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）

這道題難是難在這個(gè)ArrayList<String> res是用在argument還是返回值，糾結(jié)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??

這就想到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 }

?

轉(zhuǎn)載于:https://www.cnblogs.com/EdwardLiu/p/4339017.html

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