Find minimum adjustment cost of an array in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array of positive numbers; we replace each element from that array array so that the difference between two adjacent elements in the array is either less than or equal to a given target. Now, we have to minimize the adjustment cost, so the sum of differences between new value and old value. More precisely, we minimize ∑|A[i] – Anew[i]| where i in range 0 to n-1, here n is denoted as size of A and Anew is the array with adjacent difference less than or equal to target.

So, if the input is like [56, 78, 53, 62, 40, 7, 26, 61, 50, 48], target = 20, then the output will be 25

To solve this, we will follow these steps −

  • n := size of arr

  • table := [[0 for i in range 0 to M + 1] for i in range 0 to n]

  • for j in range 0 to M + 1, do

    • table[0, j] := |j - arr[0]|

  • for i in range 1 to n, do

    • for j in range 0 to M + 1, do

      • table[i, j] := 100000000

      • for k in range maximum of (j-target and 0) and minimum of (M and j + target), do

        • table[i,j] = minimum of table[i,j], table[i - 1,k] + |arr[i] - j|

  • ans := 10000000

  • for j in range 0 to M + 1, do

    • ans = minimum of ans and table[n-1, j]

    • return ans

Example

Let us see the following implementation to get better understanding −

 Live Demo

M = 100
def get_min_cost(arr, target):
   n = len(arr)
   table = [[0 for i in range(M + 1)] for i in range(n)]
   for j in range(M + 1):
      table[0][j] = abs(j - arr[0])
   for i in range(1, n):
      for j in range(M + 1):
         table[i][j] = 100000000
         for k in range(max(j - target, 0), min(M, j + target) + 1):
            table[i][j] = min(table[i][j], table[i - 1][k] + abs(arr[i] - j))
   ans = 10000000
   for j in range(M + 1):
      ans = min(ans, table[n - 1][j])
   return ans
arr= [56, 78, 53, 62, 40, 7, 26, 61, 50, 48]
target = 20
print(get_min_cost(arr, target))

Input

[56, 78, 53, 62, 40, 7, 26, 61, 50, 48], 20

Output

35
raja
Published on 25-Aug-2020 11:30:34
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