tsminh_3's blog

Divide into two group
By tsminh_3, history, 10 years ago, In English 
Please help me with this 

Give n ropes, each rope in length a[i] (n<=10^3). Then divide them into two group
- Sum1 = sum of all ropes in group 1
- Sum2 = sum of all ropes in group 2 
The task asked if there is a way to divide them into two group which S1=S2`
Note : the numbers of rope in each group maybe not equal to the other

Sorry for my bad at English :(
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10 years ago, # |
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Auto comment: topic has been updated by tsminh_3 (previous revision, new revision, compare).

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10 years ago, # |
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What is the size of array a?

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10 years ago, # |
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sum all the elements of the array . if sum is odd print no otherwise find subset sum of sum/2 if this exist . B-)

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    10 years ago, # ^ |
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    He has mentioned a[i] <= 10^9. You cannot solve the problem.

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10 years ago, # |
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Can you please give me the link of this question?

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10 years ago, # |
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According to Wiki Link , this problem is NP-complete and has pseudo-polynomial (O(n*sum)) time dp solution which is feasible only when sum is small. Hence, it would be nice if you could give a link to problem so that people can verify that your description and/or constraints about the problem are accurate.

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10 years ago, # |
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This is basically the subset sum problem, and it's NP-complete, so you can't expect to solve it in polynomial time. If values were smaller (maybe  ≤ 105), you could do DP.

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    10 years ago, # ^ |
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    Please can you explain how to do a DP for a[i] <  = 105 ?

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      10 years ago, # ^ |
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      At every step just update all possible sums you can reach if you added current element or if you subtracted current element. If after the last element you could have reached 0 then it is possible to split the set into 2 parts.

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        10 years ago, # ^ |
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        I still don't understand it. Would you do the updates using a map/set ? Wouldn't the total possible sums for a[i] <  = 105, n <  = 103 be 108 and storing them in a map would cause the program to exceed memory limit for sure.

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          10 years ago, # ^ |
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          Yes, I mean the total sum of elements  ≤ 105...

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          10 years ago, # ^ |
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          For i elements the total possible sums can be i * (i + 1) / 2 if the array is of numbers sequentially like 1,2,3.. and so on so it would atleast get a TLE as time taken could be and this is not even the worst case.

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      10 years ago, # ^ |
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      Let A be the array and DP[i][j] the DP matrix. DP[i][j] is true if it is possible to have a sum of j by taking some elements from the first i elements.

      At every state, you can either add the next element or not, so from a valid state DP[i][j] we can get either to DP[i + 1][j] (do not take the next element) or to DP[i + 1][j + Ai + 1] (take the next element).

      If S is the sum of all elements and is true, then you can divide the array into two parts with equal sum.

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