Mathematical explanation of Leetcode question: Container With Most Water

I was working on a medium level leetcode question 11. Container With Most Water. Besides the brute force solution with O(n^2), there is an optimal solution with complexity of O(n) by using two pointers from left and right side of the container. I am a little bit confused why this “two pointers” method must include the optimal solution. Does anyone know how to prove the correctness of this algorithm mathematically? This is an algorithm that I don’t know of. Thank you!

NumPy array row differences

I have a NumPy array vectors = np.random.randn(rows, cols). I want to find differences between its rows according to some other array diffs which is sparse and “2-hot”: containing a 1 in its column corresponding to the first row of vectors and a -1 corresponding to the second row. Perhaps an example shall make it clearer: