HackMD
1626.Best Team With No Conflicts
tags: Medium,Array,DP,Sorting
1626. Best Team With No Conflicts
題目描述
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 ith player, respectively, return the highest overall score of all possible basketball teams.
範例
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 people 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]<= 106 - 1 <=
ages[i]<= 1000
解答
Python
class Solution:
def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
Q = sorted( zip(ages,scores), key = lambda x: x[0]*10000000+x[1])
dp = [ (0, 0)] # (max_score, total_score)
#print(Q)
for age, sc in Q:
cur_max_score = -1
for max_score, total_score in dp:
if sc >= max_score:
if total_score + sc > cur_max_score:
cur_max_score = total_score + sc
else:
break
dp.append( (sc, cur_max_score) )
dp = sorted(dp, key=lambda x: x[0]*1000000 + x[1] )
#print(dp)
return max( [ x[1] for x in dp])
思路:
dp題，首先把球員按照 年紀，同年紀按照得分能力 由低到高排序
DP陣列存的是(max_score,max_total)。
其意義是在已看過的球員中，若得分能力最高為max_score, 則最大總分為max_total
接著由年紀小球員的開始看，對每個球員檢查他的分數是否小於 dp中每個項目的max_score，若是則考慮更新dp陣列。
維護DP陣列 直到看過所有球員
玉山
