Problem Statement
Best Team With No Conflicts
You are the manager of a basketball team. For the upcoming tournament, you want to choose the team with the highest overall score. The score of the team is the sum of scores of all the players in the team.
However, the basketball team is not allowed to have conflicts. A conflict exists if a younger player has a strictly higher score than an older player. A conflict does not occur between players of the same age.
Given two lists, scores and ages, where each scores[i] and ages[i] represents the score and age of the i-th player, respectively, return the highest overall score of all possible basketball teams.
Examples
Example 1:
Input: scores = [1, 3, 5, 10, 15], ages = [1, 2, 3, 4, 5]
Output: 34
Explanation: You can choose all the players.
Example 2:
Input: scores = [4, 5, 6, 5], ages = [2, 1, 2, 1]
Output: 16
Explanation: It is best to choose the last 3 players. Notice that you are allowed to choose multiple players of the same age.
Example 3:
Input: scores = [1, 2, 3, 5], ages = [8, 9, 10, 1]
Output: 6
Explanation: It is best to choose the first 3 players.
Constraints
- 1 <= scores.length, ages.length <= 1000
- scores.length == ages.length
- 1 <= scores[i] <= 10^6
- 1 <= ages[i] <= 1000
Problem Breakdown
To solve this problem, we need to:
- This problem can be solved using dynamic programming.
- We need to sort the players by age (and by score if ages are equal) to ensure that we only consider valid teams.
- After sorting, we can use a variation of the Longest Increasing Subsequence (LIS) algorithm, but instead of finding the longest subsequence, we find the subsequence with the maximum sum.
- For each player, we have two options: include them in the team or exclude them.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Best Team With No Conflicts
You are the manager of a basketball team. For the upcoming tournament, you want to choose the team with the highest overall score. The score of the team is the sum of scores of all the players in the team.
However, the basketball team is not allowed to have conflicts. A conflict exists if a younger player has a strictly higher score than an older player. A conflict does not occur between players of the same age.
Given two lists, scores and ages, where each scores[i] and ages[i] represents the score and age of the i-th player, respectively, return the highest overall score of all possible basketball teams.
Examples
Example 1:
You can choose all the players.
Example 2:
It is best to choose the last 3 players. Notice that you are allowed to choose multiple players of the same age.
Example 3:
It is best to choose the first 3 players.
Problem Breakdown
Constraints:
- 1 <= scores.length, ages.length <= 1000
- scores.length == ages.length
- 1 <= scores[i] <= 10^6
- 1 <= ages[i] <= 1000
Key Insights:
This problem can be solved using dynamic programming.
We need to sort the players by age (and by score if ages are equal) to ensure that we only consider valid teams.
After sorting, we can use a variation of the Longest Increasing Subsequence (LIS) algorithm, but instead of finding the longest subsequence, we find the subsequence with the maximum sum.
For each player, we have two options: include them in the team or exclude them.
Real-World Application
This problem has several practical applications:
Team Selection
Selecting the optimal team for a sports competition based on player attributes and constraints.
Resource Allocation
Allocating resources to maximize output while respecting hierarchical constraints.
Tournament Planning
Planning tournaments with participants of different skill levels and age groups.