After we convert the problem to the binary array version, I somehow came up with another conclusion tk determine whether it is possible for min(a1,b1) to be 1. The conclusion is: min(a1,b1) is able to reach 1 is equivalent to ''there exists 2 pairs (ai,bi),(aj,bj) which are both (1,1) AND there exists no (0,0) pairs between them.''
I am uncertain about its validity since it differs from the tutorial. It would be awesome if anyone could prove it or come up with a counterexample.
Thanks a lot!
In this case, there are a couple of counterexamples! I'll be using a 2 to reference a value of (1, 1) and 0 to represent (0, 0). Here are two of them:
0, 2, 2, 0: According your conclusion, this should result in a minimum of 1. However, you can try this out and notice that it does not work, leading to a minimum of 0.
2, 0, 2: Here, your conclusion would lead to assuming a minimum of 0. But this actually leads to a minimum of 1 (again, try working it out)!
These are a couple cases where your conclusion may be a bit off (there may be more, but these are a few I could think of at the moment). But I see where your idea came from! Good luck on your CP journey :)