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Check if a number N can be expressed in base B

Given a number N and any base B. The task is to check if N can be expressed in the form a1*b0 + a2*b1 + a3*b2 + ….+ a101*b100 where each coefficients a1, a2, a3…a101 are either 0, 1 or -1.

Examples:

Input: B = 3, N = 7 
Output: Yes 
Explanation: 
The number 7 can be expressed as 1 * 30 + (-1) * 31 + 1 * 32 = 1 – 3 + 9.

Input: B = 100, N = 50 
Output: No 
Explanation: 
There is no possible way to express the number. 
 

Approach: Below are the steps:

Below is the implementation for the above approach:




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if a number
// N can be expressed in base B
bool check(int n, int w)
{
    vector<int> a(105);
    int p = 0;
 
    // Check if n is greater than 0
    while (n > 0) {
        a[p++] = n % w;
        n /= w;
    }
 
    // Initialize a boolean variable
    bool flag = true;
 
    for (int i = 0; i <= 100; i++) {
 
        // Check if digit is 0 or 1
        if (a[i] == 0 || a[i] == 1)
            continue;
 
        // Subtract the appropriate
        // power of B from it and
        // increment higher digit
        else if (a[i] == w
                 || a[i] == w - 1)
            a[i + 1]++;
 
        else
            flag = false;
    }
 
    return flag;
}
 
// Driver Code
int main()
{
    // Given Number N and base B
    int B = 3, N = 7;
 
    // Function Call
    if (check(N, B))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}




// Java program for the above approach
class GFG{
 
// Function to check if a number
// N can be expressed in base B
static boolean check(int n, int w)
{
    int[] a = new int[105];
    int p = 0;
 
    // Check if n is greater than 0
    while (n > 0)
    {
        a[p++] = n % w;
        n /= w;
    }
 
    // Initialize a boolean variable
    boolean flag = true;
 
    for(int i = 0; i <= 100; i++)
    {
         
        // Check if digit is 0 or 1
        if (a[i] == 0 || a[i] == 1)
            continue;
 
        // Subtract the appropriate
        // power of B from it and
        // increment higher digit
        else if (a[i] == w || a[i] == w - 1)
            a[i + 1]++;
 
        else
            flag = false;
    }
    return flag;
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given number N and base B
    int B = 3, N = 7;
 
    // Function call
    if (check(N, B))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code is contributed by gauravrajput1




# Python3 program for the above approach
 
# Function to check if a number
# N can be expressed in base B
def check(n, w):
     
    a = [0 for i in range(105)];
    p = 0
  
    # Check if n is greater than 0
    while (n > 0):
        a[p] = n % w
        p += 1
        n //= w
         
    # Initialize a boolean variable
    flag = True
  
    for i in range(101):
          
        # Check if digit is 0 or 1
        if (a[i] == 0 or a[i] == 1):
            continue
  
        # Subtract the appropriate
        # power of B from it and
        # increment higher digit
        elif (a[i] == w or a[i] == w - 1):
            a[i + 1] += 1
        else:
            flag = False
     
    return flag
 
# Driver code
if __name__=="__main__":
     
    # Given number N and base B
    B = 3
    N = 7
  
    # Function call
    if (check(N, B)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by rutvik_56




// C# program for the above approach
using System;
 
class GFG{
 
// Function to check if a number
// N can be expressed in base B
static bool check(int n, int w)
{
    int[] a = new int[105];
    int p = 0;
 
    // Check if n is greater than 0
    while (n > 0)
    {
        a[p++] = n % w;
        n /= w;
    }
 
    // Initialize a bool variable
    bool flag = true;
 
    for(int i = 0; i <= 100; i++)
    {
         
        // Check if digit is 0 or 1
        if (a[i] == 0 || a[i] == 1)
            continue;
 
        // Subtract the appropriate
        // power of B from it and
        // increment higher digit
        else if (a[i] == w || a[i] == w - 1)
            a[i + 1]++;
 
        else
            flag = false;
    }
    return flag;
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given number N and base B
    int B = 3, N = 7;
 
    // Function call
    if (check(N, B))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
 
// This code is contributed by amal kumar choubey




<script>
// javascript program for the above approach   
 
    // Function to check if a number
    // N can be expressed in base B
    function check(n , w) {
        var a = Array(105).fill(0);
        var p = 0;
 
        // Check if n is greater than 0
        while (n > 0) {
            a[p++] = n % w;
            n /= w;
            n = parseInt(n);
        }
 
        // Initialize a boolean variable
        var flag = true;
 
        for (i = 0; i <= 100; i++) {
 
            // Check if digit is 0 or 1
            if (a[i] == 0 || a[i] == 1)
                continue;
 
            // Subtract the appropriate
            // power of B from it and
            // increment higher digit
            else if (a[i] == w || a[i] == w - 1)
                a[i + 1]++;
 
            else
                flag = false;
        }
        return flag;
    }
 
    // Driver Code
     
        // Given number N and base B
        var B = 3, N = 7;
 
        // Function call
        if (check(N, B))
            document.write("Yes");
        else
            document.write("No");
 
// This code is contributed by gauravrajput1
</script>

Output: 
Yes

 

Time Complexity: O(logBN) 
Auxiliary Space: O(1) 
 


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