Skip to main content

Algorithm: Recursion

The idea of calling one function from another immediately suggests the possibility of a function calling itself. Recursion is a powerful general-purpose programming technique, and is the key to numerous critically important computational applications, ranging from combinatorial search and sorting methods that provide basic support for information processing to the fast Fourier Transform for signal processing.

Induction: a method of reasoning in which you use individual ideas or facts to give you a general rule or conclusion.

Reasoning: the process by which you reach a conclusion after thinking about all the facts.

Recursive programming is directly related to mathematical induction, a technique for providing facts about discrete functions. Proving that a statement involving an integer N is true for infinitely many values of N by mathematical induction involves two steps.
step 1: the base case is to prove the statement true for some specific value or values of N(usually 0 or 1).
step 2: the induction step is the central part of the proof. For example, we typically assume that a statement is true for all positive integers less that N, then use that fact to prove it true for N.

1. N!
base case: N = 1. Returns a value without making any subsequent recursive calls. it does this for one or more special input values for which the function can be evaluated without recursion.

Induction step: N* factorial(N-1) and N decreases by one for each call, so the sequence of parameter values converges to the base case of N=1;

Converge: approach a limit as the number of terms increases without limit.

public static int factorial(int N) { 
   if (N == 1) return 1; 
   return N * factorial(N-1); 

2. Towers of Hanoi
Move only one disc a time.
Never place a disc on a smaller one.

 public static void solve(int first_disc, char aTower, char bTower, char cTower) {
        if (first_disc == 1) {
            System.out.println("Disk 1 on tower " + aTower + " moving to tower " + cTower);
        } else {
            solve(first_disc - 1, aTower, cTower, bTower);
            System.out.println("Disk " + first_disc + " on tower " + aTower + " moving to tower " + cTower);
            solve(first_disc - 1, bTower, aTower, cTower);


Popular posts from this blog

Stretch a row if data overflows in jasper reports

It is very common that some columns of the report need to stretch to show all the content in that column. But  if you just specify the property " stretch with overflow' to that column(we called text field in jasper report world) , it will just stretch that column and won't change other columns, so the row could be ridiculous. Haven't find the solution from internet yet. So I just review the properties in iReport one by one and find two useful properties(the bold highlighted in example below) which resolve the problems.   example:
<band height="20" splitType="Stretch"> <textField isStretchWithOverflow="true" pattern="" isBlankWhenNull="true"> <reportElement stretchType="RelativeToTallestObject" mode="Opaque" x="192" y="0" width="183" height="20"/> <box leftPadding="2"> <pen lineWidth="0.25"/> …

JasperReports - Configuration Reference

Spring - Operations with jdbcTemplate

This class manages all the database communication and exception handling using a java.sql.Connection that is obtained from the provided DataSource. JdbcTemplate is a stateless and threadsafe class and you can safely instantiate a single instance to be used for each DAO.

Use of Callback Methods
JdbcTemplate is based on a template style of programming common to many other parts of Spring. Some method calls are handled entirely by the JdbcTemplate, while others require the calling class to provide callback methods that contain the implementation for parts of the JDBC workflow. This is another form of Inversion of Control. Your application code hands over the responsibility of managing the database access to the template class. The template class in turn calls back to your application code when it needs some detail processing filled in. These callback methods are allowed to throw a java.sql.SQLException, since the framework will be able to catch this exception and use its built-in excepti…