java programming - chapter 11 (in thai)

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Computer Programming using Java Recursion - 11

CHAPTER 11

(Recursion)

1. (Introduction to Recursion)

1. 1) (Recursion)

2) (Recursive Method) ( ) (Iteration) 4 while for 4

3) (Recursive Programming) -

2. 2 1) (Recursion Case)

return fac(n-1), return fibo(n-1) + fibo(n-2)

2) (Base Case) return 1, return n

3. f() 0 n f(n) = (0+1+2+ +n) (Iteration: for) (Recursion)

1 2 3 4 5 6 7

public static int f(int n) { int s = 0; for(int i = n; i >= 0; i--) { s += i; } return s; }

1 2 3 4 5 6 7

public static int f(int n) { if(n

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Computer Programming using Java 11 - Recursion

1 [] f() f(5) (10 )

2 [] (6 ) 3 [] (6 )

1 2 3 4 5 6 7

public static int mul(int x, int y) { if (x >= 1) { return y + mul(x - 1, y); } else { return 0; } }

mul(4, 3) mul(5, 7) mul(20, 10) Linear Recursion

1 2 3 4 5 6 7 8

public static int gcd(int m, int n) { if (m < n) return gcd(n, m); if (m % n == 0) { return n; } else { return gcd(n, m % n); } }

gcd(28, 16) gcd(9, 14) gcd(75, 30)

Tail Recursion

1 2 3 4 5 6

1 2 3 4 5 6

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4 [] expo() (15 ) (Binary Tree) expo(0), expo(1), expo(2) expo(3)

5 [] (6 )

1 2 3 4 5 6 7

public static int expo(int n) { if (n = 1) { printX(1, x); } } public static void printX(int i, int x) { if (i

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6 [] akm(m, n) m n (10 )

n m

0 1 2 3 4 0 1 2 3

2. (Basic Recursion)

1. Linear Recursion, Tail Recursion Binary Recursion

2. (Series), (Functions) (Algorithms)

3. 0 n ( n 0) 1)

f(n) ==

n

0ii n = 0,1,2,3,

2) 2 ( 2 ) (1)

f(n) = 0 n = 0

(2)

f(n) ==

1n

0ii + n n = 1,2,3,

f(n) = f(n - 1) + n n = 1,2,3,

1

2

1 2 3 4 5 6 7 8 9

public static int akm(int m, int n) { if (m == 0) { return n + 1; } else if (n == 0) { return akm(m - 1, 1); } else { return akm(m - 1, akm(m, n - 1)); }

}

Nested Recursion

Recursion Iteration Wilhelm Ackermann

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3) 2 2 if-else 1 2

7 [] f() n Math (10 )

8 [] f() n Math (10 )

1 2 3 4 5 6 7

public static int f(int n) { if(n > 0) { return f(n - 1) + n; } else { return 0; } }

n 0

1 2 3 4 5 6 7

public static int f(int n) { if(n

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9 [] g() n Math (10 )

10 [] fac() (Factorial) n fac(5) 5! 120 (10 )

11 [] fibo() - (Fibonacci) fibo(n) = fibo(n - 1) + fibo(n - 2) n >= 2 fibo(0) = 0 fibo(1) = 1 (10 )

=

=

+

==

0 n 0

1 n 12 ni

11)n(g

n

2i

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12 [] fibo() - (Binary Tree) fibo(5) (5 )

13 [] pow() ab a b ( ) (10 )

14 [] f() n Math (10 )

113n1

2n11n1

n1)n(f

O++

++

+=

fibo(5)

fibo(4) fibo(3)

fibo(3) fibo(2) fibo(2) fibo(1)

fibo(1) fibo(2)

fibo(0)fibo(1)

Math

fibo(0)fibo(1)

fibo(0) fibo(1)

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15 [] (20 ) 1) g(n, m) = 1m - 2m + 3m - + (nm) n = 1,2,3, (10 ) 2) h(n) = n

1...41

31

211 +++ n = 1,2,3, (10 )

3. (Advanced Recursion)

1. 2 ( Overload ) Mutual Recursion

Math

Math

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2. (String) (Arrays)

3. Overload Overload

16 [] search() -1 (10 )

1 2 3 4 5 6 7 8 9 10 11 12

public static int max(int a[]) { return max(a, 0, a[0]); } public static int max(int a[], int i, int m) { if (i < a.length) { if (a[i] > m) m = a[i]; return max(a, i + 1, m); } else { return m; } }

max() Overload

max() max() max() - (Indirect Recursion)

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17 [] overHundred() 100 d (10 ) public class OverHundredNumber { public static void main(String[] args) { int d[] = { 99, 101, 13, 78, 200, 534, 47, 1234, 736 }; System.out.println(overHundred(d));

}

} //End of class 18 [] revStr() "Computer" "retupmoC" (10 )

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19 [] formulaAtoB() a b formulaAtoB(6, 15) 6 15 (10 ) 20 [] addArray() 2 (10 )

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21 [] isMatrixEquals() 2 (10 )

java programming - chapter 11 (in thai)

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