As the title proposes, we are going to talk about the dynamic programming algorithm method. The dynamic programming is one of the most discussed methods in the algorithmic writing, mainly since it refers to a large number of algorithms. Theoretically, thousands of problems can be solved with its execution.
Steadily, as you become familiar with a mass of techniques, you will see that there are lots of problems that can be solved with just only one method and that is dynamic programming algorithm method. However, the dynamic programming moves on in more stylish and well-organized way. The notion of dynamic programming means that we rupture the large problem into incremental sub-problems, where each sub-problem can be solved and the solution is most favorable one. As a result, by using such formula you can produce the final solution without changing the previously solved sub-problems or re-calculating some parts of the algorithm.
First of all, a problem is not separated from sub-problems, if the problem can be broken down into different sub-problems that are going to be reclaimed several times later on. The best illustration of this is the Fibonacci sequence principle. As everybody knows, F (N) = F (n-1) + F (n-2), but also F (n-1) = F (n-2) + F (n-3). And so on. Dynamic programming, by its nature, is the most suitable algorithm for those problems that have the complex structure. This combination has the specialty of dynamic programming.
The dynamic programming method starts from the trivial of the sub-problems; moving further, it creates the final solution. However, it's really significant that the algorithm stores the solution of each sub-problem that we use an array for this purpose. The array can be of multi-dimensional depending on how many parameters describe the solution(s).
As a result, the principle is chiefly a mathematical formula. By applying this formula, we can find the final solution depending on the prior solutions. Due to this, dynamic programming eradicates the requirement to repeatedly solve identical sub-problems. Thus, it isn't that proficient.
Nevertheless, there are only two possible moves that are possible in dynamic programming algorithm procedure. The first valid move is straight down/vertically, one step down (from [i][j] to [i+1][j]). The second valid move is diagonally one step (from [i][j] to [i+1][j+1]), implication one stop down and one step right. Knowing these are the only possible moves, the problem gets tough.
Summing these all up, dynamic programming is truly an exclusive algorithm method. However, in the real world there are lots of common algorithms based on it, as well as string algorithms such as the top common sub-sequence and longest common sub-string.