# Find minimum adjustment cost of an array in Python

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|

• 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[j] = abs(j - arr)
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