LeetCode: Permutations 解题报告

Permutations

Given a collection of numbers, return all possible permutations.

For example,
[1,2,3] have the following permutations:
[1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1].

SOLUTION 1:

经典的递归回溯题目，一次ACCEPT. 请也参考上一个题目LeetCode: Combinations 解题报告.

 public class Solution {
     public List<List<Integer>> permute(int[] num) {
         List<List<Integer>> ret = new ArrayList<List<Integer>>();
         if (num == null || num.length == 0) {
             return ret;
         }

         dfs(num, new ArrayList<Integer>(), ret);
         return ret;
     }

     public void dfs(int[] num, List<Integer> path, List<List<Integer>> ret) {
         int len = num.length;
         if (path.size() == len) {
             ret.add(new ArrayList<Integer>(path));
             return;
         }

         for (int i = 0; i < len; i++) {
             if (path.contains(num[i])) {
                 continue;
             }

             path.add(num[i]);
             dfs(num, path, ret);
             path.remove(path.size() - 1);
         }
     }
 }

SOLUTION 2:

可能有的同学觉得为什么path.contains不用hashmap来代替哩？所以主页君写了一个带hashmap的版本。结论是，在这个set规模小的时候，hashmap的性能还不

如arraylist。

原因可能在于，hashmap申请的不是一个连续的空间，而arraylist比较小的话，直接在连续内存中操作，速度会比较快。

以下是此程序的运行结果，hashmap的版本速度要慢一倍：

Test size:9
Computing time with HASHMAP: 629.0 millisec.
Test size:9
Computing time with list: 310.0 millisec.

 package Algorithms.permutation;

 import java.util.ArrayList;
 import java.util.HashSet;
 import java.util.LinkedHashMap;

 public class Permutation {
     public static void main(String[] strs) {
         int[] num = {1, 2, 3, 4, 5, 6, 7, 8, 9};
         System.out.printf("Test size:%d \n", num.length);

         Stopwatch timer1 = new Stopwatch();

         permute(num);
         System.out
                 .println("Computing time with HASHMAP: "
                         + timer1.elapsedTime() + " millisec.");

         System.out.printf("Test size:%d \n", num.length);

         Stopwatch timer2 = new Stopwatch();

         permute2(num);
         System.out
                 .println("Computing time with list: "
                         + timer2.elapsedTime() + " millisec.");
     }

     public static ArrayList<ArrayList<Integer>> permute(int[] num) {
         ArrayList<ArrayList<Integer>> ret = new ArrayList<ArrayList<Integer>>();
         if (num == null) {
             return ret;
         }

         permuteHelp(num, ret, new LinkedHashMap<Integer, Integer>());
         return ret;
     }

     public static void permuteHelp(int[] num, ArrayList<ArrayList<Integer>> ret, LinkedHashMap<Integer, Integer> set) {
         if (set.size() == num.length) {

             ArrayList<Integer> list = new ArrayList<Integer>();
             for (Integer i: set.keySet()){
                 list.add(i);
             }
             ret.add(list);
             return;
         }

         int len = num.length;
         for (int i = 0; i < len; i++) {
             if (set.containsKey(num[i])) {
                 continue;
             }

             //path.add(num[i]);
             set.put(num[i], 0);
             permuteHelp(num, ret, set);
             //path.remove(path.size() - 1);
             set.remove(num[i]);
         }
     }

     public static ArrayList<ArrayList<Integer>> permute2(int[] num) {
         ArrayList<ArrayList<Integer>> ret = new ArrayList<ArrayList<Integer>>();
         if (num == null) {
             return ret;
         }

         ArrayList<Integer> path = new ArrayList<Integer>();
         permuteHelp2(num, path, ret);
         return ret;
     }

     public static void permuteHelp2(int[] num, ArrayList<Integer> path, ArrayList<ArrayList<Integer>> ret) {
         if (path.size() == num.length) {
             ret.add(new ArrayList<Integer>(path));
             return;
         }

         int len = num.length;
         for (int i = 0; i < len; i++) {
             if (path.contains(num[i])) {
                 continue;
             }

             path.add(num[i]);
             permuteHelp2(num, path, ret);
             path.remove(path.size() - 1);
         }
     }
 }

GITHUB:

https://github.com/yuzhangcmu/LeetCode_algorithm/blob/master/dfs/Permute.java