# Find the minimum positive integer such that it is divisible by A and sum of its digits is equal to B

Given two integers A and B, the task is to find the minimum positive integer N such that N is divisible by A and the sum of the digits of N is equal to B. If number is not found then print -1.

Examples:

Input: A = 20, B = 30
Output: 49980
49980 is divisible by 20 and sum of its digit = 4 + 9 + 9 + 8 + 0 = 30

Input: A = 5, B = 2
Output: 20

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Create empty queue q that stores the value of A and B and output number as a string and create integer type 2-D array visited[][] that stores the visited digit.
• Insert Node into queue and check if queue is non-empty.
• While the queue is non-empty, pop an element from the queue and for every digit from 1 to 9, concatenate the digit after the string num and check whether the number formed is the required number.
• If the required number is found, print the number.
• Else repeat the steps while the number is less than B and the queue is non-empty while pushing the non-visited number to the queue.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Array that stores visited digits ` `int` `visited[501][5001]; ` ` `  `// Structure for queue Node. ` `struct` `Node { ` `    ``int` `a, b; ` `    ``string str; ` `}; ` ` `  `// Function to return the minimum number such that it is ` `// divisible by 'a' and sum of its digits is equals to 'b' ` `int` `findNumber(``int` `a, ``int` `b) ` `{ ` `    ``// Create queue ` `    ``queue q; ` ` `  `    ``// Initially queue is empty ` `    ``Node temp = Node{ 0, 0, ``""` `}; ` ` `  `    ``// Initialize visited to 1 ` `    ``visited[0][0] = 1; ` ` `  `    ``// Push temp in queue ` `    ``q.push(temp); ` ` `  `    ``// While queue is not empty ` `    ``while` `(!q.empty()) { ` ` `  `        ``// Get the front of the queue and pop it ` `        ``Node u = q.front(); ` `        ``q.pop(); ` ` `  `        ``// If popped element is the required number ` `        ``if` `(u.a == 0 && u.b == b) ` ` `  `            ``// Parse int from string and return it ` `            ``return` `std::stoi(u.str); ` ` `  `        ``// Loop for each digit and check the sum  ` `        ``// If not visited then push it to the queue ` `        ``for` `(``int` `i = 0; i < 10; i++) { ` `            ``int` `dd = (u.a * 10 + i) % a; ` `            ``int` `ss = u.b + i; ` `            ``if` `(ss <= b && !visited[dd][ss]) { ` `                ``visited[dd][ss] = 1; ` `                ``q.push(Node{ dd, ss, u.str + ``char``(``'0'` `+ i) }); ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Required number not found return -1. ` `    ``return` `-1; ` `} ` ` `  `// Driver code. ` `int` `main() ` `{ ` `    ``int` `a = 25, b = 1; ` `    ``cout << findNumber(a, b); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` `class` `Solution ` `{ ` `  `  `// Array that stores visited digits ` `static` `int` `visited[][]= ``new` `int``[``501``][``5001``]; ` `  `  `// Structure for queue Node. ` `static` `class` `Node { ` `    ``int` `a, b; ` `    ``String str; ` `    ``Node(``int` `a1,``int` `b1,String s) ` `    ``{ ` `        ``a=a1; ` `        ``b=b1; ` `        ``str=s; ` `    ``} ` `} ` `  `  `// Function to return the minimum number such that it is ` `// divisible by 'a' and sum of its digits is equals to 'b' ` `static` `int` `findNumber(``int` `a, ``int` `b) ` `{ ` `    ``// Create queue ` `    ``Queue q= ``new` `LinkedList(); ` `  `  `    ``// Initially queue is empty ` `    ``Node temp =``new`  `Node( ``0``, ``0``, ``""` `); ` `  `  `    ``// Initialize visited to 1 ` `    ``visited[``0``][``0``] = ``1``; ` `  `  `    ``// Push temp in queue ` `    ``q.add(temp); ` `  `  `    ``// While queue is not empty ` `    ``while` `(q.size()!=``0``) { ` `  `  `        ``// Get the front of the queue and pop it ` `        ``Node u = q.peek(); ` `        ``q.remove(); ` `  `  `        ``// If popped element is the required number ` `        ``if` `(u.a == ``0` `&& u.b == b) ` `  `  `            ``// Parse int from string and return it ` `            ``return` `Integer.parseInt(u.str); ` `  `  `        ``// Loop for each digit and check the sum  ` `        ``// If not visited then push it to the queue ` `        ``for` `(``int` `i = ``0``; i < ``10``; i++) { ` `            ``int` `dd = (u.a * ``10` `+ i) % a; ` `            ``int` `ss = u.b + i; ` `            ``if` `(ss <= b && visited[dd][ss]==``0``) { ` `                ``visited[dd][ss] = ``1``; ` `                ``q.add(``new` `Node( dd, ss, u.str + (``char``)(``'0'` `+ i) )); ` `            ``} ` `        ``} ` `    ``} ` `  `  `    ``// Required number not found return -1. ` `    ``return` `-``1``; ` `} ` `  `  `// Driver code. ` `public` `static` `void`  `main(String args[]) ` `{ ` `    ``//initilize visited ` `    ``for``(``int` `i=``0``;i<``500``;i++) ` `        ``for``(``int` `j=``0``;j<``500``;j++) ` `            ``visited[i][j]=``0``; ` `     `  `    ``int` `a = ``25``, b = ``1``; ` `    ``System.out.println(findNumber(a, b)); ` `     `  `} ` `} ` `//contributed by Arnab Kundu `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Array that stores visited digits  ` `visited ``=` `[[``0` `for` `x ``in` `range``(``501``)]  ` `              ``for` `y ``in` `range``(``5001``)]  ` ` `  `# Structure for queue Node.  ` `class` `Node: ` `     `  `    ``def` `__init__(``self``, a, b, string): ` `        ``self``.a ``=` `a ` `        ``self``.b ``=` `b ` `        ``self``.string ``=` `string ` ` `  `# Function to return the minimum number  ` `# such that it is divisible by 'a' and ` `# sum of its digits is equals to 'b'  ` `def` `findNumber(a, b):  ` ` `  `    ``# Use list as queue  ` `    ``q ``=` `[] ` ` `  `    ``# Initially queue is empty  ` `    ``temp ``=` `Node(``0``, ``0``, "")  ` ` `  `    ``# Initialize visited to 1  ` `    ``visited[``0``][``0``] ``=` `1` ` `  `    ``# Push temp in queue  ` `    ``q.append(temp)  ` ` `  `    ``# While queue is not empty  ` `    ``while` `len``(q) > ``0``:  ` ` `  `        ``# Get the front of the queue  ` `        ``# and pop it  ` `        ``u ``=` `q.pop(``0``)  ` ` `  `        ``# If popped element is the  ` `        ``# required number  ` `        ``if` `u.a ``=``=` `0` `and` `u.b ``=``=` `b:  ` ` `  `            ``# Parse int from string  ` `            ``# and return it  ` `            ``return` `int``(u.string)  ` ` `  `        ``# Loop for each digit and check the sum  ` `        ``# If not visited then push it to the queue  ` `        ``for` `i ``in` `range``(``0``, ``10``):  ` `            ``dd ``=` `(u.a ``*` `10` `+` `i) ``%` `a  ` `            ``ss ``=` `u.b ``+` `i  ` `             `  `            ``if` `ss <``=` `b ``and` `visited[dd][ss] ``=``=` `False``:  ` `                ``visited[dd][ss] ``=` `1` `                ``q.append(Node(dd, ss, u.string ``+` `str``(i)))  ` ` `  `    ``# Required number not found return -1.  ` `    ``return` `-``1` ` `  `# Driver code.  ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``a, b ``=` `25``, ``1` `    ``print``(findNumber(a, b)) ` `     `  `# This code is contributed by Rituraj Jain `

Output:

```100
```

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