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Topic: online subset sum (Read 1840 times) |
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inexorable
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online subset sum
« on: May 13th, 2011, 1:32pm » |
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You have to maintain a set of numbers, starting with an empty set.
A stream of numbers come along with an operation request. The request could be
1)Add(n) - add the number n to the set
2)Remove(n) - remove the number n if already present in set.
3)int FindSum(n) - find the sum of all the numbers in the set that are less than n.
what would be the ideal data structure to support the above operations with optimal time and space complexity?
can we prove lower bound for the data structure that supports above operations?
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Grimbal
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Re: online subset sum
« Reply #1 on: May 14th, 2011, 8:35am » |
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A binary search tree with the sub-tree total stored at each node would be perfect for that. If you balance the tree it should take O(log n) average time for all operations.
[oops, silly mistake fixed]
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| « Last Edit: May 18th, 2011, 1:36am by Grimbal » |
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inexorable
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Re: online subset sum
« Reply #2 on: May 14th, 2011, 10:27pm » |
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If it was to be implemented without writing 'redblack' trees or 'avltrees' from scratch for a balanced binary search tree.
would it be possible using c++ stl, boost ?
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spicy
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Re: online subset sum
« Reply #3 on: May 15th, 2011, 5:55am » |
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By using hash and array we can do
insert and delete in O(1) and findsum(n) in O(N)
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mmgc
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Re: online subset sum
« Reply #4 on: May 16th, 2011, 3:31am » |
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on May 14th, 2011, 8:35am, Grimbal wrote:A binary search tree with the sub-tree total stored at each node would be perfect for that. If you balance the tree it should take O(n log n) average time for all operations.
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How about just maintaining the sum ( of all numbers less than the node ) at each node in BST. time complexity - O(lg n )
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towr
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Re: online subset sum
« Reply #5 on: May 16th, 2011, 8:40am » |
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on May 16th, 2011, 3:31am, mmgc wrote:| How about just maintaining the sum ( of all numbers less than the node ) at each node in BST. time complexity - O(lg n ) |
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Then you'd need to update all nodes if you add a number that is less than all numbers already in the set. So updates wouldn't be O(log n) as they are in Grimbal's case.
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blackJack
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Re: online subset sum
« Reply #6 on: May 17th, 2011, 3:22am » |
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on May 14th, 2011, 8:35am, Grimbal wrote:A binary search tree with the sub-tree total stored at each node would be perfect for that. If you balance the tree it should take O(n log n) average time for all operations.
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O(n log n) time will be the avg time for one operation? If i am not wrong, for a balanced bst, insert , remove will take O(log n) time and findSum(n) will have to traverse the tree for nodes less than n, so O(n) time. How O(n log n) is arrived?
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Grimbal
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Re: online subset sum
« Reply #7 on: May 18th, 2011, 1:39am » |
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Oops, I meant O(log n). My finger sometime type ahead of what I mean.
And I said "on average" because I wasn't sure whether the balancing of the tree can occasionally take more than O(log n), but I guess it shouldn't.
If the sum of a node and all children is stored at each node, you should be able to return the partial sum in O(log n).
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| « Last Edit: May 18th, 2011, 1:40am by Grimbal » |
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