排列硬币

# 排列硬币

# 暴力求解
def func1(n: int):
    for i in range(1, n + 1):
        n -= i
        if n < i:
            return i


# 二分求解
def func2(n: int):
    low = 1
    high = n
    while low <= high:
        mid = (low + high) // 2
        if (mid + 1) * mid / 2 == n:
            return mid
        elif (mid + 1) * mid / 2 < n:
            low = mid + 1
        else:
            high = mid - 1


# 牛顿迭代求解   (i + n/i)/2 <= n
def func3(x: int):
    return func(1, x)


def func(x: int, n: int):
    res = (x + (2*n-x)/x) / 2
    if res == x:
        return x
    else:
        return func(res, n)


print(func1(10))
print(func2(10))
print(func3(10))