up

def bottom_up_cut_rod(n: int, prices: list):
    """
    Constructs a bottom-up dynamic programming solution for the rod-cutting problem

    Runtime: O(n^2)

    Arguments
    ----------
    n: int, the maximum length of the rod.
    prices: list, t  

def climb_stairs(n: int) -> int:
    """
    LeetCdoe No.70: Climbing Stairs
    Distinct ways to climb a n step staircase where
    each time you can either climb 1 or 2 steps.

    Args:
        n: number of steps of staircase

    Returns:
      

def count_up_to(self, limit):
    """Increments this variable until it reaches `limit`.

    When that Op is run it tries to increment the variable by `1`. If
    incrementing the variable would bring it above `limit` then the Op raises
    the excep