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

PythonServer Side ProgrammingProgramming

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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