Check if a number N can be expressed as the sum of powers of X or not

02 Jun, 2021
Given two positive numbers N and X, the task is to check if the given number N can be expressed as the sum of distinct powers of X. If found to be true, then print “Yes”, Otherwise, print “No”.
Examples:
Input: N = 10, X = 3Output: YesExplanation:The given value of N(= 10) can be written as (1 + 9) = 30 + 32. Since all the power of X(= 3) are distinct. Therefore, print Yes.
Input: N= 12, X = 4Output: No
Approach: The given problem can be solved by checking if the number N can be written in base X or not. Follow the steps below to solve the problem:
Iterate a loop until the value of N is at least 0 and perform the following steps:Calculate the value of remainder rem when N is divided by X.If the value of rem is at least 2, then print “No” and return.Otherwise, update the value of N as N / X.
Calculate the value of remainder rem when N is divided by X.
If the value of rem is at least 2, then print “No” and return.
Otherwise, update the value of N as N / X.
After completing the above steps, if there doesn’t exist any termination, then print “Yes” as the result at N can be expressed in the distinct power of X.
Below is the implementation of the above approach:
C++
Java
Python3
C#
Javascript
// C++ program for the above approach #include <bits/stdc++.h>using namespace std; // Function to check if the number N// can be expressed as the sum of// different powers of X or notbool ToCheckPowerofX(int n, int x){    // While n is a positive number    while (n > 0) {         // Find the remainder        int rem = n % x;         // If rem is at least 2, then        // representation is impossible        if (rem >= 2) {            return false;        }         // Divide the value of N by x        n = n / x;    }     return true;} // Driver Codeint main(){    int N = 10, X = 3;    if (ToCheckPowerofX(N, X)) {        cout << "Yes";    }    else {        cout << "No";    }     return 0;}
// Java program for the above approachimport java.io.*;import java.util.*; class GFG{ // Function to check if the number N// can be expressed as the sum of// different powers of X or notstatic boolean ToCheckPowerofX(int n, int x){         // While n is a positive number    while (n > 0)    {                 // Find the remainder        int rem = n % x;         // If rem is at least 2, then        // representation is impossible        if (rem >= 2)        {            return false;        }         // Divide the value of N by x        n = n / x;    }    return true;} // Driver Codepublic static void main (String[] args){    int N = 10, X = 3;    if (ToCheckPowerofX(N, X))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sanjoy_62
# Python3 program for the above approach # Function to check if the number N# can be expressed as the sum of# different powers of X or notdef ToCheckPowerofX(n, x):         # While n is a positive number    while (n > 0):                 # Find the remainder        rem = n % x         # If rem is at least 2, then        # representation is impossible        if (rem >= 2):            return False         # Divide the value of N by x        n = n // x     return True # Driver Codeif __name__ == '__main__':         N = 10    X = 3         if (ToCheckPowerofX(N, X)):        print("Yes")    else:        print("No")         # This code is contributed by bgangwar59
// C# program for the above approachusing System;class GFG{      // Function to check if the number N// can be expressed as the sum of// different powers of X or notstatic bool ToCheckPowerofX(int n, int x){         // While n is a positive number    while (n > 0)    {                 // Find the remainder        int rem = n % x;         // If rem is at least 2, then        // representation is impossible        if (rem >= 2)        {            return false;        }         // Divide the value of N by x        n = n / x;    }    return true;} // Driver codepublic static void Main(String []args){     int N = 10, X = 3;    if (ToCheckPowerofX(N, X))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}}// This code is contributed by code_hunt,
<script> // JavaScripts program for the above approach // Function to check if the number N// can be expressed as the sum of// different powers of X or notfunction ToCheckPowerofX(n, x){    // While n is a positive number    while (n > 0) {         // Find the remainder        var rem = n % x;         // If rem is at least 2, then        // representation is impossible        if (rem >= 2) {            return false;        }         // Divide the value of N by x        n = n / x;    }     return true;} // Driver Code    var N = 10, X = 3;    if (ToCheckPowerofX(N, X)) {        document.write("Yes");    }    else {        document.write("No");    } </script>
Yes
 
Time Complexity: O(log N)Auxiliary Space: O(1)
bgangwar59
sanjoy_62
code_hunt
SURENDRA_GANGWAR
maths-power
Mathematical
Mathematical
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.