    print(ans)




Kuin solution: func main()
	var n: int :: cui@inputInt()
	
	const mod: int :: 1000000007
	var comb: @Comb :: (#@Comb).init(n, mod)
	var ans: []int :: #[n + 1]int
	for k(1, n)
		var numMax: int :: (n - 1) / k + 1
		for num(1, numMax)
			var remains: int :: n - 1 - k * (num - 1)
			do ans[k] :+ comb.comb(num + remains, remains)
			do ans[k] :% mod
		end for
	end for
	for k(1, n)
		do cui@print("\{ans[k]}\n")
	end for
end func

class Comb()
	var mod: int
	var fact: []int
	var inv: []int
	
	+func init(n: int, mod: int): Comb
		do me.mod :: mod
		do me.fact :: #[n + 1]int
		do me.inv :: #[n + 1]int
		do me.fact[0] :: 1
		for i(1, n)
			do me.fact[i] :: me.fact[i - 1] * i % mod
		end for
		do me.inv[n] :: math@modPow(me.fact[n], mod - 2, mod)
		for i(n, 1, -1)
			do me.inv[i - 1] :: me.inv[i] * i % mod
		end for
		ret me
	end func
	
	+func comb(n: int, r: int): int
		ret me.fact[n] * me.inv[n - r] % me.mod * me.inv[r] % me.mod
	end func
end class