Design and Analysis of Algorithms Notes for JNTUK R13:

Design  and  Analysis of  Algorithms

An algorithm is a set of sequential steps written in ordinary English to solve a problem. Every algorithm must possess 5 properties. they are:

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1. Definiteness
2. Finiteness
3. Effectiveness
4. Input and Output
5. Generality

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Types of algorithms

1. Simple 
2. Divide and conquer
3. Backtracking.
4. Dynamic programming.
5. Branch and bound.
6. Greedy.
7. Brute force.
8. Randomised.

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• A Simple recursive algorithm solves the problem by dividing into subproblems.

• A divide-and-conquer algorithm divides the problem into no. of smaller sub-problems and solve all these sub-problems recursively then combine the solutions of the all the sub-problems, finally get the solution to the original problem.

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• A backtracking algorithm is based on a depth-first recursive search.

• Dynamic programming is generally used for optimization. A dynamic programming algorithm solves the problem by remembering past results and uses them to find new results.

• Branch and bound uses the tree structure to solve the problem. The problem can be considered as root.  As the algorithm progresses, a tree of sub-problems is formed. There are also used for optimization.

• A greedy algorithm works in stages. You choose the best a local optimal at each step, you will end up at a global optimal.

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• A brute force algorithm simply follows trial and error methodology until a satisfactory solution is found by checking all possibilities.

• A randomized algorithm works faster. Used to solve large and complex problems.