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POFind all combinations of records which sums to zero in three array lists?
 

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  1. POFind all combinations of records which sums to zero in three array lists?
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    <p>Consider there are three array list each of equal length and having positive, negative and zero in them. I had to write a program to find combinations of which sum comes to zero. So basically, if the arrays were:-</p> <pre><code>A = {0, -1, 2} B = {0, -1, -2} C = {0, -2, 0} </code></pre> <p>O/P: A[0] + B[0] + C[0], A[2] + B[2] + C[2] etc.</p> <p>I could think of two ways, 1. Have 3 for loops and calculate the sum using a[i] + b[j] + c[k], if zero print the index. Big O will be O(N^3) 2. Have two for loop but use Binary Search to find the third element which would give the sum as zero. Big O will be O(N^2LogN)</p> <p>Any other ways?</p> <p>Thanks.</p> <p><strong>EDIT:</strong> Based on the answers given below, my first soln is the fastest possible. But if the question is about "finding" the number of combinations and <strong>NOT</strong> printing them, then please see Grigor Gevorgyan answer below.</p>
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      1. USViktor Stolbin
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    1. COAre you only interested in sets that contain exactly one element from each list?
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      1. USverdesmarald
    2. COYou cannot possibly beat `Omega(N^3)` worst case runtime if you have to output all triples that sum to zero, because if all three input sets consist solely of zeros, then all combinations sum to zero and hence the *output* is of size `Omega(N^3)`. In that case even though the binary search finds the range you're after in `O(log N)` time, it's `Omega(N)` time to traverse it.
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      1. USSteve Jessop
    3. COI have a O(n^2) complexity solution but only if some assumption allowed. See plz http://stackoverflow.com/a/11603110/538514
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      1. USViktor Stolbin
 

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