Delete and Earn.java

/*
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
*/
class Solution {
    private HashMap<Integer, Integer> points = new HashMap<>();
    private HashMap<Integer, Integer> cache = new HashMap<>();
    
    private int maxPoints(int num) {
        // Check for base cases
        if (num == 0) {
            return 0;
        }
        
        if (num == 1) {
            return points.getOrDefault(1, 0);
        }
        
        if (cache.containsKey(num)) {
            return cache.get(num);
        }
        
        // Apply recurrence relation
        int gain = points.getOrDefault(num, 0);
        cache.put(num, Math.max(maxPoints(num - 1), maxPoints(num - 2) + gain));
        return cache.get(num);
    }
    
    public int deleteAndEarn(int[] nums) {
        int maxNumber = 0;
        
        // Precompute how many points we gain from taking an element
        for (int num : nums) {
            points.put(num, points.getOrDefault(num, 0) + num);
            maxNumber = Math.max(maxNumber, num);
        }
        
        return maxPoints(maxNumber);
    }
}