java语言程序设计-基础篇--课件(第20章)英文

factorial(4) Step 9: return 24 Step 0: executes factorial(4) return 4 * factorial(3) Step 8: return 6 Step 1: executes factorial(3) return 3 * factorial(2) Step 7: return 2
factorial(3)
animation
Computing Factorial
factorial(3) = 3 * factorial(2)
7
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
ght Queens puzzle is to place eight queens on a chessboard such that no two queens are on the same row, same column, or same diagonal, as shown in Figure 20.1. How do you write a program to solve this problem? A good approach to solve this problem is to use recursion.
Step 6: return 1
Step 3: executes factorial(1)
Space Required for factorial(4)
return 1 * factorial(0) Main method Step 4: executes factorial(0) Step 5: return 1 return 1
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1))
8
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1)) = 3 * ( 2 * (1 * factorial(0)))
animation
Trace Recursive factorial
factorial(4) Step 9: return 24 Step 0: executes factorial(4) return 4 * factorial(3) Step 8: return 6 Step 1: executes factorial(3) return 3 * factorial(2) Step 7: return 2
animation
Trace Recursive factorial
factorial(4) Step 9: return 24 Step 0: executes factorial(4) return 4 * factorial(3) Step 8: return 6 Step 1: executes factorial(3) return 3 * factorial(2) Step 7: return 2
13
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Trace Recursive factorial
Executes factorial(4)
factorial(4) Step 9: return 24 Step 0: executes factorial(4) return 4 * factorial(3) Step 8: return 6 Step 1: executes factorial(3) return 3 * factorial(2)
9
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1)) = 3 * ( 2 * (1 * factorial(0))) = 3 * ( 2 * ( 1 * 1)))
Objectives
4
To know what a recursive method is and the benefits of using recursive methods (§20.1). To determine the base cases in a recursive method (§§20.220.5). To understand how recursive method calls are handled in a call stack (§§20.2-20.3). To solve problems using recursion (§§20.2-20.5). To use an overloaded helper method to derive a recursive method (§20.5). To get the directory size using recursion (§20.6). To solve the Towers of Hanoi problem using recursion (§20.7). To draw fractals using recursion (§20.8). To understand the relationship and difference between recursion and iteration (§20.9).
Stack
14
Step 7: return 2
Step 2: executes factorial(2) return 2 * factorial(1)
3
Space Required for factorial(2)
5 Space 4 Space
Required for factorial(1)
Required for factorial(0)
Space Required for factorial(1) Space Required for factorial(2) Space Required for factorial(3) Space Required for factorial(4)
Space Required for factorial(2) Space Required for factorial(3) Space Required for factorial(3) Space Required for factorial(4)
12
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1)) = 3 * ( 2 * (1 * factorial(0))) = 3 * ( 2 * ( 1 * 1))) = 3 * ( 2 * 1) =3*2 =6
Step 6: return 1
Step 3: executes factorial(1) Space Required
for factorial(3) Space Required for factorial(4)
return 1 * factorial(0) Main method Step 4: executes factorial(0) Step 5: return 1 return 1
10
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1)) = 3 * ( 2 * (1 * factorial(0))) = 3 * ( 2 * ( 1 * 1))) = 3 * ( 2 * 1)
11
factorial(0) = 1; factorial(n) = n*factorial(n-1);
animation
Computing Factorial
factorial(3) = 3 * factorial(2) = 3 * (2 * factorial(1)) = 3 * ( 2 * (1 * factorial(0))) = 3 * ( 2 * ( 1 * 1))) = 3 * ( 2 * 1) =3*2
Stack Space Required for factorial(2)
1
Chapter 20 Recursion
Motivations
2
Suppose you want to find all the files under a directory that contains a particular word. How do you solve this problem? There are several ways to solve this problem. An intuitive solution is to use recursion by searching the files in the subdirectories recursively.
Stack Space Required for factorial(2)