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            Uriel's Corner

            Research Associate @ Harvard University / Research Interests: Computer Vision, Biomedical Image Analysis, Machine Learning
            posts - 0, comments - 50, trackbacks - 0, articles - 594
            Given the age and score of each players. Selected some of them to obtain the maximum total score and make sure that all the selected players with a younger age do not have a higher score than older ones (could be the same score).

            Two ways to do DP
            Approach 1: zip the age and score of each player, sort by score, then go through all the players' age and sco, update dp matrix as:
            dp[age] = max(dp[:age+1]) + sco
            return max(dp)

            Approach 2: zip the age and score of each player, sort by age, then go through all the players i, update dp matrix as:
            dp[i] = max(dp[i], dp[j] + scores_sorted_by_age[i][1]), while j < i and scores_sorted_by_age[j][1] <= scores_sorted_by_age[i][1]:
            return max(dp)

            - Time complexity:
            Both methods are O(n^2)
            - Space complexity:
            Both methods are O(n)


            Approach 1:

             1 #1626
             2 #Runtime: 285 ms (Beats 100%)
             3 #Memory 13.8 MB (Beats 80%)
             4 
             5 class Solution(object):
             6     def bestTeamScore(self, scores, ages):
             7         """
             8         :type scores: List[int]
             9         :type ages: List[int]
            10         :rtype: int
            11         """
            12         dp = [0] * (max(ages) + 1)
            13         scores_sorted_by_scores = sorted(zip(scores, ages))
            14         for sco, age in scores_sorted_by_scores:
            15             dp[age] = max(dp[:age+1]) + sco
            16         return max(dp)


            Approach 2:

             1 #1626
             2 #Runtime: 1532 ms (Beats 55%)
             3 #Memory: 13.9 MB (Beats 65%)
             4 
             5 class Solution(object):
             6     def bestTeamScore(self, scores, ages):
             7         """
             8         :type scores: List[int]
             9         :type ages: List[int]
            10         :rtype: int
            11         """
            12         dp = [0] * len(ages)
            13         scores_sorted_by_age = sorted(zip(ages, scores))
            14         for i in range(len(ages)):
            15             dp[i] = scores_sorted_by_age[i][1]
            16             for j in range(i):
            17                 if scores_sorted_by_age[j][1] <= scores_sorted_by_age[i][1]:
            18                     dp[i] = max(dp[i], dp[j] + scores_sorted_by_age[i][1])
            19         return max(dp)
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