制作砖块 Python

Question

I'm trying to solve this question:

We want to make a row of bricks that is goal inches long. We have a number of small bricks (1 inch each) and big bricks (5 inches each). Return True if it is possible to make the goal by choosing from the given bricks. This is a little harder than it looks and can be done without any loops.

 make_bricks(3, 1, 8) → True make_bricks(3, 1, 9) → False make_bricks(3, 2, 10) → True

— codingbat.com

For that, I made this code:

def make_bricks(small, big, goal):
      tam = small + big*5
      ex_gran = goal - small

      if goal <= small:
        return True
      elif ex_gran > big*5: 
        return False
      elif ex_gran <= big * 5 and (ex_gran % 5 <= small) :
        return True
      else:
        return False

And this is the result os the tests:

Expected    Run     
make_bricks(3, 1, 8) → True True    OK  
make_bricks(3, 1, 9) → False    False   OK  
make_bricks(3, 2, 10) → True    True    OK  
make_bricks(3, 2, 8) → True True    OK  
make_bricks(3, 2, 9) → False    True    X   
make_bricks(6, 1, 11) → True    True    OK  
make_bricks(6, 0, 11) → False   False   OK  
make_bricks(1, 4, 11) → True    True    OK  
make_bricks(0, 3, 10) → True    True    OK  
make_bricks(1, 4, 12) → False   True    X   
make_bricks(3, 1, 7) → True False   X   
make_bricks(1, 1, 7) → False    False   OK  
make_bricks(2, 1, 7) → True True    OK  
make_bricks(7, 1, 11) → True    True    OK  
make_bricks(7, 1, 8) → True True    OK  
make_bricks(7, 1, 13) → False   False   OK  
make_bricks(43, 1, 46) → True   True    OK  
make_bricks(40, 1, 46) → False  False   OK  
make_bricks(40, 2, 47) → True   True    OK  
make_bricks(40, 2, 50) → True   True    OK  
make_bricks(40, 2, 52) → False  False   OK  
make_bricks(22, 2, 33) → False  False   OK  
make_bricks(0, 2, 10) → True    True    OK  
make_bricks(1000000, 1000, 1000100) → True  True    OK  
make_bricks(2, 1000000, 100003) → False True    X   
make_bricks(20, 0, 19) → True   True    OK  
make_bricks(20, 0, 21) → False  False   OK  
make_bricks(20, 4, 51) → False  False   OK  
make_bricks(20, 4, 39) → True   True    OK  

Only 4 of them was wrong, but I still can't figure it out the error.

What is wrong?

Answer 1

Try first to use as many big bricks as possible, then complete with the small ones. Note that this works because the size of the big ones is a multiple of the size of the small ones, you would need another approach if the sizes were for example 2 and 5.

def make_bricks(small, big, goal):
    max_big = goal // 5  # max number of big we can use
    nb_big = min(big,  max_big)  # big ones we really use
    return small >= goal - 5 * nb_big  # True if we have enough small ones to complete

Answer 2

Error is simple:) it lies on line 16. Although the code could be shorten a lot.

First if all, notice that condition ex_gran <= big * 5 is irrelevant since the conditional before was already false ( elif ex_gran > big*5: ) and we are assuming small, big and goal are all integers, so you can take that away from the code. (Althogh this is not what is bringing troubles to the code, that's more of a style remark).

Trouble is generated by this conditional: (ex_gran % 5 <= small) .

As I understand, in the example make_bricks(1, 4, 12) your code returns True when it should return False . What happens is that the code checks whether (12 - 1) <= 4*5 which is True , and if (12 - 1) % 5 <= 1 which is also True and returns True in line 18 because of this.

Let's "fix" the code. Remember that from math we know there are integers m and r such that goal = 5*m + r (moreover r = goal % 5 ). After we know (goal-small) <= big*5 (from false evaluation in line 12) we have two cases:

Case 1: (goal - small) = big*5 , which implies goal = big*5 + small and so we should return True .

Case 2: (goal - small) < big*5 , then we know goal < big*5 + small . Here you should check whether (goal % 5) <= small . If this is false, then we can't arrange the bricks to obtain the goal length (since we don't have enough 1s to fill the residual, as in the example above). Otherwise, you should return True , since we have enough bricks to surpass the goal length and enough 1s to fill the residual.

Your code ends up looking like this (I took the liberty of renaming the variables):

def make_bricks(small_bricks, big_bricks, goal):

  if ( (5*big_bricks + small_bricks) < goal ):  #we can't reach the length

    return False

  elif  (small_bricks < (goal%5)) :   #we can surpass the length but we don't have 
                                      #enough 1s to fill goal's residual w.r.t. 5 div
    return False

  else:      #We can reach the length and have enough 1s to fill residual

    return True

notice I took away some case goal <= small as it's not needed here.

Answer 3

# This code works with those 3 tests but got some other one # wrong can some help fixed it?


def make_bricks(small, big, goal):
     big = big * 5
     if small == goal or big == goal:
          return true
      elif small + big == goal or big - small == goal:
            return True
      else:
           return False


print(make_bricks(3, 1, 8))  # → True
print(make_bricks(3, 1, 9))  # → False
print(make_bricks(3, 2, 10))  # → True

Answer 4

This should work...

def make_bricks(small, big, goal):
  total_bricks = (1 * small) + (5 * big)
  if total_bricks >= goal:
    if goal%5 == 0:
      if goal/5 <= goal:
        x = True
    elif goal%5 <= small:
        x = True
    else:
      x = False
  else:
    x = False
  return x

Answer 5

This is probably not the most efficient way but it will work.. Probably Not the most Readable

def make_bricks(small, big, goal):
  
  if (big is not 0 and (big*5+small*1 > goal) and goal % 5 <= small) or goal < small or big*5+small*1 == goal:
    return True
  else:
    return False

Answer 6

def make_bricks(small, big, goal):
    return small >= goal - 5*min(goal//5,big)