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 thesumof scores of all the players in the team. However, the basketball team is not allowed to haveconflicts. Aconflictexists if a younger player has astrictly higherscore than an older player. A conflict doesnotoccur 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`

player, respectively, return^{th}the highest overall score of all possible basketball teams.

## Logic

If we sort the input first, then we can apply dynamic programming to solve this problem with O(n^2) time complexity.

Define `dp[i]`

as the largest score if the `player[i]`

is selected. Therefore we have:

dp[i]=max(dp[j]+score[i]) for j in [0...i] if score[j]<=score[i]

## Code

class Solution: def bestTeamScore(self, scores: List[int], ages: List[int]) -> int: players = sorted(zip(ages,scores)) dp = [score for age,score in players] for i in range(1,len(players)): for j in range(i): if players[j][1] <= players[i][1]: dp[i] = max(dp[i],dp[j]+players[i][1]) return max(dp)