Meta Tree DP question. This article demonstrates the application of Tree Dynamic Programming through the Employee Vacation Optimization problem. oavoservice helps you master advanced DP techniques.
📋 Problem Background
Company organization structure is a tree. Each employee has a vacation day requirement. Rule: If an employee takes a vacation, their direct subordinates cannot take a vacation. Goal: Maximize total vacation days.
🎯 Core Idea
This is a classic Tree DP problem, similar to "House Robber III".
Solution: Tree DP
class Employee:
def __init__(self, id, vacation_days):
self.id = id
self.vacation_days = vacation_days
self.subordinates = []
def max_vacation_days(root):
def dfs(node):
if not node:
return (0, 0)
# take: current employee takes vacation
# not_take: current employee does not take vacation
take = node.vacation_days
not_take = 0
for sub in node.subordinates:
sub_take, sub_not_take = dfs(sub)
# If current takes, sub cannot
take += sub_not_take
# If current doesn't take, sub can choose either
not_take += max(sub_take, sub_not_take)
return (take, not_take)
take, not_take = dfs(root)
return max(take, not_take)
Time Complexity: O(n) Space Complexity: O(h)
🚀 Extension: Multi-level Constraints
def max_vacation_with_constraints(root, max_consecutive):
# Implementation handling consecutive level constraints
pass
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Tree DP - State definition and transition Optimization - Memoization Extension Ability - Handling complex constraints
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