How many types of algorithm are there?

Simple Recursive Algorithm: 

A recursive algorithm is an algorithm which calls itself with smaller input values.

Backtracking Algorithm:
Backtracking is a algorithm for finding all solutions to some computational problems.

Divide and conquer algorithm:
Divide and conquer algorithm works by recursively breaking down a problem into two or more sub problems of related type.

Dynamic programming algorithm:
Dynamic programming algorithm is a method for solving a complex problem by sub problems, solving each of those sub problems just once, and storing their solutions.

Branch and bound algorithm:
A branch and bound algorithm consist of a systematic enumeration of candidate solutions by means of state space search.

Brute force algorithm:
It is very general problem solving technique that consists of systematically enumerating all possible candidates for the solution.