# Print all interleavings of given two strings

Given two strings str1 and str2, write a function that prints all interleavings of the given two strings. You may assume that all characters in both strings are different

Example:

```Input: str1 = "AB",  str2 = "CD"
Output:
ABCD
ACBD
ACDB
CABD
CDAB

Input: str1 = "AB",  str2 = "C"
Output:
ABC
ACB
CAB
```

An interleaved string of given two strings preserves the order of characters in individual strings. For example, in all the interleavings of above first example, ‘A’ comes before ‘B’ and ‘C’ comes before ‘D’.

Let the length of str1 be m and the length of str2 be n. Let us assume that all characters in str1 and str2 are different. Let count(m, n) be the count of all interleaved strings in such strings. The value of count(m, n) can be written as following.

```     count(m, n) = count(m-1, n) + count(m, n-1)
count(1, 0) = 1 and count(0, 1) = 1
```

To print all interleavings, we can first fix the first character of str1[0..m-1] in output string, and recursively call for str1[1..m-1] and str2[0..n-1]. And then we can fix the first character of str2[0..n-1] and recursively call for str1[0..m-1] and str2[1..n-1]. Thanks to akash01 for providing following C implementation.

`// C/C++ program to print all interleavings of given two strings`
`#include <stdio.h>`
`#include <stdlib.h>`
`#include <string.h>`
`// The main function that recursively prints all interleavings. `
`// The variable iStr is used to store all interleavings (or `
`// output strings) one by one.  `
`// i is used to pass next available place in iStr`
`void` `printIlsRecur (``char` `*str1, ``char` `*str2, ``char` `*iStr, ``int` `m, `
`                    ``int` `n, ``int` `i)`
`{`
`    ``// Base case: If all characters of str1 and str2 have been `
`    ``// included in output string, then print the output string`
`    ``if` `(m==0 && n==0)`
`        ``printf``(``"%s\n"``, iStr) ;`
`    ``// If some characters of str1 are left to be included, then`
`    ``// include the  first character from the remaining characters`
`    ``// and recur for rest`
`    ``if` `(m != 0)`
`    ``{`
`        ``iStr[i] = str1[0];`
`        ``printIlsRecur (str1 + 1, str2, iStr, m-1, n, i+1);`
`    ``}`
`    ``// If some characters of str2 are left to be included, then`
`    ``// include the  first character from the remaining characters `
`    ``// and recur for rest`
`    ``if` `(n != 0)`
`    ``{`
`        ``iStr[i] = str2[0];`
`        ``printIlsRecur(str1, str2+1, iStr, m, n-1, i+1);`
`    ``}`
`}`
`// Allocates memory for output string and uses printIlsRecur()`
`// for printing all interleavings`
`void` `printIls (``char` `*str1, ``char` `*str2, ``int` `m, ``int` `n)`
`{`
`   ``// allocate memory for the output string`
`   ``char` `*iStr= (``char``*)``malloc``((m+n+1)*``sizeof``(``char``));`
`   ``// Set the terminator for the output string`
`   ``iStr[m+n] = ``'\0'``;`
`   ``// print all interleavings using printIlsRecur()`
`   ``printIlsRecur (str1, str2, iStr, m, n, 0);`
`   ``// free memory to avoid memory leak`
`   ``free``(iStr); `
`}`
`// Driver program to test above functions`
`int` `main()`
`{`
`    ``char` `str1[] = ``"AB"``;`
`    ``char` `str2[] = ``"CD"``;`
`    ``printIls (str1, str2, ``strlen``(str1), ``strlen``(str2));`
`    ``return` `0;`
`}`

Output:

```ABCD
ACBD
ACDB
CABD
CDAB```