Program to find minimum total distance between house and nearest mailbox in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array called houses and have another value k. Here houses[i] represents the location of the ith house along a street, we have to allocate k mailboxes in the street, and find the minimum total distance between each house and its nearest mailbox.

So, if the input is like houses = [6,7,9,16,22] k = 2, then the output will be 9 because if we place mailbox at 7 and 18, then minimum total distance from each house is |6-7|+|7-7|+|9-7|+|16- 18|+|22-18| = 1+0+2+2+4 = 9.

To solve this, we will follow these steps −

  • sort the list houses

  • Define a function util() . This will take idx, n, k

  • if k is same as 1, then

    • core := houses[quotient of (n + idx)/2]

    • return sum of all elements of [|houses[i] - core| for each i in range idx to n])

  • result := infinity

  • for i in range idx to n, do

    • if n - i < k - 1, then

      • come out from the loop

    • result := minimum of result and util(idx, i, 1) + util(i+1, n, k - 1)

  • return result

  • From the main method do the following:

  • return util(0, size of houses - 1, k)

Example

Let us see the following implementation to get better understanding

def solve(houses, k):
   houses.sort()
   def util(idx, n, k):
      if k == 1:
         core = houses[(n + idx) // 2]
         return sum([abs(houses[i] - core) for i in range(idx, n + 1)])
      result = float('inf')
      for i in range(idx, n + 1):
         if n - i < k - 1:
            break
         result = min(result, util(idx, i, 1) + util(i+1, n, k - 1))
      return result
   return util(0, len(houses) - 1, k)

houses = [6,7,9,16,22]
k = 2
print(solve(houses, k))

Input

[6,7,9,16,22], 2

Output

9
raja
Published on 06-Oct-2021 07:50:51
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