Mintoo's blog

Gradient And Hessian In Codechef CPOINT
By Mintoo, 10 years ago, In English

Can somebody explain this solution http://www.codechef.com/viewsolution/2949645 for this problem http://www.codechef.com/problems/CPOINT/.

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10 years ago, # |
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Newton's method in optimization http://en.wikipedia.org/wiki/Newton's_method_in_optimization http://en.wikipedia.org/wiki/Newton's_method_in_optimization

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10 years ago, # |
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The same problem was in ch24 qualifying round some years ago. There is another nice way to solve it using hill climbing optimization. You can start from the point (Xs = avg{Xi}, Ys = avg{Yi}) and then try to move in each of the 8 directions by some distance d = 1010 and see which point has the best result out of eight and then you repeat the move but with a smaller distnace d = d / 10. Once d reaches some convergence threshold, 1e - 9 for example, you can output the solution.

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10 years ago, # |
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I will give it a shot using 2D ternary search, though it is often hard to prove correctness in similar solutions... It is nice to see gradient and hessian applied in some algos :).

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    10 years ago, # ^ |
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    Yes, many have solved it using 2D ternary search. But ternary search took a lot of time compared to the gradient and hessian.

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