Algorithms: Greedy, Dynamic, D, and C

Greedy Algorithms

So, the greedy algorithms are those, in which best optimal solution is to be chosen at every stage.

The solution is build piece by piece.Greedy algorithms are better than dynamic programming, if applicable. As not every problem could be solved by a greedy method. For ex.0-1 knapsack problem can not be solved by greedy method.

Other problems that could be solved by greedy method are- Kruskal's MST, Prim's MST, Activity selection.

Dynamic Programming

Dynamic Programming is a paradigm that solves a given problem by breaking it into subproblems and stores the result of subproblems to avoid computing the same results again and again.

The main properties of a problem to be solved by this method are-:

1-Overlapping subproblem

2-Optimal sub Structure

For ex A fibonacci problem needs that to compute the factorial of 5 we must compute factorial of 2 , 3, 4 . So computing these again & again could be a mess, So these values are stored in lookup, and are looked before computing , if available they are restored from lookup otherwise calculated.

For ex- LCS , 0-1 Knapsack

Divide & Conquer

 Like Greedy and Dynamic Programming, D&C is also a paradigm. A typical D&C also solves the problem with 3 steps:

1. Divide: Break the problem into subproblems

2. Conquer: Recursively solve problems

3.Combine: Join the solutions

For example: Binary search, Quick Sort, Merge Sort.