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Check if N can be represented as sum of integers chosen from set {A, B}
• Last Updated : 08 Apr, 2021

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

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``?>`

## Javascript

 ``
Output:
`No` My Personal Notes arrow_drop_up