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## Discussion of Problem 1183. Brackets Sequence

some hints
Posted by hliu20 18 May 2013 15:26
1. DP,  f[i][j] represents when solving the substring from index i to j the minimum brackets should add. Then we have
1) i <= j
2) if i == j, then f[i][j] = 1. (you can add a bracket to match the one)
3) if i < j, then f[i][j] = min(f[i][k], f[k+1][j])   i<=k<=(j-1)
4) that's not the end.... a case when s[i] == s[j], get f[i+1][j-1]. should compare this value to above values in (3), and get the maximum.
2. how to show the results
when calculate f[i][j], you can use an array like ans[i][j] to record the way to get f[i][j]. for example, when f[i][j] get maximum when k = k1. so you can record k1 to ans[i][j]. Or f[i+1][j-1] get the maximum , you can record -1 to ans[i][j], or in the case i==j you get the maximum, set ans[i][j] to 0......
Then you can get result by DFS.

hope it helps :)
Re: some hints
Posted by Dmitriy 12 Feb 2018 14:20
hliu20 wrote 18 May 2013 15:26
3) if i < j, then f[i][j] = min(f[i][k], f[k+1][j])   i<=k<=(j-1)

> f[i][j] = min(f[i][k], f[k+1][j]

You determine f(k) on f(k + 1) in main cycle. But f(k + 1) is undefine for a while.
It's a good hint, but something is wrong.
Re: some hints
Posted by imaginary friend 16 Oct 2018 03:54
actually it's correct. he is going by the increasing of the first parameter. it's like he is splitting the string, trying to get answer for a bigger string based on the smaller substrings