已知一个有重复字符的字符串，打印其所有不同的字符排列

原文地址：Print all distinct permutations of a given string with duplicates

已知一个字符串，其中可能包括相同的字符。写一个函数打印这些字符的排列，但不能有重复的排列。

例子：

Input:  str[] = "AB"
Output: AB BA

Input:  str[] = "AA"
Output: AA

Input:  str[] = "ABC"
Output: ABC ACB BAC BCA CBA CAB

Input:  str[] = "ABA"
Output: ABA AAB BAA

Input:  str[] = "ABCA"
Output: AABC AACB ABAC ABCA ACBA ACAB BAAC BACA BCAA CABA CAAB CBAA

我们已经在前面讨论过了打印所有的排列，但是那个代码不能处理相同的字符，打印出来的会有相同的排序。

// Program to print all permutations of a string in sorted order.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Following function is needed for library function qsort(). */
int compare(const void *a, const void * b)
{
return ( *(char *)a - *(char *)b );
}

// A utility function two swap two characters a and b
void swap(char* a, char* b)
{
char t = *a;
*a = *b;
*b = t;
}

// This function finds the index of the smallest character
// which is greater than 'first' and is present in str[l..h]
int findCeil(char str[], char first, int l, int h)
{
// initialize index of ceiling element
int ceilIndex = l;

// Now iterate through rest of the elements and find
// the smallest character greater than 'first'
for (int i = l+1; i <= h; i++)
if (str[i] > first && str[i] < str[ceilIndex])
ceilIndex = i;

return ceilIndex;
}

// Print all permutations of str in sorted order
void sortedPermutations(char str[])
{
// Get size of string
int size = strlen(str);

// Sort the string in increasing order
qsort(str, size, sizeof( str[0] ), compare);

// Print permutations one by one
bool isFinished = false;
while (!isFinished)
{
// print this permutation
static int x = 1;
printf("%d  %s \n", x++, str);

// Find the rightmost character which is smaller than its next
// character. Let us call it 'first char'
int i;
for (i = size - 2; i >= 0; --i)
if (str[i] < str[i+1])
break;

// If there is no such chracter, all are sorted in decreasing order,
// means we just printed the last permutation and we are done.
if (i == -1)
isFinished = true;
else
{
// Find the ceil of 'first char' in right of first character.
// Ceil of a character is the smallest character greater than it
int ceilIndex = findCeil(str, str[i], i + 1, size - 1);

// Swap first and second characters
swap(&str[i], &str[ceilIndex]);

// Sort the string on right of 'first char'
qsort(str + i + 1, size - i - 1, sizeof(str[0]), compare);
}
}
}

// Driver program to test above function
int main()
{
char str[] = "ACBC";
sortedPermutations( str );
return 0;
}

输出：

1  ABCC
2  ACBC
3  ACCB
4  BACC
5  BCAC
6  BCCA
7  CABC
8  CACB
9  CBAC
10  CBCA
11  CCAB
12  CCBA

时间复杂度： O(n2 * n!)

附加空间： O(1)