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Topic: Array Problem (x-y=z for x,y in sorted array) (Read 4032 times) |
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witee
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Array Problem (x-y=z for x,y in sorted array)
« on: Jul 13th, 2010, 6:35am » |
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Given a sorted array and a constant z, find two numbers x and y, if exist, s.t. x-y = z
give the optimized solution? 
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| « Last Edit: Jul 18th, 2010, 2:16pm by Grimbal » |
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pex
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Re: Array Problem
« Reply #1 on: Jul 13th, 2010, 6:50am » |
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on Jul 13th, 2010, 6:35am, witee wrote:Given a sorted array and a constant z, find two numbers x and y, if exist, s.t. x-y = z
give the optimized solution? |
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There is a trivial O(n) algorithm:
| hidden: | - start with i=0, j=0
- at every iteration:
- compute d = a[j]-a[i]
- if d = z: done
- if d > z: i++
- if d < z: j++
- terminate when an index runs out of bounds |
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nakli
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Re: Array Problem
« Reply #2 on: Jul 13th, 2010, 8:10am » |
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This neatly finds one such pair(x,y).
How fast can we find all such existing pairs?
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towr
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Re: Array Problem
« Reply #3 on: Jul 13th, 2010, 2:56pm » |
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You can find the rest by continuing in the same way. Same time complexity.
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Grimbal
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Re: Array Problem
« Reply #4 on: Jul 15th, 2010, 3:02pm » |
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Yep. Whenever you find a solution, print it and advance both i and j to the next higher value in the array.
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pex
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Re: Array Problem
« Reply #5 on: Jul 17th, 2010, 3:32am » |
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There are some issues with equal values though: suppose you are looking for a sum of 11 and the array is
... 4 4 ... 7 7 ...
This means that there are four (4,7) pairs. After finding the first such pair, advancing one (or both) of the pointers will make you miss at least one other pair. So a bit of bookkeeping is required.
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Grimbal
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Re: Array Problem
« Reply #6 on: Jul 18th, 2010, 2:11pm » |
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I understood the problem as following:
find pairs (x,y) s.t. x and y exist in the array and x-y=z.
So duplicates don't count.
If duplicates did count, I would say in your case you need to return 4 pairs:
(41,71), (41,72), (42,71), (42,72)
(looking for x+y=11 or x-y=-3)
That would make the output size O(n2) as worst case and no solution could be faster than that.
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birbal
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Re: Array Problem
« Reply #7 on: Jul 24th, 2010, 7:51am » |
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on Jul 18th, 2010, 2:11pm, Grimbal wrote:I understood the problem as following:
find pairs (x,y) s.t. x and y exist in the array and x-y=z.
So duplicates don't count.
If duplicates did count, I would say in your case you need to return 4 pairs:
(41,71), (41,72), (42,71), (42,72)
(looking for x+y=11 or x-y=-3)
That would make the output size O(n2) as worst case and no solution could be faster than that. |
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Size of the output would be O(n2), we we need not iterate through each pair, we can count number of 4s ( 2 in this case) and number of 7s ( also 2 ) and can say ( 4 , 7 ) - 2*2 times.
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qddaichy
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Re: Array Problem (x-y=z for x,y in sorted array)
« Reply #8 on: Jan 26th, 2014, 10:28pm » |
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Just want to see the solution
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