# Check whether a binary string can be formed by concatenating given N numbers sequentially

Given a sequence of ‘n’ numbers (without leading zeros), the task is to find whether it is possible to create a binary string by concatenating these numbers sequentially.
If possible, then print the binary string formed, otherwise print “-1”.

Examples :

Input: arr[] = {10, 11, 1, 0, 10}
Output: 10111010
All the numbers contain the digits ‘1’ and ‘0’ only. So it is possible to form a binary string by concatenating
these numbers sequentially which is 10111010.

Input: arr[] = {1, 2, 11, 10}
Output: -1
One of the numbers contains the digit ‘2’ which cannot be a part of any binary string.
So, the output is -1.

Approach: The main observation is that we can only concatenate those numbers which contain the digits ‘1’ and ‘0’ only. Otherwise, it is impossible to form a binary string.

Below is the implementation of the above approach :

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function that returns false if``// the number passed as argument contains``// digit(s) other than '0' or '1'``bool` `isBinary(``int` `n)``{``    ``while` `(n != 0) {``        ``int` `temp = n % 10;``        ``if` `(temp != 0 && temp != 1) {``            ``return` `false``;``        ``}``        ``n = n / 10;``    ``}``    ``return` `true``;``}` `//Function that checks whether the ``//binary string can be formed or not``void` `formBinaryStr(``int` `n, ``int` `a[])``{``    ``bool` `flag = ``true``;` `    ``// Empty string for storing``    ``// the binary number``    ``string s = ``""``;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// check if a[i] can be a``        ``// part of the binary string``        ``if` `(isBinary(a[i]))` `            ``// Conversion of int into string``            ``s += to_string(a[i]);``        ``else` `{` `            ``// if a[i] can't be a part``            ``// then break the loop``            ``flag = ``false``;``            ``break``;``        ``}``    ``}` `    ``// possible to create binary string``    ``if` `(flag)``        ``cout << s << ``"\n"``;` `    ``// impossible to create binary string``    ``else``        ``cout << ``"-1\n"``;``}` `// Driver code``int` `main()``{` `    ``int` `a[] = { 10, 1, 0, 11, 10 };``    ``int` `N = ``sizeof``(a) / ``sizeof``(a[0]);` `    ``formBinaryStr(N, a);` `    ``return` `0;``}`

## Java

 `// Java  implementation of the approach``import` `java.util.*;``class` `Solution``{``// Function that returns false if``// the number passed as argument contains``// digit(s) other than '0' or '1'``static` `boolean` `isBinary(``int` `n)``{``    ``while` `(n != ``0``) {``        ``int` `temp = n % ``10``;``        ``if` `(temp != ``0` `&& temp != ``1``) {``            ``return` `false``;``        ``}``        ``n = n / ``10``;``    ``}``    ``return` `true``;``}` `//Function that checks whether the ``//binary String can be formed or not``static` `void` `formBinaryStr(``int` `n, ``int` `a[])``{``    ``boolean` `flag = ``true``;` `    ``// Empty String for storing``    ``// the binary number``    ``String s = ``""``;` `    ``for` `(``int` `i = ``0``; i < n; i++) {` `        ``// check if a[i] can be a``        ``// part of the binary String``        ``if` `(isBinary(a[i]))` `            ``// Conversion of int into String``            ``s += ``""``+a[i];``        ``else` `{` `            ``// if a[i] can't be a part``            ``// then break the loop``            ``flag = ``false``;``            ``break``;``        ``}``    ``}` `    ``// possible to create binary String``    ``if` `(flag)``        ``System.out.print( s + ``"\n"``);` `    ``// impossible to create binary String``    ``else``        ``System.out.print( ``"-1\n"``);``}` `// Driver code``public` `static` `void` `main(String args[])``{` `    ``int` `a[] = { ``10``, ``1``, ``0``, ``11``, ``10` `};``    ``int` `N = a.length;` `    ``formBinaryStr(N, a);``}``}``//contributed by Arnab Kundu`

## Python3

 `# Python3 implementation of the approach ` `# Function that returns false if the ``# number passed as argument contains ``# digit(s) other than '0' or '1' ``def` `isBinary(n): ` `    ``while` `n !``=` `0``: ``        ``temp ``=` `n ``%` `10``        ``if` `temp !``=` `0` `and` `temp !``=` `1``: ``            ``return` `False``        ` `        ``n ``=` `n ``/``/` `10``    ` `    ``return` `True` `# Function that checks whether the ``# binary string can be formed or not ``def` `formBinaryStr(n, a):` `    ``flag ``=` `True` `    ``# Empty string for storing ``    ``# the binary number ``    ``s ``=` `"" ``    ``for` `i ``in` `range``(``0``, n): ` `        ``# check if a[i] can be a ``        ``# part of the binary string ``        ``if` `isBinary(a[i]) ``=``=` `True``: ``            ` `            ``# Conversion of int into string ``            ``s ``+``=` `str``(a[i]) ``        ` `        ``else``: ``            ``# if a[i] can't be a part ``            ``# then break the loop ``            ``flag ``=` `False``            ``break` `    ``# possible to create binary string ``    ``if` `flag ``=``=` `True``:``        ``print``(s) ` `    ``# impossible to create binary string ``    ``else``:``        ``cout << ``"-1\n"` `# Driver code ``if` `__name__ ``=``=` `"__main__"``: ` `    ``a ``=` `[``10``, ``1``, ``0``, ``11``, ``10``] ``    ``N ``=` `len``(a) ` `    ``formBinaryStr(N, a) ` `# This code is contributed by Rituraj Jain `

## C#

 `// C#  implementation of the approach``using` `System;` `public` `class` `Solution``{``// Function that returns false if ``// the number passed as argument contains ``// digit(s) other than '0' or '1' ``public` `static` `bool` `isBinary(``int` `n)``{``    ``while` `(n != 0)``    ``{``        ``int` `temp = n % 10;``        ``if` `(temp != 0 && temp != 1)``        ``{``            ``return` `false``;``        ``}``        ``n = n / 10;``    ``}``    ``return` `true``;``}` `//Function that checks whether the  ``//binary String can be formed or not ``public` `static` `void` `formBinaryStr(``int` `n, ``int``[] a)``{``    ``bool` `flag = ``true``;` `    ``// Empty String for storing ``    ``// the binary number ``    ``string` `s = ``""``;` `    ``for` `(``int` `i = 0; i < n; i++)``    ``{` `        ``// check if a[i] can be a ``        ``// part of the binary String ``        ``if` `(isBinary(a[i]))``        ``{` `            ``// Conversion of int into String ``            ``s += ``""` `+ a[i];``        ``}``        ``else``        ``{` `            ``// if a[i] can't be a part ``            ``// then break the loop ``            ``flag = ``false``;``            ``break``;``        ``}``    ``}` `    ``// possible to create binary String ``    ``if` `(flag)``    ``{``        ``Console.Write(s + ``"\n"``);``    ``}` `    ``// impossible to create binary String ``    ``else``    ``{``        ``Console.Write(``"-1\n"``);``    ``}``}` `// Driver code ``public` `static` `void` `Main(``string``[] args)``{` `    ``int``[] a = ``new` `int``[] {10, 1, 0, 11, 10};``    ``int` `N = a.Length;` `    ``formBinaryStr(N, a);``}``}` `// This code is contributed by Shrikant13`

## PHP

 ``

## Javascript

 ``

Output
`10101110`

Complexity Analysis:

• Time Complexity: O(N*log(MAX)), where N is the length of the array and MAX is the maximum number in the array
• Auxiliary Complexity: O(M), where M is the length of the string

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