Difference between 'Largest Rectangle in Histogram' and 'Container With Most Water'

Question

http://www.leetcode.com/onlinejudge

I am not able to see the difference between these two questions. To me, these two questions are same, but they are NOT.

Can someone give me some hints that explain why they are different.

Thank you

Answer 1

The "container of water" solution will allow the water to rise above intermediate positions. With the "largest rectangle" problem, the rectangle cannot rise above intermediate bars.

Answer 2

The "container of water" question is not as clearly described as the largest rectangle one, however I've been asked the water one in an interview.

The container of water one is basically asking for the area of the biggest "valley" in between the bars on a histogram. Looking at the histogram in the largest rectangle example, the answer would be "1" because there are two troughs made by the graph, a 1x1 trough on the left side, and a 1x1 trough on the right side. The max of these is of course, 1.