# Delete And Earn Problem

## Description

LeetCode Problem 740.

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:

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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:

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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

## Sample C++ Code

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class Solution {
public:
int deleteAndEarn(vector<int>& nums) {
int n = 10001;
//take the total sum by each number
vector<int> sum(n, 0);
vector<int> dp(n, 0);
for (auto num: nums) {
sum[num] += num;
}
dp[0] = 0;
dp[1] = sum[1];
//now apply the house robbing concept
for (int i = 2; i < n; i++) {
dp[i] = max(dp[i-2] + sum[i], dp[i-1]);
}
return dp[n-1];
}
};