Find if neat arrangement of cups and shelves can be made in Python

Suppose we have three different types of cups in array p and saucers in array q and m number of shelves, we have to check whether a neat arrangement of cups and shelves can be made.

We can say that arrangement of the cups and saucers will be neat if it follows these conditions − 1. No shelf can hold both cups and saucers. 2. A self may contain at most 5 cups. 3. A self may contain at most 10 saucers.

So, if the input is like p = [4, 3, 7] q = [5, 9, 10] m = 11, then the output will be True as total number of cups = 14, 3 shelves are required, total saucers = 24, 3 shelves are required. So, total required shelves = 3 + 3 = 6, which is smaller than given number of shelves m.

To solve this, we will follow these steps −

• sum_p := 0, sum_q := 0

• for i in range 0 to size of p, do

  • sum_p := sum_p + p[i]

• for i in range 0 to size of q, do

  • sum_q := sum_q + q[i]

• m_p :=(sum_p + 4) / 5

• m_q :=(sum_q + 9) / 10

• if m_p + m_q <= m, then

  • return True

• otherwise,

  • return False

Example

Let us see the following implementation to get better understanding −

def is_valid(p, q, m):
   sum_p = 0
   sum_q = 0
   for i in range(0, len(p)):
      sum_p += p[i]
   for i in range(0,len(q)):
      sum_q += q[i]
   m_p = (sum_p + 5 - 1) / 5
   m_q = (sum_q + 10 - 1) / 10
   if(m_p + m_q <= m):
      return True
   else:
      return False
p = [4, 3, 7]
q = [5, 9, 10]
m = 11

print(is_valid(p ,q ,m))

Input

[4, 3, 7], [5, 9, 10], 11

Output

True