The syllabus for the interviews is very clear and simple:
1) Dynamic Programming
2) Super recursion (permutation, combination,...2^n, m^n, n!...etc. type of program. (NP hard, NP programs)
3) Probability related programs
4) Graphs: BFS/DFS are usually enough
5) All basic data structures from Arrays/Lists to circular queues, BSTs, Hash tables, B-Trees, and Red-Black trees, and all basic algorithms like sorting, binary search, median,...
6) Problem solving ability at a level similar to TopCoder Division 1, 250 points. If you can consistently solve these, then you are almost sure to get in with 2-weeks brush up.
7) Review all old interview questions in Glassdoor to get a feel. If you can solve 95% of them at home (including coding them up quickly and testing them out in a debugger + editor setup), you are in good shape.
Practice coding--write often and write a lot. If you can think of a solution, you should be able to code it easily...without much thought.
9) Very good to have for design interview: distributed systems knowledge and practical experience.
10) Good understanding of basic discrete math, computer architecture, basic math.
11) Coursera courses and assignments give a lot of what you need to know.
12) Note that all the above except the first 2 are useful in "real life" programming too!
Interview 1:
Graph related question and super recursion
Interview 2:
Design discussion involving a distributed system with writes/reads going on at different sites in parallel.
Interview 3:
Array and Tree related questions
Interview 4:
Designing a simple class to do something. Not hard, but not easy either. You need to know basic data structures very well to consider different designs and trade-offs.
Interview 5:
Dynamic programming,
Computer architecture and low level perf. enhancement question which requires knowledge of Trees, binary search, etc.
Conclusion: "It's not the best who win the race; it's the best prepared who win it."