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I am trying to show that the best case time complexity of Quicksort is $$\Omega(n \log n)$$.

The following recurrence describes the best-case time complexity of Quicksort:

$$T(n) = \min_{0 \le q \le n-1} \left(T(q) + T(n-q-1) \right) + \Theta(n).$$

But I have difficulty in proving that $$T(n) = \Omega(n \log n)$$ using the recurrence above.

So how to solve this recurrence?

## Best way to gain traffic in a subreddit

Hello!
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## Find Best N Points From a Graph

I’ve given a task and wonder if there are any better solutions.

1. Distance of district pairs

2. Population of pairs

Goal is:

• Find n districts at which its population and districts x miles range districts’ population is max.

Extra information:

• Unique district size is tens of hundreds.

As an example, if I pick up district A, population will be A‘s population plus other districts’ population which are less than x miles far away from it. Total population will be n districts at which population is calculated as I mentioned.

What I’ve tried:

1. Brute Force
2. Generic Algorithms

What I planning to do:

1. A* Search

My question is, there may be any other solution (optimal if possible) instead of these one. i.e. sorting districts by their population, merging x miles nearest to them into one until I get n districts.

Any ideas?

## which algorithm is the best and which one is the worst. Why?

Three different techniques to solve the GCD problem

1 Euclid’s algorithm

2 Consecutive integer checking algorithm .An algorithm based on the definition of GCD

3 Middle-school procedure .Prime factorization

From above which algorithm is the best and which one is the worst. Why?