What is the main approach to solving the Best Team With No Conflicts problem?

The problem is solved using dynamic programming. First, sort the players by age and score, then use dynamic programming to find the maximum score by considering each player in order.

How do I avoid conflicts between players when selecting a team?

To avoid conflicts, sort players by age, and if two players have the same age, sort them by their score. Then, use dynamic programming to ensure the team selection adheres to the no-conflict rule.

What are the time and space complexities of the solution?

The time complexity is O(n^2), where n is the number of players, due to the nested loops in dynamic programming. The space complexity is O(n) due to the dp array.

Can the problem be solved with a greedy approach?

A greedy approach is not optimal for this problem, as it may miss the best combination of players. Dynamic programming ensures the optimal solution is found.

What edge cases should I consider when solving this problem?

Consider edge cases like all players having the same age or score, or when no valid team can be formed due to conflicts between all players.

#1626

Medium

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

无矛盾的最佳球队

假设你是球队的经理。对于即将到来的锦标赛，你想组合一支总体得分最高的球队。球队的得分是球队中所有球员的分数总和。然而，球队中的矛盾会限制球员的发挥，所以必须选出一支没有矛盾的球队。如果一名年龄较小球员的分数严格大于一名年龄较大的球员，则存在矛盾。同龄球员之间不会发生矛盾。给你两个列表…

数组动态规划排序

题目描述

假设你是球队的经理。对于即将到来的锦标赛，你想组合一支总体得分最高的球队。球队的得分是球队中所有球员的分数总和。

然而，球队中的矛盾会限制球员的发挥，所以必须选出一支 没有矛盾 的球队。如果一名年龄较小球员的分数 严格大于 一名年龄较大的球员，则存在矛盾。同龄球员之间不会发生矛盾。

给你两个列表 scores 和 ages，其中每组 scores[i] 和 ages[i] 表示第 i 名球员的分数和年龄。请你返回 所有可能的无矛盾球队中得分最高那支的分数 。

示例 1：

输入：scores = [1,3,5,10,15], ages = [1,2,3,4,5]
输出：34
解释：你可以选中所有球员。

示例 2：

输入：scores = [4,5,6,5], ages = [2,1,2,1]
输出：16
解释：最佳的选择是后 3 名球员。注意，你可以选中多个同龄球员。

示例 3：

输入：scores = [1,2,3,5], ages = [8,9,10,1]
输出：6
解释：最佳的选择是前 3 名球员。

提示：

1 <= scores.length, ages.length <= 1000
scores.length == ages.length
1 <= scores[i] <= 10⁶
1 <= ages[i] <= 1000

lightbulb

解题思路

方法一：排序 + 动态规划

我们可以将球员按照分数从小到大排序，如果分数相同，则按照年龄从小到大排序。

接下来，使用动态规划求解。

我们定义 $f[i]$ 表示以排序后的第 $i$ 个球员作为最后一个球员的最大得分，那么答案就是 $\max_{0 \leq i < n} f[i]$ 。

对于 $f[i]$ ，我们可以枚举 $0 \leq j \lt i$ ，如果第 $i$ 个球员的年龄大于等于第 $j$ 个球员的年龄，则 $f[i]$ 可以从 $f[j]$ 转移而来，转移方程为 $f[i] = \max(f[i], f[j])$ 。然后我们将第 $i$ 个球员的分数加到 $f[i]$ 中，即 $f[i] += scores[i]$ 。

最后，我们返回 $\max_{0 \leq i < n} f[i]$ 即可。

时间复杂度 $O(n^2)$ ，空间复杂度 $O(n)$ 。其中 $n$ 为球员的数量。

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class Solution:
    def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
        arr = sorted(zip(scores, ages))
        n = len(arr)
        f = [0] * n
        for i, (score, age) in enumerate(arr):
            for j in range(i):
                if age >= arr[j][1]:
                    f[i] = max(f[i], f[j])
            f[i] += score
        return max(f)

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Assess if the candidate recognizes the need to sort players to avoid conflicts.
question_mark
Check if the candidate can explain dynamic programming in the context of maximizing the score.
question_mark
Evaluate how the candidate handles edge cases, such as when all players are of the same age or score.

warning

常见陷阱

外企场景

error
Forgetting to sort the players correctly, which could lead to conflicts and incorrect results.
error
Using a greedy approach instead of dynamic programming, missing the optimal team combination.
error
Not considering edge cases like players of the same age or when no valid team can be formed.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Consider additional constraints where the number of players is limited or when there is an upper bound on the team size.
arrow_right_alt
Change the problem to allow conflicts if the difference in scores is small.
arrow_right_alt
Introduce other constraints, such as a fixed number of players that must be selected.

help

常见问题

外企场景

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