Not able to understand one Top Coder entry on Greedy Algorithms

I am actually practicing Greedy Algorithms and There is a problem on topcoder.. So need some help....

The problem is about Robust 开发者_JAVA百科Computer System.. http://www.topcoder.com/stat?c=problem_statement&pm=2235&rd=5070

I don't understand what is MFC. (Maximum Failure Count)?

If somebody can put light on the explanation of MFC with simple example then that would be help!!

Thanks..

In case you don't have an account, and can't follow the link, here's the question:

In a robust computer system, one of the most important pieces is the cooling. Without proper cooling, processors can heat up to over 400 degrees C. The reliability of a system can be measured by determining how many fans can fail without risking the system processor. Each fan can be assigned a value indicating how much capacity it has to cool the system, and we can define a minimum cooling capacity, which the sum of the fan capacities must exceed to properly cool the system. We define a Failure Set as a set of fans which are not necessary to cool the system. In other words, if the fans in a Failure Set break, the system can still be properly cooled by the remaining fans. The count of a Failure Set is the number of fans in the set.

To measure the reliability, we will define two values, the Maximum Failure Set (MFS) and the Maximum Failure Count (MFC). A MFS is a Failure Set of fans with the largest count possible. A set of fans may have more than one MFS (see below). A Failure Set is an MFS if and only if there are no Failure Sets with a higher count. The MFC is the largest value such that all fan sets with count <= MFC are Failure Sets. In other words, any set of fans of size MFC or less can fail, and the system will still be properly cooled by the remaining fans.

Consider the fan set with capacities 1, 2, 3, and a cooling requirement of 2. Two MFSs with a count of 2 exist: fans 1 and 3, or fans 1 and 2. However, the MFC is not 2 because fans 2 and 3 is not a Failure set (fan 1 could not cool the system properly by itself). Thus, the MFC is 1, because if any single fan fails, the system can still be cooled.

You will be given a int[] capacities, which designates how many units of cooling each fan provides, and an int minCooling, which designates the minimum units of cooling required to cool the system. Your method should return a int[], where the first value should be the number of fans in the Maximum Failure Set (MFS), and the second value should be the Maximum Failure Count (MFC).

We define a Failure Set as a set of fans which are not necessary to cool the system. In other words, if the fans in a Failure Set break, the system can still be properly cooled by the remaining fans. The count of a Failure Set is the number of fans in the set.

A Failure Set is an MFS if and only if there are no Failure Sets with a higher count.

It's all in the problem statement. What's not clear?

Just as in the problem statement:

The MFC is the largest value such that all fan sets with count <= MFC are Failure Sets. In other words, any set of fans of size MFC or less can fail, and the system will still be properly cooled by the remaining fans.

MFC means that if we arbitrarily choose n<=MFC fans to fail, then the system could still provide the necessary cooling requirement. However, there exist at least one case that if we choose MFC + 1 fans to fail the system would not provide the needed cooling requirement.

Good luck on TopCoder & Happy Learning!

Spoiler:

Just find the minimum number of fans M that their capacities sum is bigger than the (total capacity - cooling requirement). These fans must be the largest ones, hence the greedy algorithm part. M - 1 is the answer.