740. Delete and Earn

Question

Given an array nums of integers, you can perform operations on the array.

In each operation, you pick any nums[i] and delete it to earn nums[i] points. After, you must delete every element equal to nums[i] - 1 or nums[i] + 1.

You start with 0 points. Return the maximum number of points you can earn by applying such operations.

Example 1:

Input: nums = [3, 4, 2]
Output: 6
Explanation:
Delete 4 to earn 4 points, consequently 3 is also deleted.
Then, delete 2 to earn 2 points. 6 total points are earned.



Example 2:

Input: nums = [2, 2, 3, 3, 3, 4]
Output: 9
Explanation:
Delete 3 to earn 3 points, deleting both 2's and the 4.
Then, delete 3 again to earn 3 points, and 3 again to earn 3 points.
9 total points are earned.

Note:

The length of nums is at most 20000.
Each element nums[i] is an integer in the range [1, 10000].

Solution

Method 1: dp

This question is related to 198. House Robber

When we take a value, we will take all of this value.

class Solution {
  public int deleteAndEarn(int[] nums) {
      int len = nums.length;
      if(len == 0) return 0;
      int max = 0;
      for(int num : nums){            
          max = Math.max(max, num);
      }
      int[] val = new int[max + 1];
      for(int num : nums)
          val[num]++;
      int[] dp = new int[max + 1];
      for(int i = 1; i < dp.length; i++){
          dp[i] = Math.max(dp[i - 1], (i > 1 ? dp[i - 2]: 0) + i * val[i]);
      }
      return dp[max];
  }
}