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leetcode动态规划—打家劫舍系列

news 来源：原创 2025/6/1 10:50:00

lc198 打家劫舍

对于房屋i，考虑偷与不偷

偷i：dp[i-2] + nums[i]

不偷i ：dp[i-1]

class Solution:def rob(self, nums: List[int]) -> int:#dp[i]: 考虑编号【0-i】房间，偷取的最大金额为dp[i]#dp[i] = max(dp[i-1], dp[i-2]+nums[i])#求解dp[n-1]n = len(nums)if n < 2:return nums[0]dp = [0] * ndp[0] = nums[0]dp[1] = max(nums[0], nums[1])for i in range(2, n):dp[i] = max(dp[i-1], dp[i-2]+nums[i])return dp[n-1]

lc213 打家劫舍II

拆分为两种情况

考虑头，不考虑尾

考虑尾，不考虑头

class Solution:def rob(self, nums: List[int]) -> int:def rob1(nums):n = len(nums)if n < 2:return nums[0]dp = [0] * ndp[0] = nums[0]dp[1] = max(nums[0], nums[1])for i in range(2, n):dp[i] = max(dp[i-1], dp[i-2]+nums[i])return dp[n-1]n = len(nums)if n < 2:return nums[0]return max(rob1(nums[0:n-1]), rob1(nums[1:n]))

lc337 打家劫舍III

动态规划法

每层用一个dp数组来存储状态

层与层的状态转移依赖返回值决定，因此是后序遍历

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:def rob(self, root: Optional[TreeNode]) -> int:#dp[0] 不偷父节点得到的最大金额#dp[1] 偷父节点得到的最大金额def post_traversal(node):if not node:return (0, 0)dp_left = post_traversal(node.left)dp_right = post_traversal(node.right)#偷父节点, 不偷左右孩子val1 = node.val + dp_left[0] + dp_right[0]#不偷父节点，可考虑左右孩子val0 = max(dp_left[0], dp_left[1]) + max(dp_right[0], dp_right[1])return (val0, val1)return max(post_traversal(root)[0], post_traversal(root)[1])

记忆递归法

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:def rob(self, root: Optional[TreeNode]) -> int:used_map = {}def post_traversal(node):if not node:return 0if used_map.get(node) is not None:return used_map[node]#偷父节点 不考虑左右孩子val1 = node.valif node.left:val1 += post_traversal(node.left.left) + post_traversal(node.left.right)if node.right:val1 += post_traversal(node.right.left) + post_traversal(node.right.right)#不偷父节点, 考虑左右孩子val2 = post_traversal(node.left) + post_traversal(node.right)res = max(val1, val2)used_map[node] = resreturn resreturn post_traversal(root)