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  1. PO
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    <p>Can be done in <strong><em>O(n^2)</em></strong> with <em>2 pointers method</em>.<br/> <br/> Sort the arrays. Now do following:<br/> Set <strong><em>ans = 0</em></strong>.<br/> Have an external loop running through array <strong><em>a</em></strong> with index <strong><em>i</em></strong>. Now set <strong><em>j = 0, k = n - 1</em></strong>.<br/> Look at <strong><em>sum = a[ i ] + b[ j ] + c[ k ]</em></strong>.<br/> If <strong><em>sum &lt; 0</em></strong>, increase <strong><em>j</em></strong>.<br/> If <strong><em>sum > 0</em></strong> decrease <strong><em>k</em></strong>.<br/> If <strong><em>sum == 0</em></strong>, find the range of elements equal to <strong><em>b[ j ]</em></strong> and <strong><em>c[ k ]</em></strong> and add ranges lengths product to the answer. Then set <strong><em>j</em></strong> and <strong><em>k</em></strong> to first elements out of that ranges.<br/> This works because arrays are sorted and addition is a linear function.<br/> Internal part runs in <strong>O(n)</strong>, with overall <strong>O(n^2)</strong> complexity.</p> <p>Example code in C++:</p> <pre class="lang-cpp prettyprint-override"><code>sort( a, a + n ); sort( b, b + n ); sort( c, c + n ); ans = 0; for( i = 0; i &lt; n; ++i ) { j = 0, k = n - 1; while( j &lt; n &amp;&amp; k &gt; 0 ) { sum = a[ i ] + b[ j ] + c[ k ]; if( sum &lt; 0 ) ++j; else if( sum &gt; 0 ) --k; else { // find the equal range for( jj = j; jj &lt; n &amp;&amp; b[ jj ] == b[ j ]; ++jj ); for( kk = k; kk &gt;= 0 &amp;&amp; c[ kk ] == c[ k ]; --kk ); // add pairs quantity from these ranges ans += ( jj - j ) * ( k - kk ); j = jj, k = kk; } } </code></pre> <p><em><strong>Note</em></strong>: Sorting of array <strong><em>a</em></strong> is not necessary, just did it to look good :)</p>
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    1. POFind all combinations of records which sums to zero in three array lists?
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    1. USGrigor Gevorgyan
    1. USGrigor Gevorgyan
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    1. POFind all combinations of records which sums to zero in three array lists?
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    1. COIt misses some valid i,j,k triples. See Steve Jessop's comment to the question
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      1. USjfs
    2. CO@J.F.Sebastian: Oh, thanks, I forgot about the same values. Edited the answer to consider equal ranges.
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      1. USGrigor Gevorgyan
    3. COthanks for the help. I had also mentioned sorting in my answer - to get the soln faster. But noticing an issue, for my given example, it doesn't print a[0], b[0] and c[0]; a[2], b[2], c[0] combinations. I am trying to look, do you have any ideas?
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