leetcode练习 Delete and Earn
2018-01-07 22:02
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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:
Example 2:
Note:
The length of nums is at most 20000.
Each element nums[i] is an integer in the range [1, 10000].
又是一道动态规划的题目,这次是凭着感觉写的,试了试,居然过了,原理想的并不是很明白,相信日后一定能研究透动态规划。
只有个大概的感觉:
我发现选中一个数时必然会把这个数出现的所有次数计算到后,就把每个数的代价统一计算,保存到数组values,如果原数组没有涉及到这个数,就记为0。
设了个专门用来动态规划的dp(其实是因为知道在动态规划的分类下的题目才故意这么做)
初始状态:dp[1]=values[1],只能取1了。dp[2]为values[1],values[2]的较大值。
状态转移:dp[i] = max(dp[i-1],dp[i-2]+values[i])
该决定这个数取还是不取的时候,如果不取这个数(选择dp[i-1],因为选择dp[i-1]的时候是必然不会取到values[i]的)那么就选dp[i-1],如果取这个数,当前值就会变成dp[i-2]+values[i],因为values[i-1]是一定不会取到的,至于i+1如何处理,我也说不清楚。基本是凭感觉在写。
其实换个思路,题目的意思也就是,给出你一串从1~10000的数的价值,让你在这些数里面选出价值最大的组合。条件是相邻的数不能同时选。这样看来的话,算法感觉稍微能理解了一丢丢。。。。。。为了利益最大化,不相邻的能选就要选,所以选dp[i-2]?感觉还是有点不对头,但总归有了那么点感觉,还是需要勤加练习才行。
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].
又是一道动态规划的题目,这次是凭着感觉写的,试了试,居然过了,原理想的并不是很明白,相信日后一定能研究透动态规划。
class Solution { public: int deleteAndEarn(vector<int>& nums) { sort(nums.begin(), nums.end()); vector<int> values(10001, 0); for(int i = 0; i < nums.size(); i++) { values[nums[i]] += nums[i]; } vector<int> dp(10001, 0); dp[1] = values[1]; dp[2] = max(values[1], values[2]); for (int i = 3; i < 10001; i++) { dp[i] = max(dp[i-1], dp[i-2]+values[i]); } return dp[10000]; } };
只有个大概的感觉:
我发现选中一个数时必然会把这个数出现的所有次数计算到后,就把每个数的代价统一计算,保存到数组values,如果原数组没有涉及到这个数,就记为0。
设了个专门用来动态规划的dp(其实是因为知道在动态规划的分类下的题目才故意这么做)
初始状态:dp[1]=values[1],只能取1了。dp[2]为values[1],values[2]的较大值。
状态转移:dp[i] = max(dp[i-1],dp[i-2]+values[i])
该决定这个数取还是不取的时候,如果不取这个数(选择dp[i-1],因为选择dp[i-1]的时候是必然不会取到values[i]的)那么就选dp[i-1],如果取这个数,当前值就会变成dp[i-2]+values[i],因为values[i-1]是一定不会取到的,至于i+1如何处理,我也说不清楚。基本是凭感觉在写。
其实换个思路,题目的意思也就是,给出你一串从1~10000的数的价值,让你在这些数里面选出价值最大的组合。条件是相邻的数不能同时选。这样看来的话,算法感觉稍微能理解了一丢丢。。。。。。为了利益最大化,不相邻的能选就要选,所以选dp[i-2]?感觉还是有点不对头,但总归有了那么点感觉,还是需要勤加练习才行。
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