Question

Is there an algorithm that will take two columns of numbers and determine if they have a value in common?

Two columns:

One increases by .3 with each value. The other increases erratically. I want to determine if the two columns have a value in common.

.3  .1
.6  .2
.9  .4
1.2  .5
1.5  .9
1.8  .13

Answer 1

If both series are increasing (or sorted¹ in general), there is an O(n) solution. You can’t do any better than that, because you need to look at every element in the erratically-increasing list at least once in the worst case.

Simply traverse both at the same time in a zipper-like fashion: Always get the next element from the list, that currently has a smaller element than the other one.

> .3   .1 < | > .3   .1   | > .3   .1   |   .3   .1   |   .3   .1   |   .3   .1   
  .6   .2   |   .6   .2 < |   .6   .2   | > .6   .2   | > .6   .2   | > .6   .2   
  .9   .4   |   .9   .4   |   .9   .4 < |   .9   .4 < |   .9   .4   |   .9   .4   
  .12  .5   |   .12  .5   |   .12  .5   |   .12  .5   |   .12  .5 < |   .12  .5   
  .15  .9   |   .15  .9   |   .15  .9   |   .15  .9   |   .15  .9   |   .15  .9 < 
  .18  .13  |   .18  .13  |   .18  .13  |   .18  .13  |   .18  .13  |   .18  .13  

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¹Where sorted means with respect to a total order.