A permutation is an act of rearranging or reordering elements of a set or string etc.

**For n elements, n! (n factorial) permutations are possible.**

Ex-> Possible permutations of abc are abc, acb, bac, bca, cab, cba.

Here, given a string with n elements, we have to generate all possible permutation of this string.

### Algorithm

- Start with the original string str and call the function find_permuation() with parameters original string, start index(0) and end index(str.size()-1).
- Iterate through every element of the string and perform the following operation i.e, for(i in the range start to end-1).
- For every ith element of the string swap it with the 0th element, i.e, swap(str[start],str[i])
- Fix the current element, and again call the find_permuatation() function with parameters: the updated string, start index = current start index + 1 and original end index i.e, find_permuatation(str, start+1, end);
- After the current recursion terminates, re-swap the ith index with the 0th index i.e., swap(str[i],str[start])
- If start == end, we have reached the end of the recursion and found the permutation, print it and return
- Repeat step 2 to step 6 for every string element.

```
find_permutation(str, start, end){
if(start == end)
print(str)
for i in range [start to end){
swap(str[start], str[i]);
//we fixed the ith index and now in next recursion
//we will work with the remaining string elements
find_permutation(str, start+1, end);
swap(str[i], str[start]);
}
return 0;
}
```

### Implementation of the above Algorithm in CPP

### Output

`abc`

acb

bac

bca

cba

cab

###

Time Complexity

The time complexity of the above algorithm is O(N*N!) where N is the size of the string.

This post was originally published at **nlogn**

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