What is an algorithm?

                An algorithm is a procedure followed to accomplish a specific task. An algorithm is the idea behind any reasonable computer program. To be interesting, an algorithm must solve a general, well-specified problem. An algorithmic problem is specified by describing the complete set of instances it must work on and of its output after running on one of these instances. This distinction, between a problem and an instance of a problem, is fundamental. For example, the algorithmic problem known as sorting is defined as follows:
Problem: Sorting
Input: A sequence of n keys a1,...,an.
Output: The permutation (reordering) of the input sequence such that a 1 ≤ a 2 ≤ ···≤a n−1 ≤ a n.
                 An instance of sorting might be an array of names, like {Mike, Bob, Sally, Jill,Jan }, or a list of numbers like {154, 245, 568, 324, 654, 324}. Determining that you are dealing with a general problem is your first step towards solving it. An algorithm is a procedure that takes any of the possible input instances and transforms it to the desired output. There are many different algorithms for solving the problem of sorting. For example, insertion sort is a method for sorting that starts with a single element (thus forming a trivially sorted list) and then incrementally inserts the remaining elements so that the list stays sorted.

source:algorithm design manual

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Method 5:Hill Climbing Technique

                  Hill climbing is a technique for certain classes of optimization problems.This Methode is used by newton to find roots. The idea is to start with a sub-optimal solution to a problem (i.e., start at the base of a hill) and then repeatedly improve the solution (walk up the hill) until some condition is maximized (the top of the hill is reached).
Hill-Climbing Methodology
1. Construct a sub-optimal solution that meets the constraints of the problem
2. Take the solution and make an improvement upon it
3. Repeatedly improve the solution until no more improvements are necessary/possible

                One of the most popular hill-climbing problems is the network flow problem. Although network flow may sound somewhat specific it is important because it has high expressive power: for example, many algorithmic problems encountered in practice can actually be considered special cases of network flow. After covering a simple example of the hill-climbing approach for a numerical problem we cover network flow and then present examples of applications of network flow.

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Method 4: Greedy Algorithm

                         In the backtracking algorithms we looked at, we saw algorithms that found decision points and recursed over all options from that decision point. A greedy algorithm can be thought of as a backtracking algorithm where at each decision point "the best" option is already known and thus can be picked without having to recurse over any of the alternative options.
                         The name "greedy" comes from the fact that the algorithms make decisions based on a single criterion, instead of a global analysis that would take into account the decision's effect on further steps. As we will see, such a backtracking analysis will be unnecessary in the case of greedy algorithms, so it is not greedy in the sense of causing harm for only short-term gain.
                         Unlike backtracking algorithms greedy algorithm can't be made for every problem. Not every problem is "solvable" using greedy algorithms. Viewing the finding solution to an optimization problem as a hill climbing problem greedy algorithms can be used for only those hills where at every point taking the steepest step would lead to the peak always.
                         Greedy algorithms tend to be very efficient and can be implemented in a relatively straightforward fashion. Many a times in O(n) complexity as there would be a single choice at every point. However, most attempts at creating a correct greedy algorithm fail unless a precise proof of the algorithm's correctness is first demonstrated. When a greedy strategy fails to produce optimal results on all inputs, we instead refer to it as a heuristic instead of an algorithm. Heuristics can be useful when speed is more important than exact results (for example, when "good enough" results are sufficient).

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Understanding an Algorithm

Understanding an Algorithm

The Best Video that Decribes the Concept Algorithm Very good By  David J. Malan

In TED-Ed Event. 

source: youtube.com  publisher: TED-Ed

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