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

0 0 4 minutes read

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 <bits/stdc++.h>
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

<?php
// PHP 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
function checkIfPossibleRec($x, $a, $b,
                            $isPossible, $n)
{
    // base condition
    if ($x > $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

<script>
 
// Javascript 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
function 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);
}
 
function checkPossible(n, a, b) 
{
    var isPossible = Array(n + 1).fill(false);
     
    checkIfPossibleRec(0, a, b, isPossible, n);
    return isPossible[n];
}
 
// Driver code
var a = 3, b = 7, n = 8;
if (checkPossible(a, b, n))
    document.write("Yes");
else
    document.write("No");
 
// This code is contributed by todaysgaurav 
 
</script>

Output:

No

Time Complexity: O(2^n) , recursive function time complexity
Auxiliary Space: O(n), as extra space of size (n+1) is used to make a boolean array

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!