Meta 动态规划面试：员工休假优化问题

Meta 面试中的树形 DP 题目。本文通过员工休假优化问题，展示树形动态规划的应用csvosupport* 助你掌握高级 DP 技巧

📋 问题背景

公司组织结构是一棵树，每个员工有休假天数需求。规则：

• 如果员工休假，其直接下属不能休假
• 求最大总休假天

🎯 核心思路

这是经典的树DP 问题，类打家劫舍 III"

解法：树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: 当前员工休假
        # not_take: 当前员工不休
        take = node.vacation_days
        not_take = 0
        
        for sub in node.subordinates:
            sub_take, sub_not_take = dfs(sub)
            
            # 如果当前员工休假，下属不能休
            take += sub_not_take
            
            # 如果当前员工不休假，下属可选择休或不休
            not_take += max(sub_take, sub_not_take)
        
        return (take, not_take)
    
    take, not_take = dfs(root)
    return max(take, not_take)

时间复杂度： O(n) 空间复杂度： O(h)

🚀 扩展：多层限

def max_vacation_with_constraints(root, max_consecutive):
    def dfs(node, parent_took, consecutive_count):
        if not node:
            return 0
        
        # 选择1：当前员工休
        take = 0
        if not parent_took and consecutive_count < max_consecutive:
            take = node.vacation_days
            for sub in node.subordinates:
                take += dfs(sub, True, consecutive_count + 1)
        
        # 选择2：当前员工不休假
        not_take = 0
        for sub in node.subordinates:
            not_take += dfs(sub, False, 0)
        
        return max(take, not_take)
    
    return dfs(root, False, 0)

💼 csvosupport 助力

树形 DP - 状态定义和转移 *优化技 - 记忆化搜 扩展能力 - 处理复杂约束

联系 csvosupport，专DP 面试辅助

*标签 #Meta #动态规#树形DP #VO辅助 #面试辅助 #一亩三分地

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