an even number of trees are left along one side of a country road you ve been assigned the job to plant these trees at an even interval on both sides of the road the length and width of the road are variable and a pair of trees must be planted at the beginning at 0 and at the end at length of the road only one tree can be moved at a time the goal is to calculate the lowest amount of distance that the trees have to be moved before they are all in a valid position returns the minimum distance that trees have to be moved before they are all in a valid state parameters tree listint a sorted list of integers with all trees position along the road length int an integer with the length of the road width int an integer with the width of the road returns a float number with the total distance trees have been moved returns the minimum distance that trees have to be moved before they are all in a valid state parameters tree list int a sorted list of integers with all trees position along the road length int an integer with the length of the road width int an integer with the width of the road returns a float number with the total distance trees have been moved
from math import sqrt

def planting_trees(trees, length, width):
    
    trees = [0] + trees

    n_pairs = int(len(trees)/2)

    space_between_pairs = length/(n_pairs-1)

    target_locations = [location*space_between_pairs for location in range(n_pairs)]

    cmatrix = [[0 for _ in range(n_pairs+1)] for _ in range(n_pairs+1)]
    for r_i in range(1, n_pairs+1):
        cmatrix[r_i][0] = cmatrix[r_i-1][0] + sqrt(
                width + abs(trees[r_i]-target_locations[r_i-1])**2)
    for l_i in range(1, n_pairs+1):
        cmatrix[0][l_i] = cmatrix[0][l_i-1] + abs(trees[l_i]-target_locations[l_i-1])

    for r_i in range(1, n_pairs+1):
        for l_i in range(1, n_pairs+1):
            cmatrix[r_i][l_i] = min(
                cmatrix[r_i-1][l_i] + sqrt(width + (trees[l_i + r_i]-target_locations[r_i-1])**2),
                cmatrix[r_i][l_i-1] + abs(trees[l_i + r_i]-target_locations[l_i-1])
            )

    return cmatrix[n_pairs][n_pairs]