# Fundamental concept of Problem solving

### Program design & implementation

There are two types of designing approach: |

1. Top down design. |

2. Bottom up design. |

Both have been describe together with examples. |

Any problem can be dealt with two ways, viz. top down or bottom up. A simple example is given here to illustrate the concept. |

Sorting an array of numbers involves the following two steps: |

1. Comparison |

2. Exchange |

1. Top down design: |

At the top level, an algorithm has to be formulated to carry out sorting. Once the algorithm is confirmed, then the algorithms for comparison and exchange are formulated, before implementation of the entire algorithm. |

Therefore, in this approach, one begins from the top level without bothering about the minute details for implementation, to start with. |

2. Bottom up design: |

The bottom up approach is just the reverse. The lower level tasks are first carried out and are then integrated to provide the solution. |

In this method, lower level structures of the program are developed first and then progressively higher level structures are created. |

Here the algorithms for exchange and comparison will be formulated before formulating the algorithm for the whole problem. |

In any case, dividing the problem into small tasks and then solving each task provides the solution. |

If the program development is assumed to be a single task and the program statements are developed in sequence, then it is quite likely that the program may not work. |

Therefore, either the top down or bottom up methodology has to be adopted for dividing the problem into smaller modules and then solving it. |

Difference between Top design and Bottom up approach: |

In the top down methodology, the overall structure is defined before getting into details, but in the bottom up approach, the details are worked out first before defining the overall structure. |

Implementation |

A good program is one which contains a main function and the main function calls procedures or sub-programs or functions to carry out specific tasks. |

The subprograms are dependent on the main program. They do what the main program asks them to do. |

Each language gives different names to sub-programs. Sub programs are known as functions in C. |

The quality of program will also get enhanced when the program is made modular as mentioned above with functions. |

Each function will receive input and may return some output to the called program. |

By dividing the problem into a number of functions, the problem can be divided and conquered. |

This facilities focus on small programs and dealing with one problem at a time. |