用C打印字符串的所有排列
我正在学习回溯和递归，我坚持使用算法来打印字符串的所有排列。我使用bell algorithm进行排列解决了但是我无法理解递归方法。我搜索了网络，发现了这段代码：
void permute(char *a, int i, int n)
{
int j;
if (i == n)
printf("%s\n", a);
else
{
for (j = i; j <= n; j++)
{
swap((a+i), (a+j));
permute(a, i+1, n);
swap((a+i), (a+j));
}
}
}
这个算法基本上如何工作我无法理解？我甚至尝试过干跑！
如何应用回溯？
它是否比贝尔算法更有效地计算排列？
9 个答案:
答案 0 :(得分：24)
该算法基本上适用于此逻辑：
字符串X的所有排列与X中每个可能字符的所有排列相同，并且与字符串X中没有该字母的所有排列相结合。
也就是说，“abcd”的所有排列都是
- “a”与“bcd”的所有排列相结合
- “b”与“acd”的所有排列相结合
- “c”与“坏”的所有排列相结合
- “d”与“bca”的所有排列相结合
该算法特别是不对子串执行递归，而是在输入字符串上执行递归，不使用额外的内存来分配子串。 “回溯”撤消对字符串的更改，使其保持原始状态。
答案 1 :(得分：11)
代码有2个问题，两者都与n相关，字符串的假定长度。代码for (j = i; j <= n; j++) { swap((a+i), (a+j)); ...交换字符串的空字符'\0'并提供代码截断结果。检查原来的(i == n) (i == (n-1))。
通过调用swap()两次有效撤消其原始交换来应用回溯。
贝尔算法的复杂度顺序相同。
#include <stdio.h>
void swap(char *a, char *b) { char t = *a; *a = *b; *b = t; }
void permute(char *a, int i, int n) {
// If we are at the last letter, print it
if (i == (n-1)) printf("%s\n", a);
else {
// Show all the permutations with the first i-1 letters fixed and
// swapping the i'th letter for each of the remaining ones.
for (int j = i; j < n; j++) {
swap((a+i), (a+j));
permute(a, i+1, n);
swap((a+i), (a+j));
}
}
}
char s[100];
strcpy(s, "ABCD");
permute(s, 0, strlen(s));
答案 2 :(得分：9)
您找到的代码是正确的！该算法将字符串中的当前字符与所有后续字符交换，并递归调用该函数。用文字难以解释。下图可能对您有所帮助。
在第二次交换中正在进行反向跟踪以反转第一次交换的效果，即我们将返回到原始字符串，现在将使用当前字符交换数组中的下一个字符。算法的时间复杂性。因为循环运行n次并且置换函数被称为n，所以是O（n * n！）！倍。 （对于第一次迭代，它被称为n次;对于第二次迭代（n-1）次，依此类推）。
来源：http://www.geeksforgeeks.org/write-a-c-program-to-print-all-permutations-of-a-given-string/
答案 3 :(得分：5)
递归确实简化了它：
public static void permutation(String str)
{
permutation("", str);
}
private static void permutation(String prefix, String str)
{
int n = str.length();
if (n == 0) {
System.out.println(prefix);
} else {
for (int i = 0; i < n; i++)
permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
}
}
答案 4 :(得分：1)
伪代码：
String permute(String a[])
{
if (a[].length == 1)
return a[];
for (i = 0, i < a[].length(); i++)
append(a[i], permute(a[].remove(i)));
}
答案 5 :(得分：1)
I create more specific but not efficient Program for permutation for general string.
It's work nice way.
//ubuntu 13.10 and g++ compiler but it's works on any platform and OS
//All Permutation of general string.
#include<iostream>
#include<stdio.h>
#include<string>
#include<string.h>
using namespace std;
int len;
string str;
void permutation(int cnum)
{
int mid;
int flag=1;
int giga=0;
int dead=0;
int array[50];
for(int i=0;i<len-1;i++)
{
array[50]='\0';
dead=0;
for(int j=cnum;j<len+cnum;j++)
{
mid=j%len;
if(mid==cnum && flag==1)
{
cout<<str[mid];
array[dead]=mid;
dead++;
flag=0;
}
else
{
giga=(i+j)%len;
for(int k=0;k<dead;k++)
{
if((array[k]==giga) && flag==0)
{
giga=(giga+1)%len;
}
}
cout<<str[giga];
array[dead]=giga;
dead++;
}
}
cout<<endl;
flag=1;
}
}
int main()
{
cout<<"Enter the string :: ";
getline(cin,str);
len=str.length();
cout<<"String length = "<<len<<endl;
cout<<"Total permutation = "<<len*(len-1)<<endl;
for(int j=0;j<len;j++)
{
permutation(j);
}
return 0;
}
答案 6 :(得分：0)
# include <stdio.h>
/* Function to swap values at two pointers */
void swap (char *x, char *y)
{
char temp;
temp = *x;
*x = *y;
*y = temp;
}
/* Function to print permutations of string
This function takes three parameters:
1. String
2. Starting index of the string
3. Ending index of the string. */
void permute(char *a, int i, int n)
{
int j;
if (i == n)
printf("%s\n", a);
else
{
for (j = i; j <= n; j++)
{
swap((a+i), (a+j));
permute(a, i+1, n);
swap((a+i), (a+j)); //backtrack
}
}
}
/* Driver program to test above functions */
int main()
{
char a[] = "ABC";
permute(a, 0, 2);
getchar();
return 0;
}
答案 7 :(得分：0)
def perms(s):
if len(s) < 1:
return [s]
ps = []
for i in range(0, len(s)):
head, tail = s[i], s[0:i] + s[i + 1:]
ps.extend([head + tailp for tailp in perms(tail)])
return ps
答案 8 :(得分：-1)
我在GeeksForGeeks分析了这个回溯算法的执行时遇到了同样的问题。亲自看看它是如何执行的。有时打印值确实有助于可视化程序的执行
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 0 //////// l = 0 //////// r = 2 //////// string = ABC
permute(a, l+1, r); ==== Values send to permute i.e. string= ABC //////// (l+1) = 1 //////// r = 2
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 1 //////// l = 1 //////// r = 2 //////// string = ABC
permute(a, l+1, r); ==== Values send to permute i.e. string= ABC //////// (l+1) = 2 //////// r = 2
ABC
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 1 //////// l = 1 //////// r = 2 //////// string = ABC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 2 //////// l = 1 //////// r = 2 //////// string = ACB
permute(a, l+1, r); ==== Values send to permute i.e. string= ACB //////// (l+1) = 2 //////// r = 2
ACB
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 2 //////// l = 1 //////// r = 2 //////// string = ABC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i));++++ Backtract swap //////// i= 0 //////// l = 0 //////// r = 2 //////// string = ABC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 1 //////// l = 0 //////// r = 2 //////// string = BAC
permute(a, l+1, r); ==== Values send to permute i.e. string= BAC //////// (l+1) = 1 //////// r = 2
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 1 //////// l = 1 //////// r = 2 //////// string = BAC
permute(a, l+1, r); ==== Values send to permute i.e. string= BAC //////// (l+1) = 2 //////// r = 2
BAC
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 1 //////// l = 1 //////// r = 2 //////// string = BAC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 2 //////// l = 1 //////// r = 2 //////// string = BCA
permute(a, l+1, r); ==== Values send to permute i.e. string= BCA //////// (l+1) = 2 //////// r = 2
BCA
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 2 //////// l = 1 //////// r = 2 //////// string = BAC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i));++++ Backtract swap //////// i= 1 //////// l = 0 //////// r = 2 //////// string = ABC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 2 //////// l = 0 //////// r = 2 //////// string = CBA
permute(a, l+1, r); ==== Values send to permute i.e. string= CBA //////// (l+1) = 1 //////// r = 2
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 1 //////// l = 1 //////// r = 2 //////// string = CBA
permute(a, l+1, r); ==== Values send to permute i.e. string= CBA //////// (l+1) = 2 //////// r = 2
CBA
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 1 //////// l = 1 //////// r = 2 //////// string = CBA
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i)); ~~~~ Forward swap the //////// i= 2 //////// l = 1 //////// r = 2 //////// string = CAB
permute(a, l+1, r); ==== Values send to permute i.e. string= CAB //////// (l+1) = 2 //////// r = 2
CAB
______________________________________________________________________
swap((a+l), (a+i));++++ Backtract swap //////// i= 2 //////// l = 1 //////// r = 2 //////// string = CBA
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
swap((a+l), (a+i));++++ Backtract swap //////// i= 2 //////// l = 0 //////// r = 2 //////// string = ABC
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
------------------------------END OF BACKTRACK--------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------
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