Permutation I,II

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还要有多典型的DFS + backtracking，之前写的乱七八糟凑出来的，后来用了这个思想好写多了。所以啊，要掌握思想就得先多看些范例。但是，dp看了这么多，还是好多dp不出来额。。。再接再励吧亲！

注意问interviewer array里面的元素是unique的吗？！

1，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].

public class Solution {    public List<List<Integer>> permute(int[] num) {        List<List<Integer>> res = new ArrayList<>();        List<Integer> list = new ArrayList<>();        boolean[] visited = new boolean[num.length];        helper(res, list, num, visited);        return res;    }        public void helper(List<List<Integer>> res, List<Integer> list, int[] num, boolean[] visited) {        if (list.size() == num.length) {            res.add(new ArrayList<Integer>(list));            return;        }                for (int i = 0; i < num.length; i++) {            if (!visited[i]) {                list.add(num[i]);                visited[i] = true;  //如果不要visited数组，直接call list.contains(i)，每个call的复杂度是O（n）                helper(res, list, num, visited);                list.remove(list.size()-1);                visited[i] = false;            }        }    }}

2. 如果array中有重复元素呢？ -》重复？先把Array sort

public class Solution {    public List<List<Integer>> permuteUnique(int[] num) {        if (num == null || num.length == 0) return null;        Arrays.sort(num);        List<List<Integer>> res = new ArrayList<>();        List<Integer> ls = new ArrayList<>();        boolean[] visited = new boolean[num.length];        helper(res, ls, num, visited);        return res;       }        public void helper(List<List<Integer>> res,  List<Integer> list, int[] num, boolean[] visited){        if(list.size() == num.length){            res.add(new ArrayList<Integer>(list));            return;        }                for (int i = 0; i < num.length; i++) {            if (visited[i] || (i > 0 && !visited[i-1] && num[i] == num[i-1])) {                continue;            }            list.add(num[i]);            visited[i] = true;            helper(res, list, num, visited);            visited[i] = false;            list.remove(list.size() - 1);        }    }}

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