数据结构学习----递归(Java实现)

普通递归：

package com.clarck.datastructure.digit;

public class Digit_9 {
    /**
     * 递归方法
     * 
     * @param i
     * @param n
     */
    static void count(int i, int n) {
        if (i < n) {
            System.out.print(i + " ");
            count(i + 1, n);
        }
        System.out.print(i + " ");
    }

    public static void main(String[] args) {
        int i, j, n = 9;
        for (i = 1; i <= n; i++) {
            for (j = n; j > i; j--) {
                System.out.print("  ");
            }
            count(1, i);
            System.out.println();
        }
    }
}

运行结果：

                1 
              1 2 1 
            1 2 3 2 1 
          1 2 3 4 3 2 1 
        1 2 3 4 5 4 3 2 1 
      1 2 3 4 5 6 5 4 3 2 1 
    1 2 3 4 5 6 7 6 5 4 3 2 1 
  1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 
1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 

 

求 n！：

package com.clarck.datastructure.digit;

/**
 * 求 n！
 * 
 * @author clarck
 * 
 */
public class Factorial {
    /**
     * 求阶乘n!,递归方法
     * 
     * @param n
     * @return
     */
    public static int factorial(int n) {
        if (n < 0) {
            throw new java.lang.IllegalArgumentException("n = " + n);
        }

        if (n == 0 || n == 1) {
            return 1;
        }

        return n * factorial(n - 1);
    }
    
    public static void main(String[] args) {
        int n = 5;
        System.out.println(n + "!=" + factorial(n));
        
        System.out.println(n + "!=" + toString(n) + factorial(n));
    }

    public static String toString(int n) {
        if (n > 0) {
            return toString(n, "");
        }
        
        throw new java.lang.IllegalArgumentException("n = " + n);
    }
    
    public static String toString(int n, String str) {
        if (n == 0 || n == 1) {
            return "";
        } else {
            str += n + "*" + (n -1) + "!=" + toString(n - 1, str);
            return str;
        }
    }
}

运行结果：

5!=120
5!=5*4!=4*3!=3*2!=2*1!=120

 

用递归算法求Fibonacci数列：

package com.clarck.datastructure.digit;

/**
 * 用递归算法求Fibonacci数列
 * 
 * @author clarck
 * 
 */
public class Fibonacci {
    /**
     * 返回Fibonacci数列第n项，递归方法
     * @param n
     * @return
     */
    public static int fib(int n) {
        if (n < 0) {
            throw new java.lang.IllegalArgumentException("n = " + n);
        }
        
        if (n == 0 || n == 1) {
            return n;
        }
        
        return fib(n - 2) + fib(n - 1);
    }
    
    public static void main(String[] args) {
        for (int i = 0; i <= 24; i++) {
            System.out.print(fib(i) + " ");
        }
        System.out.println();
    }
}

运行结果：

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368