# My thoughts for the min_heap solution

• This problem is same as LC 378, so the solution is same. However, I guess most of us are confused by following method:
if current min is (num1[m], num2[n]), we only insert (num1[m], num2[n+1]) into the heap, not (num1[m+1], num2[n]), unless n=0.

We know we are extending the min_heap, but why in only 1 direction?
In fact, if num1[m]+num2[n+1] > num1[m+1]+num2[n], then num1[m]+num2[n+1] > num1[m+1]+num2[n-1].
If (num1[m+1],num2[n-1]) is already in min heap, then we are definitely safe, because (num1[m+1], num2[n]) will be inserted into queue before we pop out (num1[m], num2[n+1]).
What if (num1[m+1],num2[n-1]) is not in queue? Well, then how about (num1[m+1],num2[n-2]), (num1[m+1],num2[n-3]), ... etc? One of them should be in the queue because (num1[m+1],num2[0]) is in the queue. And we know that we will extend 2 directions when n==0.

This is some easy induction, but people may feel confused in the first and easily introduce duplicate pairs.

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