Definition of Advanced algorithm:

                               It is the Step by step procedure design to perform an opration, and which (like a map or flowchart) will lead to the result if followed correctly. Algorithms have a definite beginning and a definite end, and a finite number of steps. An algorithm produces the same output inforation given the same input information, and several short algorithms can be combined to perform complex tasks such as writting a computer program

Example of advanced algorithm in real world application:

      There is lot of examples in this real world application using an advanced algorithm.   

        Here I consider the electronic usage in real world application.

1) Electronic usage:

      By using advanced algorithm method we build electronic chips in present days by implement for various integer and floating-point sizes in computer hardware or in microcode.  In arbitrary precision technique , it's common to use long multiplication with the base set to 2^w, where w is the number of bits in a word, for multiplying relatively small numbers.

To multiply two numbers with n digits using this method, one needs about n² operations. More formally: using a natural size metric of number of digits, the time complexity of multiplying two n-digit numbers using long multiplication is Θ(n²).

 By using this advanced technology of algorithm we can easily solve the problem facing of

*overflow

*time complexity of multiplying n-digit

*memory usage

*Reduce the complexity

                 When implemented in software, long multiplication algorithms have to deal with overflow during additions, which can be expensive. For this reason, a typical approach is to represent the number in a small base b such that, for example, 8b² is a represent able machine integer (for example Richard Brent used this approach in his Fortran package MP); we can then perform several additions before having to deal with overflow. When the number becomes too large, we add part of it to the result or carry and map the remaining part back to a number less than b; this process is called normalization.