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剑指 Offer II 084. 含有重复元素集合的全排列

题目描述

给定一个可包含重复数字的整数集合 nums ，按任意顺序 返回它所有不重复的全排列。

 

示例 1：

输入：nums = [1,1,2]
输出：
[[1,1,2],
 [1,2,1],
 [2,1,1]]

示例 2：

输入：nums = [1,2,3]
输出：[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

 

提示：

  • 1 <= nums.length <= 8
  • -10 <= nums[i] <= 10

 

注意：本题与主站 47 题相同： https://leetcode.cn/problems/permutations-ii/

解法

方法一

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class Solution:
    def permuteUnique(self, nums: List[int]) -> List[List[int]]:
        n = len(nums)
        res = []
        path = [0] * n
        used = [False] * n
        nums.sort()

        def dfs(u):
            if u == n:
                res.append(path.copy())
                return
            for i in range(n):
                if used[i] or (i > 0 and nums[i] == nums[i - 1] and not used[i - 1]):
                    continue
                path[u] = nums[i]
                used[i] = True
                dfs(u + 1)
                used[i] = False

        dfs(0)
        return res

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class Solution {
    public List<List<Integer>> permuteUnique(int[] nums) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> path = new ArrayList<>();
        int n = nums.length;
        boolean[] used = new boolean[n];
        Arrays.sort(nums);
        dfs(0, n, nums, used, path, res);
        return res;
    }

    private void dfs(
        int u, int n, int[] nums, boolean[] used, List<Integer> path, List<List<Integer>> res) {
        if (u == n) {
            res.add(new ArrayList<>(path));
            return;
        }
        for (int i = 0; i < n; ++i) {
            if (used[i] || (i > 0 && nums[i] == nums[i - 1] && !used[i - 1])) {
                continue;
            }
            path.add(nums[i]);
            used[i] = true;
            dfs(u + 1, n, nums, used, path, res);
            used[i] = false;
            path.remove(path.size() - 1);
        }
    }
}

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class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        int n = nums.size();
        vector<vector<int>> res;
        vector<int> path(n, 0);
        vector<bool> used(n, false);
        sort(nums.begin(), nums.end());
        dfs(0, n, nums, used, path, res);
        return res;
    }

    void dfs(int u, int n, vector<int>& nums, vector<bool>& used, vector<int>& path, vector<vector<int>>& res) {
        if (u == n) {
            res.emplace_back(path);
            return;
        }
        for (int i = 0; i < n; ++i) {
            if (used[i] || (i > 0 && nums[i] == nums[i - 1] && !used[i - 1])) continue;
            path[u] = nums[i];
            used[i] = true;
            dfs(u + 1, n, nums, used, path, res);
            used[i] = false;
        }
    }
};

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func permuteUnique(nums []int) [][]int {
    n := len(nums)
    res := make([][]int, 0)
    path := make([]int, n)
    used := make([]bool, n)
    sort.Ints(nums)
    dfs(0, n, nums, used, path, &res)
    return res
}

func dfs(u, n int, nums []int, used []bool, path []int, res *[][]int) {
    if u == n {
        t := make([]int, n)
        copy(t, path)
        *res = append(*res, t)
        return
    }
    for i := 0; i < n; i++ {
        if used[i] || (i > 0 && nums[i] == nums[i-1] && !used[i-1]) {
            continue
        }
        path[u] = nums[i]
        used[i] = true
        dfs(u+1, n, nums, used, path, res)
        used[i] = false
    }
}

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using System.Collections.Generic;
using System.Linq;

public class Solution {
    public IList<IList<int>> PermuteUnique(int[] nums) {
        var results = new List<IList<int>>();
        var temp = new List<int>();
        var count = nums.GroupBy(n => n).ToDictionary(g => g.Key, g => g.Count());
        Search(count, temp, results);
        return results;
    }

    private void Search(Dictionary<int, int> count, IList<int> temp, IList<IList<int>> results)
    {
        if (!count.Any() && temp.Any())
        {
            results.Add(new List<int>(temp));
            return;
        }
        var keys = count.Keys.ToList();
        foreach (var key in keys)
        {
            temp.Add(key);
            --count[key];
            if (count[key] == 0) count.Remove(key);
            Search(count, temp, results);
            temp.RemoveAt(temp.Count - 1);
            if (count.ContainsKey(key))
            {
                ++count[key];
            }
            else
            {
                count[key] = 1;
            }
        }
    }
}

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class Solution {
    func permuteUnique(_ nums: [Int]) -> [[Int]] {
        var res = [[Int]]()
        var path = [Int]()
        var used = [Bool](repeating: false, count: nums.count)
        let sortedNums = nums.sorted()
        dfs(0, sortedNums.count, sortedNums, &used, &path, &res)
        return res
    }

    private func dfs(
        _ u: Int, _ n: Int, _ nums: [Int], _ used: inout [Bool], _ path: inout [Int], _ res: inout [[Int]]
    ) {
        if u == n {
            res.append(path)
            return
        }
        for i in 0..<n {
            if used[i] || (i > 0 && nums[i] == nums[i - 1] && !used[i - 1]) {
                continue
            }
            path.append(nums[i])
            used[i] = true
            dfs(u + 1, n, nums, &used, &path, &res)
            used[i] = false
            path.removeLast()
        }
    }
}

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