给定一个大小为N的数组nums[] ，任务是打印数组nums[] 的所有可能的不同排列(包括重复项)。
Input: nums[] = { 1, 2, 2 }
Output:
1 2 1
2 1 2
2 2 1
Input: nums[] = { 1, 1 }
Output: 1 1
方法：按照以下步骤解决问题
- 遍历数组。
- 生成数组的排列。
- 设置重复元素之间的选择顺序。
- 如果I> 0 && NUMS [I] == NUMS [I – 1]：添加NUMS [i]于仅当NUMS [I – 1]的当前排列访问已在置换加入，即[I – 1]是真的。
- 否则，继续。
- 使用这种方法，打印生成的不同排列。
检查此递归树以了解代码的实现细节。
下面是上述方法的实现：
C++14
// C++ Program to implement
// the above approach
#include
using namespace std;
// Function to fill the vector curr
// while maintaining the indices visited
// in the array num
void backtrack(vector& nums,
vector& curr,
vector >& ans,
vector& visited)
{
// If current permutation is complete
if ((int)curr.size() == (int)nums.size()) {
ans.push_back(curr);
}
// Traverse the input vector
for (int i = 0; i < (int)nums.size();
i++) {
// If index is already visited
if (visited[i])
continue;
// If the numebr is dupicate
if (i > 0 and nums[i] == nums[i - 1]
and !visited[i - 1])
continue;
// Set visited[i] flag as true
visited[i] = true;
// Push nums[i] to current vector
curr.push_back(nums[i]);
// Recursive function call
backtrack(nums, curr,
ans, visited);
// Backtrack to the previous
// state by unsetting visited[i]
visited[i] = false;
// Pop nums[i] and place at
// the back of the vector
curr.pop_back();
}
}
// Function to pre-process the vector num
vector > permuteDuplicates(
vector& nums)
{
// Sort the array
sort(nums.begin(), nums.end());
// Stores distinct permutations
vector > ans;
vector visited(
(int)nums.size(), false);
// Store the current permutation
vector curr;
// Find the distinct permutations of num
backtrack(nums, curr, ans, visited);
return ans;
}
// Function call to print all distinct
// permutations of the vector nums
void getDistinctPermutations(vector nums)
{
// Find the distinct permutations
vector > ans
= permuteDuplicates(nums);
// Traverse every row
for (int i = 0; i < (int)ans.size();
i++) {
// Traverse every column
for (int j = 0; j < (int)ans[i].size();
j++) {
cout << ans[i][j] << " ";
}
cout << '\n';
}
}
// Driver Code
int main()
{
// Input
vector nums = { 1, 2, 2 };
// Function call to print
// all distinct permutations
getDistinctPermutations(nums);
return 0;
} Java
// Java Program to implement
// the above approach
import java.io.*;
import java.util.*;
class GFG {
static ArrayList nums = new ArrayList();
static ArrayList curr = new ArrayList();
static ArrayList> ans = new ArrayList>();
static ArrayList visited = new ArrayList();
// Function to fill the vector curr
// while maintaining the indices visited
// in the array num
static void backtrack()
{
// If current permutation is complete
if (curr.size() == nums.size())
{
ans.add(curr);
for(int i = 0; i < curr.size(); i++)
{
System.out.print(curr.get(i) +" ");
}
System.out.println();
}
// Traverse the input vector
for (int i = 0; i < (int)nums.size();
i++)
{
// If index is already visited
if (visited.get(i))
continue;
// If the numebr is dupicate
if (i > 0 && (nums.get(i) == nums.get(i - 1)) && !visited.get(i - 1))
continue;
// Set visited[i] flag as true
visited.set(i, true);
// Push nums[i] to current vector
curr.add(nums.get(i));
// Recursive function call
backtrack();
// Backtrack to the previous
// state by unsetting visited[i]
visited.set(i, false);
// Pop nums[i] and place at
// the back of the vector
curr.remove(curr.size() - 1);
}
}
// Function to pre-process the vector num
static ArrayList> permuteDuplicates()
{
// Sort the array
Collections.sort(nums);
for(int i = 0; i < nums.size(); i++)
{
visited.add(false);
}
// Find the distinct permutations of num
backtrack();
return ans;
}
// Function call to print all distinct
// permutations of the vector nums
static void getDistinctPermutations()
{
ans = permuteDuplicates();
}
// Driver code
public static void main (String[] args)
{
// Input
nums.add(1);
nums.add(2);
nums.add(2);
// Function call to print
// all distinct permutations
getDistinctPermutations();
}
}
// This code is contributed by avanitrachhadiya2155 Python3
# Python3 Program to implement
# the above approach
# Function to fill the vector curr
# while maintaining the indices visited
# in the array num
def backtrack():
global ans, curr, visited, nums
# If current permutation is complete
# print(ans)
if (len(curr) == len(nums)):
print(*curr)
# Traverse the input vector
for i in range(len(nums)):
# If index is already visited
if (visited[i]):
continue
# If the numebr is dupicate
if (i > 0 and nums[i] == nums[i - 1] and visited[i - 1]==False):
continue
# Set visited[i] flag as true
visited[i] = True
# Push nums[i] to current vector
curr.append(nums[i])
# Recursive function call
backtrack()
# Backtrack to the previous
# state by unsetting visited[i]
visited[i] = False
# Pop nums[i] and place at
# the back of the vector
del curr[-1]
# Function to pre-process the vector num
def permuteDuplicates(nums):
global ans, visited, curr
nums = sorted(nums)
# Find the distinct permutations of num
backtrack()
return ans
# Function call to print all distinct
# permutations of the vector nums
def getDistinctPermutations(nums):
global ans, curr, visited
# Find the distinct permutations
ans = permuteDuplicates(nums)
# Driver Code
if __name__ == '__main__':
visited = [False]*(5)
ans,curr = [], []
nums = [1, 2, 2]
# Function call to print
# all distinct permutations
getDistinctPermutations(nums)
# This code is contributed by mohit kumar 29.C#
// C# Program to implement
// the above approach
using System;
using System.Collections.Generic;
public class GFG{
static List nums = new List();
static List curr = new List();
static List> ans = new List>();
static List visited = new List();
// Function to fill the vector curr
// while maintaining the indices visited
// in the array num
static void backtrack()
{
// If current permutation is complete
if (curr.Count == nums.Count)
{
ans.Add(curr);
for(int i = 0; i < curr.Count; i++)
{
Console.Write(curr[i] +" ");
}
Console.WriteLine();
}
// Traverse the input vector
for (int i = 0; i < (int)nums.Count;
i++)
{
// If index is already visited
if (visited[i])
continue;
// If the numebr is dupicate
if (i > 0 && (nums[i] == nums[i-1]) && !visited[i-1])
continue;
// Set visited[i] flag as true
visited[i] = true;
// Push nums[i] to current vector
curr.Add(nums[i]);
// Recursive function call
backtrack();
// Backtrack to the previous
// state by unsetting visited[i]
visited[i] = false;
// Pop nums[i] and place at
// the back of the vector
curr.RemoveAt(curr.Count - 1);
}
}
// Function to pre-process the vector num
static List> permuteDuplicates()
{
// Sort the array
nums.Sort();
for(int i = 0; i < nums.Count; i++)
{
visited.Add(false);
}
// Find the distinct permutations of num
backtrack();
return ans;
}
// Function call to print all distinct
// permutations of the vector nums
static void getDistinctPermutations()
{
ans = permuteDuplicates();
}
// Driver code
static public void Main (){
// Input
nums.Add(1);
nums.Add(2);
nums.Add(2);
// Function call to print
// all distinct permutations
getDistinctPermutations();
}
}
// This code is contributed by rag2127 输出：
1 2 2
2 1 2
2 2 1时间复杂度： O(N! * N)
辅助空间：O(N!*N)
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