4.16 Recursion

1. Exam Points

• Predict results of recursion based on a given scenario.
• Analyze the behavior of a given recursive code segment.

2. Knowledge Points

(1) Recursion

• A recursive method is a method that calls itself.
• Recursive methods contain at least one base case, which halts the recursion, and at least one recursive call.
• Recursion is another form of repetition.
• Any recursive solution can be replicated through the use of an iterative approach and vice versa.

(2) Examples

• Example 1: print before recursion : first print and then do recursion.
  

  public static void printSth(int n) {
  	
      if (n > 3) { // the condition to halt recursion
          return;
      }
  
      // here print is before recursion, so first print and then do recursion
      System.out.print(n + " "); 
      printSth(n + 1); // recursion
  }
  
  public static void main(String[] args) {
      printSth(1);
  }
  

  • Analysis:
    
    • how n changes: 1 2 3 4
    • when print is executed: n = 1, 2, 3 (when n is 4, return, no printing)
    • Print result: 1 2 3
    • Process:
      
• Example 2: print after recursion : first do recursion and then print when recursion is done, so printing is done reversely.
  

  public static void printSth(int n) {
  	
      if (n > 3) { // the condition to halt recursion
          return;
      }
  
      printSth(n + 1); // recursion
      
      // here print is after recursion, so first do recursion and print after recursion is done
      System.out.print(n + " "); 
  }
  
  public static void main(String[] args) {
      printSth(1);
  }
  

  • Analysis:
    
    • how n changes: 1 2 3 4
    • when print is executed: n = 1, 2, 3 (when n is 4, return, no printing)
    • Print result: 3 2 1
    • Process:
      
• Example 3: multiple recursion in a method.
  

  public static int recur(int n) {
  
      if (n <= 1) {
          return 1;
      } else {
          return (recur(n - 2) + recur(n - 1));
      }
  }
  
  public static void main(String[] args) {
      // predict output
      System.out.println(recur(4));
  }
  

  • Analysis:
    
    • recur(4) -> recur(2) + recur(3)
    • recur(2) -> recur(0) + recur(1) = 1 + 1 = 2
    • recur(3) -> recur(1) + recur(2) = 1 + 2 = 3
    • so, recur(4) = recur(2) + recur(3) = 2 + 3 = 5

3. Exercises

• Practice
• Solution