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    <p>If k is very close to 1 or N, any algorithm that generates the sorted sums lazily could simply be run until the kth or N-kth item pops out.</p> <p>In particular, I'm thinking of best-first search of the following space: (a,b) means the ath item from A, the first list, added to the bth from B, the second. </p> <p>Keep in a best=lowest priority queue pairs (a,b) with cost(a,b) = A[a]+B[b].</p> <p>Start with just (1,1) in the priority queue, which is the minimum. </p> <pre><code>Repeat until k items popped: pop the top (a,b) if a&lt;|A|, push (a+1,b) if a=1 and b&lt;|B|, push (a,b+1) </code></pre> <p>This gives you a saw-tooth comb connectivity and saves you from having to mark each (a,b) visited in an array. Note that cost(a+1,b)>=cost(a,b) and cost(a,b+1)>=cost(a,b) because A and B are sorted.</p> <p>Here's a picture of a comb to show the successor generation rule above (you start in the upper left corner; a is the horizontal direction):</p> <pre><code>|------- |------- |------- </code></pre> <p>It's just best-first exploration of (up to) all |A|*|B| tuples and their sums.</p> <p>Note that the most possible items pushed before popping k is 2*k, because each item has either 1 or 2 successors. Here's a possible queue state, where items pushed into the queue are marked <code>*</code>:</p> <pre><code>|--*---- |-*----- *------- </code></pre> <p>Everything above and to the left of the <code>*</code> frontier has already been popped.</p> <p>For the <code>N-k&lt;k</code> case, do the same thing but with reversed priority queue order and exploration order (or, just negate and reverse the values, get the (N-k)th least, then negate and return the answer).</p> <p>See also: sorted list of pairwise sums <a href="https://stackoverflow.com/questions/826/efficiently-get-sorted-sums-of-a-sorted-list">on SO</a>, or the <a href="http://maven.smith.edu/~orourke/TOPP/P41.html" rel="nofollow noreferrer">Open problems project</a>.</p>
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    1. POHow to find kth largest number in pairwise sums like setA + setB?
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    1. USJonathan Graehl
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    1. POHow to find kth largest number in pairwise sums like setA + setB?
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    1. COYes, this is exactly a nice solution. In such a case, if we have sorted A and B, we can get kth largest with O(min(klgk, klgn)), right?
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