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# Find if it is possible to make a binary string which contains given number of “0”, “1” , “01” and “10” as sub sequences

• Difficulty Level : Medium
• Last Updated : 31 May, 2022

Given four integers l, m, x, and y. The task is to check whether it is possible to make a binary string consisting of l 0’s, m 1’s, x “01” and y “10” as sub-sequences in it.
Examples:

Input: l = 3, m = 2, x = 4, y = 2
Output: Yes
Possible string is “00110”. It contains 3 0’s, 2 1’s,
4 “01” sub-sequences and 2 “10” sub-sequences.
Input: l = 3, m = 2, x = 4, y = 3
Output: No
No such binary string exists.

Approach: The possible string is always of form 00…11…00…. First consists of some number of zeroes, then all ones, and then the remaining number of zeros.
Let l1 be the number of zeros before ones and l2 be the number of zeros after ones then the equations are:

1. l1 + l2 = l (Total number of zeros).
2. l1 * m = x (Number of “01” sub-sequences).
3. m * l2 = y (Number of “10” sub-sequences).

From the above three equations, we get x + y = l * m. If this equation fails for the given values then the string is not possible else print Yes.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function that returns true if it is possible to` `// make a binary string consisting of l 0's, m 1's,` `// x "01" sub-sequences and y "10" sub-sequences` `bool` `isPossible(``int` `l, ``int` `m, ``int` `x, ``int` `y)` `{` `    ``if` `(l * m == x + y)` `        ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `l = 3, m = 2, x = 4, y = 2;`   `    ``if` `(isPossible(l, m, x, y))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach ` `class` `sol` `{` `    `  `// Function that returns true if it is possible to ` `// make a binary string consisting of l 0's, m 1's, ` `// x "01" sub-sequences and y "10" sub-sequences ` `static` `boolean` `isPossible(``int` `l, ``int` `m, ``int` `x, ``int` `y) ` `{ ` `    ``if` `(l * m == x + y) ` `        ``return` `true``; `   `    ``return` `false``; ` `} `   `// Driver code ` `public` `static` `void` `main(String args[])` `{ ` `    ``int` `l = ``3``, m = ``2``, x = ``4``, y = ``2``; `   `    ``if` `(isPossible(l, m, x, y)) ` `        ``System.out.print(``"Yes"``); ` `    ``else` `        ``System.out.print(``"No"``); `   `} ` `}`   `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 implementation of the approach `   `# Function that returns true if it is possible to ` `# make a binary string consisting of l 0's, m 1's, ` `# x "01" sub-sequences and y "10" sub-sequences ` `def` `isPossible(l, m, x, y) :` `    `  `    ``if` `(l ``*` `m ``=``=` `x ``+` `y) :` `        ``return` `True``; `   `    ``return` `False``; `   `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``l ``=` `3``; m ``=` `2``; x ``=` `4``; y ``=` `2``; `   `    ``if` `(isPossible(l, m, x, y)) :` `        ``print``(``"Yes"``); ` `    ``else` `:` `        ``print``(``"No"``); ` `        `  `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach ` `using` `System;`   `class` `sol` `{` `    `  `// Function that returns true if it is possible to ` `// make a binary string consisting of l 0's, m 1's, ` `// x "01" sub-sequences and y "10" sub-sequences ` `static` `Boolean isPossible(``int` `l, ``int` `m, ``int` `x, ``int` `y) ` `{ ` `    ``if` `(l * m == x + y) ` `        ``return` `true``; `   `    ``return` `false``; ` `} `   `// Driver code ` `public` `static` `void` `Main(String []args)` `{ ` `    ``int` `l = 3, m = 2, x = 4, y = 2; `   `    ``if` `(isPossible(l, m, x, y)) ` `        ``Console.WriteLine(``"Yes"``); ` `    ``else` `        ``Console.WriteLine(``"No"``); ` `} ` `}`   `// This code is contributed by Arnab Kundu`

## Javascript

 ``

Output:

`Yes`

Time Complexity : O(1)

Auxiliary Space: O(1)

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