# Check if a binary string contains all permutations of length k

Given a binary string and k, to check whether it’s contains all permutations of length k or not.

Examples:

Input : Binary string 11001 k : 2 Output : Yes 11001 contains all possibilities of binary sequences with k = 2, 00, 01, 10, 11 Input : Binary string: 1001 k : 2 Output: No 1001 does not contain all possibilities of binary sequences with k = 2. Here 11 sequence is missing

**Explanation:**

In this example one binary sequence of length k is not found it is 0110.

So all binary sequences with k=4 will be 2^{4}=16. they are following

0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111,

1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111

All should be sub string of given binary string then print Yes otherwise No

**Algorithm**

Taking binary string and the size k. In binary string we check binary sequences are matched or not. Binary sequence is made of size k, as we know that in binary using 0 and 1 digit so to generate total binary subsets is 2^{k} element. The main idea behind it, to store all binary value in list as string and then compare list all item to given binary string as subset. If all are occur inside the binary string then print “Yes” otherwise print “No”.

## JAVA

`// Java program to Check a binary string ` `// contains all permutations of length k. ` ` ` `import` `java.util.*; ` `public` `class` `Checkbinary { ` ` ` ` ` `// to check all Permutation in given String ` ` ` `public` `static` `boolean` `tocheck(String s, ` `int` `k) ` ` ` `{ ` ` ` `List<String> list = BinarySubsets(k); ` ` ` ` ` `// to check binary sequences are available ` ` ` `// in string or not ` ` ` `for` `(String b : list) ` ` ` `if` `(s.indexOf(b) == -` `1` `) ` ` ` `return` `false` `; ` ` ` ` ` `return` `true` `; ` ` ` `} ` ` ` ` ` `// to generate all binary subsets of given length k ` ` ` `public` `static` `List<String> BinarySubsets(` `int` `k) ` ` ` `{ ` ` ` `// Declare the list as String ` ` ` `List<String> list = ` `new` `ArrayList<>(); ` ` ` ` ` `// to define the format of binary of ` ` ` `// given length k ` ` ` `String format = ` `"%0"` `+ k + ` `"d"` `; ` ` ` ` ` `// returns the string representation of the ` ` ` `// unsigned integer value represented by ` ` ` `// the argument in binary (base 2) using ` ` ` `// Integer.toBinaryString and convert it ` ` ` `// into integer using Integer.valueOf. ` ` ` `// Loop for 2<sup>k</sup> elements ` ` ` `for` `(` `int` `i = ` `0` `; i < Math.pow(` `2` `, k); i++) ` ` ` `{ ` ` ` `// To add in the list all possible ` ` ` `// binary sequence of given length ` ` ` `list.add(String.format(format, ` ` ` `Integer.valueOf(Integer.toBinaryString(i)))); ` ` ` ` ` `/* To Show all binary sequence of given ` ` ` `length k ` ` ` `System.out.println(String.format(format, ` ` ` `Integer.valueOf(Integer.toBinaryString(i))));*/` ` ` `} ` ` ` `return` `list; ` ` ` `} ` ` ` ` ` `// drive main ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `String str = ` `"11001"` `; ` ` ` `int` `num = ` `2` `; ` ` ` `if` `(tocheck(str, num)) ` ` ` `System.out.println(` `"Yes"` `); ` ` ` `else` ` ` `System.out.println(` `"No"` `); ` ` ` `} ` `} ` |

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Output:

Yes

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