What type of government is the most efficient and why?
This depends a great deal on what you mean by efficiency.
If you define efficiency as the ability to get its way, the most efficient form of government is totalitarianism. A totalitarian regime can decide what it wants very quickly. This is in contrast to a democracy like our own. Right now, we have serious troubles with our system of Medicare, for example, and with our government debt. The problem is that we cannot do anything about it because our political parties do not agree on what to do. In a totalitarian system this problem does not arise. The government simply decides what to do on its own without having to worry about what the people want or what they think. This is efficient in one sense of the word.
However, if you define efficient as being able to last a long time, a democracy is most efficient. In a democracy, the people feel connected to the government. They feel that the government represents them and generally has their best interests in mind. Therefore, they are not likely to radically rebel against the government and the government will tend to remain fairly stable over time. In this sense of efficiency, democracies are most efficient.