Given a number **N** and a digit **K** (1 < K <= 9), the task is to find two integers **A** and **B** such that **A + B = N** and digit K is **not present** in either A or B.

**Examples:**

Input:N = 443, K = 4Output:256, 187Explanation:

Sum = 256 + 187 = 443 = N

Also, K(4) is not present in 256 or 187

Hence, 256 and 187 are valid output.

Input:N = 678, K = 9Output:311, 367Explanation:

Sum = 311 + 367 = 678 = N

Also, K(9) is not present in 311 or 367

Hence, 311 and 367 are valid output.

**Naive Approach:**

A simple approach is to run a loop and consider each element (say A) from 1 to N-1. Since the sum of A and B has to be N, corresponding B will be (N – A). Now check if both A and B contain K or not, if no, then print A and B. This approach will fail for larger inputs like N = 10^{18}.

**Time complexity:** O(N)**Auxiliary Space:** O(1)

**Efficient Approach:**

The given problem can be solved much more efficiently. The idea is to break each digit **D** of N into two parts **D1** and **D2** such that D1 + D2 = D. Take two strings **A** and **B**, A will contain all D1’s, and string B will contain all D2’s.

For example, N = 4467 and K = 4

D D1 D24 2 2 4 2 2 6 6 0 7 7 0

Here, A will be 2267 and B will be 2200.

Detailed steps of this approach are as follows: **1.** Traverse **N** and consider each of its digit **D**. **2.** If digit D is same as K, break it into D1 = D / 2 and D2 = D / 2 + D % 2.

D % 2 is added to D2 to ensure that D1 + D2 = D for both even and odd D. **3.** Else, break it into D1 = D and D2 = 0. **4.** Keep appending D1’s to string A and D2’s to string B. **5.** Finally, print string A and B, after removing leading zeros(if any).

Below is the implementation of the above approach:

## C++

`// C++ implementation of` `// the above approach` `#include <iostream>` `using` `namespace` `std;` `string removeLeadingZeros(string str)` `{` ` ` `// Count leading zeros` ` ` `int` `i = 0;` ` ` `int` `n = str.length();` ` ` `while` `(str[i] == ` `'0'` `&& i < n)` ` ` `i++;` ` ` `// It removes i characters` ` ` `// starting from index 0` ` ` `str.erase(0, i);` ` ` `return` `str;` `}` `void` `findPairs(` `int` `sum, ` `int` `K)` `{` ` ` `string A, B;` ` ` `A = ` `""` `;` ` ` `B = ` `""` `;` ` ` `string N = to_string(sum);` ` ` `int` `n = N.length();` ` ` `// Check each digit of the N` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `int` `D = N[i] - ` `'0'` `;` ` ` `// If digit is K break it` ` ` `if` `(D == K) {` ` ` `int` `D1, D2;` ` ` `D1 = D / 2;` ` ` `// For odd numbers` ` ` `D2 = D / 2 + D % 2;` ` ` `// Add D1 to A and D2 to B` ` ` `A = A + ` `char` `(D1 + ` `'0'` `);` ` ` `B = B + ` `char` `(D2 + ` `'0'` `);` ` ` `}` ` ` `// If the digit is not K,` ` ` `// no need to break` ` ` `// string D in A and 0 in B` ` ` `else` `{` ` ` `A = A + ` `char` `(D + ` `'0'` `);` ` ` `B = B + ` `'0'` `;` ` ` `}` ` ` `}` ` ` `// Remove leading zeros` ` ` `A = removeLeadingZeros(A);` ` ` `B = removeLeadingZeros(B);` ` ` `// Print the answer` ` ` `cout << A << ` `", "` `<< B << endl;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `N = 33673;` ` ` `int` `K = 3;` ` ` `findPairs(N, K);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the above approach` `class` `GFG{` `static` `String removeLeadingZeros(String str)` `{` ` ` ` ` `// Count leading zeros` ` ` `int` `i = ` `0` `;` ` ` `int` `n = str.length();` ` ` ` ` `while` `(str.charAt(i) == ` `'0'` `&& i < n)` ` ` `i++;` ` ` `// It removes i characters` ` ` `// starting from index 0` ` ` `str = str.substring(i);` ` ` `return` `str;` `}` `static` `void` `findPairs(` `int` `sum, ` `int` `K)` `{` ` ` `String A, B;` ` ` `A = ` `""` `;` ` ` `B = ` `""` `;` ` ` `String N = String.valueOf(sum);` ` ` `int` `n = N.length();` ` ` `// Check each digit of the N` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `{` ` ` `int` `D = N.charAt(i) - ` `'0'` `;` ` ` ` ` `// If digit is K break it` ` ` `if` `(D == K)` ` ` `{` ` ` `int` `D1, D2;` ` ` `D1 = D / ` `2` `;` ` ` ` ` `// For odd numbers` ` ` `D2 = D / ` `2` `+ D % ` `2` `;` ` ` ` ` `// Add D1 to A and D2 to B` ` ` `A = A + (` `char` `)(D1 + ` `'0'` `);` ` ` `B = B + (` `char` `)(D2 + ` `'0'` `);` ` ` `}` ` ` ` ` `// If the digit is not K,` ` ` `// no need to break` ` ` `// String D in A and 0 in B` ` ` `else` ` ` `{` ` ` `A = A + (` `char` `)(D + ` `'0'` `);` ` ` `B = B + ` `'0'` `;` ` ` `}` ` ` `}` ` ` ` ` `// Remove leading zeros` ` ` `A = removeLeadingZeros(A);` ` ` `B = removeLeadingZeros(B);` ` ` `// Print the answer` ` ` `System.out.print(A + ` `", "` `+ B + ` `"\n"` `);` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `33673` `;` ` ` `int` `K = ` `3` `;` ` ` `findPairs(N, K);` `}` `}` `// This code is contributed by sapnasingh4991` |

## Python3

`# Python3 implementation of the` `# above approach` `def` `removeLeadingZeros(` `Str` `):` ` ` ` ` `# Count leading zeros` ` ` `i ` `=` `0` ` ` `n ` `=` `len` `(` `Str` `)` ` ` ` ` `while` `(` `Str` `[i] ` `=` `=` `'0'` `and` `i < n):` ` ` `i ` `+` `=` `1` ` ` ` ` `# It removes i characters` ` ` `# starting from index 0` ` ` `Str` `=` `Str` `[i:]` ` ` `return` `Str` ` ` `def` `findPairs(` `Sum` `, K):` ` ` ` ` `A ` `=` `""` ` ` `B ` `=` `""` ` ` ` ` `N ` `=` `str` `(` `Sum` `)` ` ` `n ` `=` `len` `(N)` ` ` `# Check each digit of the N` ` ` `for` `i ` `in` `range` `(n):` ` ` ` ` `D ` `=` `int` `(N[i]) ` `-` `int` `(` `'0'` `)` ` ` ` ` `# If digit is K break it` ` ` `if` `(D ` `=` `=` `K):` ` ` `D1 ` `=` `D ` `/` `/` `2` `;` ` ` ` ` `# For odd numbers` ` ` `D2 ` `=` `(D ` `/` `/` `2` `) ` `+` `(D ` `%` `2` `)` ` ` `# Add D1 to A and D2 to B` ` ` `A ` `=` `A ` `+` `(` `str` `)(D1 ` `+` `int` `(` `'0'` `))` ` ` `B ` `=` `B ` `+` `(` `str` `)(D2 ` `+` `int` `(` `'0'` `))` ` ` ` ` `# If the digit is not K,` ` ` `# no need to break` ` ` `# String D in A and 0 in B` ` ` `else` `:` ` ` `A ` `=` `A ` `+` `(` `str` `)(D ` `+` `int` `(` `'0'` `))` ` ` `B ` `=` `B ` `+` `'0'` ` ` ` ` `# Remove leading zeros` ` ` `A ` `=` `removeLeadingZeros(A)` ` ` `B ` `=` `removeLeadingZeros(B)` ` ` ` ` `# Print the answer` ` ` `print` `(A ` `+` `", "` `+` `B)` ` ` `# Driver code` `N ` `=` `33673` `K ` `=` `3` `findPairs(N, K)` `# This code is contributed divyeshrabadiya07` |

## C#

`// C# implementation of the above approach` `using` `System;` `class` `GFG{` ` ` `static` `String removeLeadingZeros(String str)` `{` ` ` ` ` `// Count leading zeros` ` ` `int` `i = 0;` ` ` `int` `n = str.Length;` ` ` ` ` `while` `(str[i] == ` `'0'` `&& i < n)` ` ` `i++;` ` ` ` ` `// It removes i characters` ` ` `// starting from index 0` ` ` `str = str.Substring(i);` ` ` ` ` `return` `str;` `}` ` ` `static` `void` `findPairs(` `int` `sum, ` `int` `K)` `{` ` ` ` ` `String A, B;` ` ` `A = ` `""` `;` ` ` `B = ` `""` `;` ` ` ` ` `String N = String.Join(` `""` `, sum);` ` ` `int` `n = N.Length;` ` ` ` ` `// Check each digit of the N` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `{` ` ` `int` `D = N[i] - ` `'0'` `;` ` ` ` ` `// If digit is K break it` ` ` `if` `(D == K)` ` ` `{` ` ` `int` `D1, D2;` ` ` `D1 = D / 2;` ` ` ` ` `// For odd numbers` ` ` `D2 = D / 2 + D % 2;` ` ` ` ` `// Add D1 to A and D2 to B` ` ` `A = A + (` `char` `)(D1 + ` `'0'` `);` ` ` `B = B + (` `char` `)(D2 + ` `'0'` `);` ` ` `}` ` ` ` ` `// If the digit is not K,` ` ` `// no need to break` ` ` `// String D in A and 0 in B` ` ` `else` ` ` `{` ` ` `A = A + (` `char` `)(D + ` `'0'` `);` ` ` `B = B + ` `'0'` `;` ` ` `}` ` ` `}` ` ` ` ` `// Remove leading zeros` ` ` `A = removeLeadingZeros(A);` ` ` `B = removeLeadingZeros(B);` ` ` ` ` `// Print the answer` ` ` `Console.Write(A + ` `", "` `+ B + ` `"\n"` `);` `}` ` ` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `N = 33673;` ` ` `int` `K = 3;` ` ` ` ` `findPairs(N, K);` `}` `}` `// This code is contributed by sapnasingh4991` |

**Output:**

11671, 22002

**Time complexity:** O(M)**Auxiliary Space:** O(M)

Here, M is the number of digits in N.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**