solve House Robber

Author: saubhik

problems/house_robber.py

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+from typing import List
+
+
+class Solution:
+    # Dynamic Programming Take 1
+    #
+    # Time: O(n)
+    # Space: O(1)
+    #
+    # The sub problem at index i is:
+    # What is the maximum amount that I can rob if we consider only the numbers from
+    # index 0 to index i.
+    #
+    # It is the maximum of:
+    # 1. maximum amount that I can rob if I consider numbers from index 0 to
+    #    index i-1. Call it prev_max.
+    # 2. maximum amount that I can rob if I consider numbers from index 0 to
+    #    index i-2 + the number at index i. Call it curr_max.
+    def rob(self, nums: List[int]) -> int:
+        curr_max = prev_max = 0
+        for num in nums:
+            curr_max, prev_max = max(prev_max + num, curr_max), curr_max
+        return curr_max
+
+
+class SolutionTwo:
+    # Dynamic Programming Take 2
+    #
+    # Time: O(n)
+    # Space: O(1)
+    #
+    # I often tend to think of DP sub problem as: What is the answer to the
+    # optimization objective for some intermediate index i, and including the index i.
+    #
+    # Note that difference above is that we might not include index i.
+    #
+    # Then the answer to the global optimization problem is the maximum of the
+    # optimized answers to these sub problems as we iterate over all possible index i.
+    #
+    # Maximum amount I can rob including house at index i is the maximum of:
+    # 1. Maximum amount I can rob including house at index i-2 + nums[i].
+    # 2. Maximum amount I can rob including house at index i-3 + nums[i].
+    #
+    # So, we need to keep 3 DP state variables.
+    # Call them:
+    # ls = last sum
+    # lls = second last sum
+    # llls = third last sum
+    def rob(self, nums: List[int]) -> int:
+        ls = lls = llls = ans = 0
+        for i in range(len(nums)):
+            ls, lls, llls = max(lls + nums[i], llls + nums[i]), ls, lls
+            ans = max(ans, ls)
+        return ans

tests/test_house_robber.py

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+import unittest
+
+from house_robber import Solution, SolutionTwo
+
+
+class TestHouseRobber(unittest.TestCase):
+    def test_example_1(self):
+        assert Solution().rob(nums=[1, 2, 3, 1]) == 4
+        assert SolutionTwo().rob(nums=[1, 2, 3, 1]) == 4
+
+    def test_example_2(self):
+        assert Solution().rob(nums=[2, 7, 9, 3, 1]) == 12
+        assert SolutionTwo().rob(nums=[2, 7, 9, 3, 1]) == 12
+
+    def test_example_3(self):
+        assert Solution().rob(nums=[2, 1, 1, 2]) == 4
+        assert SolutionTwo().rob(nums=[2, 1, 1, 2]) == 4