几个经典的递归小程序

 1 /*
 2  * 取球问题：
 3  * 从n个球中取出m个有多少种取法？
 4  */
 5 
 6 public class Main {
 7 
 8     public static void main(String[] args) {
 9         System.out.println(quQiu(10, 3));
10     }
11 
12     static int quQiu(int n, int m) {
13         if (n < m) {
14             return 0;
15         }
16         if (n == m) {
17             return 1;
18         }
19         if (m == 0) {
20             return 1;
21         }
22         return quQiu(n - 1, m) + quQiu(n - 1, m - 1); // 弄一个特殊球，再分该球取不取两种情况
23     }
24 
25 }

 1 /*
 2  * 全排列问题：
 3  * 求n个元素的全排列？
 4  */
 5 
 6 public class Main {
 7 
 8     public static void main(String[] args) {
 9         char[] a = "ABCDEFG".toCharArray();
10         paiLie(a, 0);
11     }
12 
13     static void paiLie(char[] a, int index) {
14         if (index == a.length) {
15             System.out.println(a);
16         }
17         for (int i = index; i < a.length; i++) {
18             char temp = a[index];
19             a[index] = a[i];
20             a[i] = temp;
21 
22             paiLie(a, i + 1);
23 
24             temp = a[index]; // 回溯
25             a[index] = a[i];
26             a[i] = temp;
27         }
28     }
29 
30 }

 1 /*
 2  * 计算m个A，n个B可以组成多少排列？
 3  * 如:AABB,ABB......
 4  */
 5 
 6 public class Main {
 7 
 8     public static void main(String[] args) {
 9         System.out.println(paiLie(2, 1));
10     }
11     
12     static int paiLie(int m,int n){
13         if(m==0||n==0){
14             return 1;
15         }
16         return paiLie(m-1, n)+paiLie(m, n-1);
17     }
18 
19 }

/*
 * 最大子序列长度：
 * 求两个串的最大公共子序列长度？
 */

public class Main {

    public static void main(String[] args) {
        System.out.println(ziXuLieChangDu("abc", "xbacd"));
    }

    static int ziXuLieChangDu(String s1, String s2) {
        if (s1.length() <= 0 || s2.length() <= 0) {
            return 0;
        }
        if (s1.charAt(0) == s2.charAt(0)) { // 假设首位相等
            return 1 + ziXuLieChangDu(s1.substring(1), s2.substring(1));
        } else {
            return Math.max(ziXuLieChangDu(s1.substring(1), s2), ziXuLieChangDu(s1, s2.substring(1)));
        }
    }

}

 1 /*
 2  * 整数分化问题:
 3  * 对于给定的正整数n，打印所有分化部分
 4  */
 5 
 6 public class Main {
 7 
 8     public static void main(String[] args) {
 9         int[] a = new int[6];
10         fenHua(6, a, 0);
11     }  
12 
13     static void fenHua(int n, int[] a, int index) {
14         if (n <= 0) {
15             for (int i = 0; i < index; i++) {
16                 System.out.print(a[i] + " ");
17             }
18             System.out.println();
19         }
20         for (int i = n; i > 0; i--) {
21             if (index > 0 && i > a[index - 1]) {        //先大后小
22                 continue;
23             }
24             a[index] = i;
25             fenHua(n - i, a, index + 1);
26         }
27     }
28 
29 }