740. Delete and Earn

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740. Delete and Earn

题目描述

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.

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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.
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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

给定一个数组nums，可以执行如下操作：
在每次操作中，必须删除所有等于nums[i]- 1或nums[i]+ 1的元素，记录数组内剩余数字的总和
循环操作，求最大值。

解题思路

动态规划
dict[num]储存数字num的个数
maxNum表示数组内的最大值
dp表示删除不大于num的所有数字的最大值

代码

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func deleteAndEarn(_ nums: [Int]) -> Int {
    var dict = [Int: Int]()
    var maxNum = 0
    for num in nums {
        dict[num] = (dict[num] ?? 0) + 1
        maxNum = max(maxNum, num)
    }
    //为防止数组越界
    var dp = Array(repeating: 0, count: maxNum + 3)
    for num in 1...maxNum + 1 {
        dp[num] = max(dp[num - 1], (num > 2 ? dp[num - 2] : 0) + (dict[num] ?? 0) *
num)
    }
    return dp[maxNum]
}
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