Climbing Stairs - Print Path

stair climbing， print out all of possible solutions of the methods to climb a stars, you are allowed climb one or two steps for each time; what is time/space complexity? （use recursion）

这道题难是难在这个ArrayList<String> res是用在argument还是返回值，纠结了好久

Recursion 解法：

 1 package fib;

 2 

 3 import java.util.ArrayList;

 4 

 5 public class climbingstairs {

 6     

 7     public ArrayList<String> climb (int n) {

 8         if (n <= 0) return null;

 9         ArrayList<String> res = new ArrayList<String>();

10         if (n == 1) {

11             res.add("1");

12             return res;

13         }

14         if (n == 2) {

15             res.add("2");

16             res.add("12");

17             return res;

18         }

19         ArrayList<String> former2 =  climb(n-2); 

20         for (String item : former2) {

21             res.add(item+Integer.toString(n));

22         }

23         ArrayList<String> former1 = climb(n-1);

24         for (String item : former1) {

25             res.add(item+Integer.toString(n));

26         }

27         return res;

28     }

29 

30     

31     public static void main(String[] args) {

32         climbingstairs obj = new climbingstairs();

33         ArrayList<String> res = obj.climb(6);

34         for (String item : res) {

35             System.out.println(item);

36         }

37     }

38 

39 }

Sample input : 6

Sample Output: 

246
1246
1346
2346
12346
1356
2356
12356
2456
12456
13456
23456
123456

 

 follow up: could you change the algorithm to save space? 

这就想到DP，用ArrayList<ArrayList<String>>

 1 import java.util.ArrayList;

 2 

 3 public class climbingstairs {

 4     

 5     public ArrayList<String> climb (int n) {

 6         if (n <= 0) return null;

 7         ArrayList<ArrayList<String>> results = new ArrayList<ArrayList<String>>();

 8         for (int i=1; i<=n; i++) {

 9             results.add(new ArrayList<String>());

10         }

11         if (n >= 1) {

12             results.get(0).add("1");

13         }

14         if (n >= 2) {

15             results.get(1).add("2");

16             results.get(1).add("12");

17         }

18 

19         for (int i=3; i<=n; i++) {

20             ArrayList<String> step = results.get(i-1);

21             ArrayList<String> former2 = results.get(i-3);

22             for (String item : former2) {

23                 step.add(item+Integer.toString(i));

24             }

25             ArrayList<String> former1 = results.get(i-2);

26             for (String item : former1) {

27                 step.add(item+Integer.toString(i));

28             }

29         }

30         return results.get(n-1);

31     }

32 

33     

34     public static void main(String[] args) {

35         climbingstairs obj = new climbingstairs();

36         ArrayList<String> res = obj.climb(5);

37         for (String item : res) {

38             System.out.println(item);

39         }

40     }

41 

42 }