# Check if N can be represented as sum of integers chosen from set {A, B}

Given three integers N, A and B, the task is to find whether N can be represented as sum of A’s and B’s.

Examples:

Input: N = 11, A = 2, B = 3
Output: Yes
2 + 2 + 2 + 2 + 3 = 11

Input: N = 8, A = 3, B = 7
Output: No

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

Approach: An efficient solution is to call a recursive function starting with zero (because zero is always possible). If function call is fun(x) then recursively call fun(x + a) and fun(x + b) (because if x is possible then x + a and x + b are also possible). Return out of the function if x > n.

Below is the implementation of the above approach:

## C++

 `// CPP program to find if number N can ` `// be represented as sum of a's and b's ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find if number N can ` `// be represented as sum of a's and b's ` `void` `checkIfPossibleRec(``int` `x, ``int` `a, ``int` `b, ` `                   ``bool` `isPossible[], ``int` `n) ` `{ ` `    ``// base condition ` `    ``if` `(x > n) ` `        ``return``; ` ` `  `    ``// if x is already visited ` `    ``if` `(isPossible[x]) ` `        ``return``; ` ` `  `    ``// set x as possible ` `    ``isPossible[x] = ``true``; ` ` `  `    ``// recursive call ` `    ``checkIfPossibleRec(x + a, a, b, isPossible, n); ` `    ``checkIfPossibleRec(x + b, a, b, isPossible, n); ` `} ` ` `  `bool` `checkPossible(``int` `n, ``int` `a, ``int` `b) ` `{ ` `    ``bool` `isPossible[n + 1] = { ``false` `}; ` `    ``checkIfPossibleRec(0, a, b, isPossible, n); ` `    ``return` `isPossible[n]; ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``int` `a = 3, b = 7, n = 8; ` `    ``if` `(checkPossible(a, b, n)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find if number N can ` `// be represented as sum of a's and b's ` ` `  `import` `java.util.*; ` `class` `solution ` `{ ` ` `  `// Function to find if number N can ` `// be represented as sum of a's and b's ` `static` `void` `checkIfPossibleRec(``int` `x, ``int` `a, ``int` `b, ` `                                ``boolean` `isPossible[], ``int` `n) ` `{ ` `    ``// base condition ` `    ``if` `(x > n) ` `        ``return``; ` ` `  `    ``// if x is already visited ` `    ``if` `(isPossible[x]) ` `        ``return``; ` ` `  `    ``// set x as possible ` `    ``isPossible[x] = ``true``; ` ` `  `    ``// recursive call ` `    ``checkIfPossibleRec(x + a, a, b, isPossible, n); ` `    ``checkIfPossibleRec(x + b, a, b, isPossible, n); ` `} ` ` `  `static` `boolean` `checkPossible(``int` `n, ``int` `a, ``int` `b) ` `{ ` `    ``boolean` `isPossible[]=``new` `boolean``[n + ``1``]; ` `    ``for``(``int` `i=``0``;i<=n;i++) ` `    ``isPossible[i]=``false``; ` `    ``checkIfPossibleRec(``0``, a, b, isPossible, n); ` `    ``return` `isPossible[n]; ` `} ` ` `  `// Driver program ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `a = ``3``, b = ``7``, n = ``8``; ` `    ``if` `(checkPossible(a, b, n)) ` `        ``System.out.print(``"Yes"``); ` `    ``else` `        ``System.out.print( ``"No"``); ` ` `  `} ` ` `  `} ` `//contributed by Arnab Kundu `

## Python3

 `# Python3 program to find if number N can  ` `# be represented as sum of a's and b's  ` ` `  `# Function to find if number N can  ` `# be represented as sum of a's and b's  ` `def` `checkIfPossibleRec(x, a, b, isPossible, n):  ` ` `  `    ``# base condition  ` `    ``if` `x > n: ` `        ``return` ` `  `    ``# If x is already visited  ` `    ``if` `isPossible[x]:  ` `        ``return` ` `  `    ``# Set x as possible  ` `    ``isPossible[x] ``=` `True` ` `  `    ``# Recursive call  ` `    ``checkIfPossibleRec(x ``+` `a, a, b, isPossible, n)  ` `    ``checkIfPossibleRec(x ``+` `b, a, b, isPossible, n)  ` ` `  `def` `checkPossible(n, a, b): ` ` `  `    ``isPossible ``=` `[``False``] ``*` `(n ``+` `1``)  ` `    ``checkIfPossibleRec(``0``, a, b, isPossible, n)  ` `    ``return` `isPossible[n]  ` ` `  ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``a, b, n ``=` `3``, ``7``, ``8` `    ``if` `checkPossible(a, b, n):  ` `        ``print``(``"Yes"``)  ` `    ``else``: ` `        ``print``(``"No"``)  ` ` `  `# This code is contributed by Rituraj Jain `

## C#

 `// C# program to find if number N can  ` `// be represented as sum of a's and b's  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// Function to find if number N can  ` `// be represented as sum of a's and b's  ` `static` `void` `checkIfPossibleRec(``int` `x, ``int` `a, ``int` `b,  ` `                               ``bool` `[]isPossible, ``int` `n)  ` `{  ` `    ``// base condition  ` `    ``if` `(x > n)  ` `        ``return``;  ` ` `  `    ``// if x is already visited  ` `    ``if` `(isPossible[x])  ` `        ``return``;  ` ` `  `    ``// set x as possible  ` `    ``isPossible[x] = ``true``;  ` ` `  `    ``// recursive call  ` `    ``checkIfPossibleRec(x + a, a, b, isPossible, n);  ` `    ``checkIfPossibleRec(x + b, a, b, isPossible, n);  ` `}  ` ` `  `static` `bool` `checkPossible(``int` `n, ``int` `a, ``int` `b)  ` `{  ` `    ``bool` `[]isPossible = ``new` `bool``[n + 1];  ` `    ``for``(``int` `i = 0; i <= n; i++)  ` `    ``isPossible[i] = ``false``;  ` `        ``checkIfPossibleRec(0, a, b, isPossible, n);  ` `    ``return` `isPossible[n];  ` `}  ` ` `  `// Driver Code  ` `static` `public` `void` `Main () ` `{ ` `    ``int` `a = 3, b = 7, n = 8;  ` `    ``if` `(checkPossible(a, b, n))  ` `        ``Console.WriteLine(``"Yes"``);  ` `    ``else` `        ``Console.WriteLine( ``"No"``);  ` `} ` `} ` ` `  `// This code is contributed by Sach_Code `

## PHP

 ` ``\$n``) ` `        ``return``; ` ` `  `    ``// if x is already visited ` `    ``if` `(``\$isPossible` `== true) ` `        ``return``; ` ` `  `    ``// set x as possible ` `    ``\$isPossible``[``\$x``] = true; ` ` `  `    ``// recursive call ` `    ``checkIfPossibleRec(``\$x` `+ ``\$a``, ``\$a``, ``\$b``, ` `                       ``\$isPossible``, ``\$n``); ` `    ``checkIfPossibleRec(``\$x` `+ ``\$b``, ``\$a``, ``\$b``, ` `                       ``\$isPossible``, ``\$n``); ` `} ` ` `  `function` `checkPossible(``\$n``, ``\$a``, ``\$b``) ` `{ ` `    ``\$isPossible``[``\$n` `+ 1] = ``array``(false); ` `    ``checkIfPossibleRec(0, ``\$a``, ``\$b``, ``\$isPossible``, ``\$n``); ` `    ``return` `\$isPossible``; ` `} ` ` `  `// Driver Code ` `\$a` `= 3; ` `\$b` `= 7; ` `\$n` `= 8; ` `if` `(checkPossible(``\$a``, ``\$b``, ``\$n``)) ` `    ``echo` `"No"``; ` `else` `    ``echo` `"Yes"``; ` ` `  `// This code is contributed by Sach_Code ` `?> `

Output:

```No
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