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删除并获得点数

Delete and Earn

专题
Algorithmic Programming / 算法编程
难度
L3
来源
Citadel

题目详情

问题:删除并获得点数

考察:动态规划、数组

来源:Citadel

链接:https://www.jointaro.com/interviews/questions/delete-and-earn/

You are given an integer array nums. You want to maximize the number of points you get by performing the following operation any number of times:

  • Pick any nums[i] and delete it to earn nums[i] points. Afterwards, you must delete every element equal to nums[i] - 1 and every element equal to nums[i] + 1.

Return the maximum number of points you can earn by applying the above operation some number of times.

 

Example 1:

Input: nums = [3,4,2]
Output: 6
Explanation: You can perform the following operations:
- Delete 4 to earn 4 points. Consequently, 3 is also deleted. nums = [2].
- Delete 2 to earn 2 points. nums = [].
You earn a total of 6 points.

Example 2:

Input: nums = [2,2,3,3,3,4]
Output: 9
Explanation: You can perform the following operations:
- Delete a 3 to earn 3 points. All 2's and 4's are also deleted. nums = [3,3].
- Delete a 3 again to earn 3 points. nums = [3].
- Delete a 3 once more to earn 3 points. nums = [].
You earn a total of 9 points.

 

Constraints:

  • 1 <= nums.length <= 2 * 104
  • 1 <= nums[i] <= 104
解析

思路:把相同数字的贡献合并成 points[x] = x * count[x]。选择 x 就不能选择 x-1 和 x+1,问题转化为 House Robber,在数值轴上做动态规划。

复杂度:设最大值为 M,时间 O(n+M),空间可 O(M) 或排序后 O(u)。