740. Delete and Earn

MediumLeetCode

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 * 10^4
• 1 <= nums[i] <= 10^4

How to solve the problem

• Optimized Dynamic Programming

class Solution:
    def deleteAndEarn(self, nums: List[int]) -> int:
        sum = [0] * (max(nums) + 1) # Store the total value for each unique number
        for num in nums: 
            sum[num] += num  # Accumulate total value for each number

        def rob(nums):  # Standard House Robber DP solution
            f0 = f1 = 0
            for num in nums:
                f0, f1 = f1, max(f0 + num, f1)
            return f1

        return rob(sum) # Apply House Robber DP to the new array

Complexity

Time complexity: O(n) Space complexity: O(1)