Hd7's blog

How to approach this DP problem.
By Hd7, history, 5 years ago, In English

Hi Codeforces Community, I have just solved this problem.
Link problems
Even though I solved it by myself, i still feel i'm missing anything, i feel uncomfortable.
The problem requires we find out k ranges (size = m) in the way that sum of all elements in every ranges is maximal. I came up with the ideal that:
$$$f(i,j)$$$ is the maximum sum of all elements in j range (size = m) when we have already gone to a[i]. So

$$$f(i,j) = max(f(i-1,j), f(i-m, j-1) + \sum_{x=i-m+1}^{i} a_x)$$$

The answer will be $$$f(n,k)$$$.
I still feel like i don't understand it absolutely. As usual, i try to form my DP problem to a graph and find the shortest (or longest) path depended on statement.
I want to ask the way you approach for a DP problem.
Thanks in advance, i am studying dynamic programming.

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5 years ago, # |
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I think the easiest way to understand dp problem is to imagine brute force solution. After that, u can see, which things happens many times (we calculate the same thing lots of times) (It calls "Recursion tree") Then, u can easy remember the value, which u got after first calculation (it calls "Memoisation") So solution is: write brute force solution + add memoisation -> PROFIT :)

what i am talking about: 59102892

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    5 years ago, # ^ |
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    Brute force for problems like that is not easy (for me). Thanks for your reply

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