删除并获得点数
Delete and Earn
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 earnnums[i]points. Afterwards, you must delete every element equal tonums[i] - 1and every element equal tonums[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 * 1041 <= 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)。