# Binary string with given frequencies of sums of consecutive pairs of characters

Given three integers P, Q, and R, the task is to generate a binary string with P, Q, and R pairs of consecutive characters with sum 0, 1, and 2 respectively.
Examples:

Input: P = 1, Q = 2, R = 2
Output: 111001
Explanation:
Substrings “00”, “10”, “01”, and “11” have sums 0, 1, 1, and 2 respectively.
Thus, the following set of substrings { {“11”}, {“11”}, {“10”}, {“00”}, {“01”} } satisfy the given constraints. Hence, the string formed by the substrings is 111001.
Input: P = 3, Q = 1, R = 0
Output: 10000

Approach: In order to solve this problem, we need to follow the following steps:

• If P and R are non-zero, then there is at least one pair of consecutive characters with sum 1. Thus, if Q provided is 0, in such a case, then no such string can be formed. Hence, return -1.
• If Q is zero, and only one of P and R is non-zero, then append 0 P+1 times if P is non-zero or append 1 R+1 time if R is non-zero.
• If all of them are non-zero:
• Append 0 and 1 P + 1 and Q + 1 times respectively.
• Append 0 and 1 alternatingly Q – 1 time.

Below is the implementation of the above approach:

 `// C++ program to generate a binary` `// string with given frequencies` `// of sums of consecutive` `// pair of characters`   `#include ` `using` `namespace` `std;`   `// A Function that generates` `// and returns the binary string` `string build_binary_str(``int` `p,` `                        ``int` `q, ``int` `r)` `{`   `    ``// P: Frequency of consecutive` `    ``// characters with sum 0` `    ``// Q: Frequency of consecutive` `    ``// characters with sum 1` `    ``// R: Frequency of consecutive` `    ``// characters with sum 2`   `    ``string ans = ``""``;`   `    ``// If no consecutive` `    ``// character adds up to 1` `    ``if` `(q == 0) {`   `        ``// Not possible if both P` `        ``// and Q are non - zero` `        ``if` `(p != 0 && r != 0) {` `            ``return` `"-1"``;` `        ``}`   `        ``else` `{`   `            ``// If P is not equal to 0` `            ``if` `(p) {`   `                ``// Append 0 P + 1 times` `                ``ans = string(p + 1, ``'0'``);` `            ``}` `            ``else` `{` `                ``// Append 1 R + 1 times` `                ``ans = string(r + 1, ``'1'``);` `            ``}` `        ``}` `    ``}` `    ``else` `{`   `        ``// Append "01" to satisfy Q` `        ``for` `(``int` `i = 1; i <= q + 1; i++) {` `            ``if` `(i % 2 == 0) {` `                ``ans += ``'0'``;` `            ``}` `            ``else` `{` `                ``ans += ``'1'``;` `            ``}` `        ``}`   `        ``// Append "0" P times` `        ``ans.insert(1, string(p, ``'0'``));`   `        ``// Append "1" R times` `        ``ans.insert(0, string(r, ``'1'``));` `    ``}` `    ``return` `ans;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `p = 1, q = 2, r = 2;` `    ``cout << build_binary_str(p, q, r);` `    ``return` `0;` `}`

 `// Java program to generate a binary` `// String with given frequencies` `// of sums of consecutive` `// pair of characters` ` ``class` `GFG{` ` `  `// A Function that generates` `// and returns the binary String` `static` `String build_binary_str(``int` `p,` `                               ``int` `q, ``int` `r)` `{` ` `  `    ``// P: Frequency of consecutive` `    ``// characters with sum 0` `    ``// Q: Frequency of consecutive` `    ``// characters with sum 1` `    ``// R: Frequency of consecutive` `    ``// characters with sum 2` `    ``String ans = ``""``;` ` `  `    ``// If no consecutive` `    ``// character adds up to 1` `    ``if` `(q == ``0``) ` `    ``{` ` `  `        ``// Not possible if both P` `        ``// and Q are non - zero` `        ``if` `(p != ``0` `&& r != ``0``) ` `        ``{` `            ``return` `"-1"``;` `        ``}` ` `  `        ``else` `        ``{` `          `  `            ``// If P is not equal to 0` `            ``if` `(p > ``0``) ` `            ``{` ` `  `                ``// Append 0 P + 1 times` `                ``ans = Strings(p + ``1``, ``'0'``);` `            ``}` `            ``else` `            ``{` `                ``// Append 1 R + 1 times` `                ``ans = Strings(r + ``1``, ``'1'``);` `            ``}` `        ``}` `    ``}` `    ``else` `    ``{` ` `  `        ``// Append "01" to satisfy Q` `        ``for` `(``int` `i = ``1``; i <= q + ``1``; i++) ` `        ``{` `            ``if` `(i % ``2` `== ``0``) ` `            ``{` `                ``ans += ``'0'``;` `            ``}` `            ``else` `            ``{` `                ``ans += ``'1'``;` `            ``}` `        ``}` ` `  `        ``// Append "0" P times` `        ``ans = ans.substring(``0``, ``1``) + Strings(p, ``'0'``) + ans.substring(``1``);` ` `  `        ``// Append "1" R times` `        ``ans = Strings(r, ``'1'``) + ans;` `    ``}` `    ``return` `ans;` `}` ` `  `static` `String Strings(``int` `p, ``char` `c) ` `{` `    ``String ans = ``""``;` `    ``for` `(``int` `i = ``0``; i < p; i++)` `        ``ans += c;` `    ``return` `ans;` `}` ` `  `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `p = ``1``, q = ``2``, r = ``2``;` `    ``System.out.print(build_binary_str(p, q, r));` `}` `}`   `// This code is contributed by shikhasingrajput`

 `# Python3 program to generate a binary` `# string with given frequencies` `# of sums of consecutive` `# pair of characters`   `# A Function that generates` `# and returns the binary string` `def` `build_binary_str(p, q, r):` `    `  `    ``# P: Frequency of consecutive` `    ``# characters with sum 0` `    ``# Q: Frequency of consecutive` `    ``# characters with sum 1` `    ``# R: Frequency of consecutive` `    ``# characters with sum 2` `    ``ans ``=` `""`   `    ``# If no consecutive` `    ``# character adds up to 1` `    ``if` `(q ``=``=` `0``):` `        `  `        ``# Not possible if both P` `        ``# and Q are non - zero` `        ``if` `(p !``=` `0` `and` `r !``=` `0``):` `            ``return` `"-1"`   `        ``else``:` `            `  `            ``# If P is not equal to 0` `            ``if` `(p):` `                `  `                ``# Append 0 P + 1 times` `                ``temp ``=` `""` `                ``for` `i ``in` `range``(p ``+` `1``):` `                    ``temp ``+``=` `'0'` `                    `  `                ``ans ``=` `temp` `                `  `            ``else``:` `                `  `                ``# Append 1 R + 1 times` `                ``temp ``=` `""` `                ``for` `i ``in` `range``(r ``+` `1``):` `                    ``temp ``+``=` `'1'` `                    `  `                ``ans ``=` `temp`   `    ``else``:` `        `  `        ``# Append "01" to satisfy Q` `        ``for` `i ``in` `range``(``1``, q ``+` `2``):` `            ``if` `(i ``%` `2` `=``=` `0``):` `                ``ans ``+``=` `'0'` `            ``else``:` `                ``ans ``+``=` `'1'`   `        ``# Append "0" P times` `        ``temp ``=` `""` `        ``for` `i ``in` `range``(p):` `            ``temp ``+``=` `'0'` `            `  `        ``st ``=` `""` `        ``st ``+``=` `ans[``0``]` `        ``st ``+``=` `temp` `        `  `        ``for` `i ``in` `range``(``1``, ``len``(ans)):` `            ``st ``+``=` `ans[i]` `            `  `        ``ans ``=` `st`   `        ``# Append "1" R times` `        ``temp ``=` `""` `        ``for` `i ``in` `range``(r):` `            ``temp ``+``=` `'1'`   `        ``ans ``=` `temp ``+` `ans` `        `  `    ``return` `ans`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``p ``=` `1` `    ``q ``=` `2` `    ``r ``=` `2` `    `  `    ``print``(build_binary_str(p, q, r))`   `# This code is contributed by Surendra_Gangwar`

 `// C# program to generate a binary` `// String with given frequencies` `// of sums of consecutive` `// pair of characters` `using` `System;` `class` `GFG{` ` `  `// A Function that generates` `// and returns the binary String` `static` `String build_binary_str(``int` `p,` `                               ``int` `q, ``int` `r)` `{ ` `  ``// P: Frequency of consecutive` `  ``// characters with sum 0` `  ``// Q: Frequency of consecutive` `  ``// characters with sum 1` `  ``// R: Frequency of consecutive` `  ``// characters with sum 2` `  ``String ans = ``""``;`   `  ``// If no consecutive` `  ``// character adds up to 1` `  ``if` `(q == 0) ` `  ``{ ` `    ``// Not possible if both P` `    ``// and Q are non - zero` `    ``if` `(p != 0 && r != 0) ` `    ``{` `      ``return` `"-1"``;` `    ``}`   `    ``else` `    ``{          ` `      ``// If P is not equal to 0` `      ``if` `(p > 0) ` `      ``{ ` `        ``// Append 0 P + 1 times` `        ``ans = Strings(p + 1, ``'0'``);` `      ``}` `      ``else` `      ``{` `        ``// Append 1 R + 1 times` `        ``ans = Strings(r + 1, ``'1'``);` `      ``}` `    ``}` `  ``}` `  ``else` `  ``{ ` `    ``// Append "01" to satisfy Q` `    ``for` `(``int` `i = 1; i <= q + 1; i++) ` `    ``{` `      ``if` `(i % 2 == 0) ` `      ``{` `        ``ans += ``'0'``;` `      ``}` `      ``else` `      ``{` `        ``ans += ``'1'``;` `      ``}` `    ``}`   `    ``// Append "0" P times` `    ``ans = ans.Substring(0, 1) + ` `          ``Strings(p, ``'0'``) + ` `          ``ans.Substring(1);`   `    ``// Append "1" R times` `    ``ans = Strings(r, ``'1'``) + ans;` `  ``}` `  ``return` `ans;` `}`   `  ``static` `String Strings(``int` `p, ``char` `c) ` `  ``{` `    ``String ans = ``""``;` `    ``for` `(``int` `i = 0; i < p; i++)` `      ``ans += c;` `    ``return` `ans;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `Main(String[] args)` `  ``{` `    ``int` `p = 1, q = 2, r = 2;` `    ``Console.Write(build_binary_str(p, ` `                                   ``q, r));` `  ``}` `}`   `// This code is contributed by 29AjayKumar`

Output:
```111001

```

Time Complexity: O(P + Q + R)

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