Fix keon#768

Author: cawibo

algorithms/dp/__init__.py

@@ -20,3 +20,4 @@
 from .word_break import *
 from .int_divide import *
 from .k_factor import *
+from .planting_trees import *

algorithms/dp/planting_trees.py

@@ -0,0 +1,45 @@
+"""
+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 L and width W of the road
+are variable, and a pair of trees must be planted at the beginning (at 0) and at the end (at L) 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.
+"""
+
+from math import sqrt
+import sys
+
+def planting_trees(trees, L, W):
+    """
+    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.
+            L (int): An integer with the length of the road.
+            W (int): An integer with the width of the road.
+
+        Returns:
+            A float number with the total distance trees have been moved.
+    """
+    trees = [0] + trees
+
+    n_pairs = int(len(trees)/2)
+
+    space_between_pairs = L/(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 ri in range(1, n_pairs+1):
+        cmatrix[ri][0] = cmatrix[ri-1][0] + sqrt(W + abs(trees[ri]-target_locations[ri-1])**2)
+    for li in range(1, n_pairs+1):
+        cmatrix[0][li] = cmatrix[0][li-1] + abs(trees[li]-target_locations[li-1])
+
+    for ri in range(1, n_pairs+1):
+        for li in range(1, n_pairs+1):
+            cmatrix[ri][li] = min(
+                cmatrix[ri-1][li] + sqrt(W + (trees[li + ri]-target_locations[ri-1])**2),
+                cmatrix[ri][li-1] + abs(trees[li + ri]-target_locations[li-1])
+            )
+
+    return cmatrix[n_pairs][n_pairs]

tests/test_dp.py

@@ -13,7 +13,8 @@
     longest_increasing_subsequence,
     longest_increasing_subsequence_optimized,
     longest_increasing_subsequence_optimized2,
-    int_divide,find_k_factor
+    int_divide,find_k_factor,
+    planting_trees
 )
 
 
@@ -182,6 +183,32 @@ def test_kfactor(self):
         k5=1
         self.assertEqual(find_k_factor(n5,k5),71284044)
 
+class TestPlantingTrees(unittest.TestCase):
+    def test_simple(self):
+        # arrange
+        trees = [0, 1, 10, 10]
+        L = 10
+        W = 1
+
+        # act
+        res = planting_trees(trees, L, W)
+
+        print(res)
+        # assert
+        self.assertEqual(res, 2.414213562373095)
+
+    def test_simple2(self):
+        # arrange
+        trees = [0, 3, 5, 5, 6, 9]
+        L = 10
+        W = 1
+
+        # act
+        res = planting_trees(trees, L, W)
+
+        print(res)
+        # assert
+        self.assertEqual(res, 9.28538328578604)
 
 if __name__ == '__main__':
     unittest.main()