Problem Link:
https://www.codechef.com/problems/GRHARSH
I see all the solutions have 2D dp solution.
I was thinking dp[i] = max gold at the time i.
Is this correct?How to solve it using 1-D dp?
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Problem Link:
https://www.codechef.com/problems/GRHARSH
I see all the solutions have 2D dp solution.
I was thinking dp[i] = max gold at the time i.
Is this correct?How to solve it using 1-D dp?
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It's never why isn't it $$$1D$$$ dp. Dp only depends on the necessary information. Can you compress all the necessary information in $$$1$$$ dimension. If you can't think of any such value, it's probably not. The necessary information is the amount of gold you can earn if the subarray left is $$$l$$$ to $$$r$$$. The $$$l$$$ and $$$r$$$ values are probably the $$$2$$$ Dimensions, and it stores the maximum amount of gold you can get if you reach this state.
dp[i] = max gold at the time i.
Let's look at why this is an incomplete state.
The example test case is
1 2 3 4 5
. If you just want the max gold at time $$$1$$$, you would choose $$$5$$$. However that is not optimal because you need to wait until the last turn.i cannot see any recurrence relation that allows us to only use the maximum gold at time $$$i$$$.
I would choose the min value first so that jars which had greater initial value will get time to fill themselves ? So i would start with 1 then 2 then 3 and so on till 5.
Try :
$$$10^9,\ 1,\ 2,\ 3,\ 10^9-1,\ 10^9-1,\ 10^9-1$$$
Your approach is more like a greedy solution. If you want to check whether a greedy is correct, think of a test-case where your assumption is incorrect. Though while practicing, you should be able to prove it formally.