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

Python Server Side Programming Programming

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

Arnab Chakraborty

Updated on: 2021-10-06T07:50:51+05:30

1K+ Views

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