Solve Two Robbery Optimization Variants

Part 1: The Linear Warehouse

You are tasked with scheduling security patrols in a warehouse consisting of a line of n storage units, where each unit i has a value v[i]. Due to security regulations, you cannot monitor two adjacent storage units. Given an array v of non-negative integers, find the maximum total value you can secure.

Example

v = [2, 7, 9, 3, 1] Result: 12 (Select units 0, 2, and 4: 2 + 9 + 1 = 12)

Part 2: The Hierarchical Warehouse

Now consider a warehouse structured like a binary tree, where each node is a storage unit. If you monitor a unit, you cannot monitor its direct parent or its children. Given the root of the tree, calculate the maximum total value you can secure.

Function Signature

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def max_value_linear(v: List[int]) -> int:
    pass

def max_value_tree(root: TreeNode) -> int:
    pass

Constraints

• For linear: 1 <= len(v) <= 10^5
• For tree: Number of nodes is between 1 and 10^4
• Values v[i] are between 0 and 10^4

Edge Cases

• Empty lists or trees.
• Linear arrays with 1 or 2 elements.
• Skewed trees (essentially a linked list).