题目描述：

LeetCode 740. Delete and Earn

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].

题目大意：

给定整数数组nums，执行如下操作：

挑选任意数字nums[i]，得到nums[i]分，同时需要删除所有等于nums[i] - 1和nums[i] + 1的整数。

求最大得分。

解题思路：

动态规划（Dynamic Programming）

dp[x]表示删除不大于x的所有数字的最大得分。

cnt[x]存储数字x的个数。

状态转移方程：

dp[x] = max(dp[x - 1], dp[x - 2] + cnt[x] * x)

Python代码：

class Solution(object):
    def deleteAndEarn(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        cnt = collections.Counter(nums)
        maxn = max(nums + [0])
        dp = [0] * (maxn + 10)
        for x in range(1, maxn + 1):
            dp[x] = max(dp[x - 1], dp[x - 2] + cnt[x] * x)
        return dp[maxn]

 

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