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

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 = 2Output: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 = 3Output:No

No such binary string exists.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the

Essential Maths for CP Courseat a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please referComplete Interview Preparation Course.

**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:

**l1 + l2 = l**(Total number of zeros).**l1 * m = x**(Number of “01” sub-sequences).**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 <bits/stdc++.h>` `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

`<script>` `// Javascript 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` `function` `isPossible(l, m, x, y)` `{` ` ` `if` `(l * m == x + y)` ` ` `return` `true` `;` ` ` `return` `false` `;` `}` `// Driver code` ` ` `let l = 3, m = 2, x = 4, y = 2;` ` ` `if` `(isPossible(l, m, x, y))` ` ` `document.write(` `"Yes"` `);` ` ` `else` ` ` `document.write(` `"No"` `);` `</script>` |

**Output:**

Yes