Hi Guys,
can anyone help me solve this problem using DP ? is that even possible ?
http://acm.timus.ru/problem.aspx?space=1&num=1005
So far only the brute force (generate all permutations) approach seems to be working.
Many thanks
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Use bit-masks. Take a integer number and look at its bits. If i-bit is 1, then we put stone i+1 in first pile, else in second pile. You need check all numbers between 0 and 2^N - 1 (all possible variants of ones).
It's not DP, but it's fast brut force O (N * 2^N). Also this task can be solved by time O (N * 2^(N/2)) with method meet-in-middle.
For dp solution you can use idea of Knapsack problem.
dp[i][j] = true iff using some of i first stones we can get the pile of weight j.
Look. Let f[i][j]=1 if using some of i first stones we can get the pile of weight j.
Then f[i][j]=f[i-1][j] | f[i-1][j-a[i]];
Exactly =) I forgot about it. But with 2 lines it'll work also, only 4 Mb(or 500 Kb) of 16 Mb.
Divide-and-conquer technique solves this problem in O(2^(N/2)*N)