Dynamic Programming (DP) is an algorithmic technique for solving an optimization problem by breaking it down into simpler sub-problems and taking advantage of the fact that the optimal solution to the overall problem is dependent on the optimal solution to its sub-problems.

Recursion is a problem-solving technique in which the solution is dependent on solutions to smaller instances of the same problem. Computing factorials is a classic example of recursive programming.

Every recursive program follows the same basic sequence of steps:

Set up the algorithm. Recursive programs frequently require a seed value, to begin with. This is accomplished by either using a parameter passed to the function or by providing a non-recursive gateway function that sets up the seed values for the recursive calculation.

Check to see if the current value(s) being processed correspond to the base case. If so, process the value and return it.

Rephrase the solution in terms of a smaller or simpler sub-problem or sub-problems.

Apply the algorithm to the sub-problem.

In order to formulate an answer, combine the results.

Return the results.

Hashing is a technique or process that uses a hash function to map keys and values into a hash table. It is done to allow for quicker access to elements. The efficiency of mapping is determined by the hash function’s efficiency.

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