C++ represents the number of powers of a number

Discuss the problem of expressing one number by using the power of another number. Given two numbers, x and y. We need to determine whether y can be expressed in terms of powers of x, where each power of As an example of power representation, we can form an equation −

Input: x = 4, y = 11
Output: true
Explanation: 4^2 - 4^1 - 4^0 = 11 Hence y can be represented in the power of x.

Input: x = 2, y = 19
Output: true
Explanation: 2^4 + 2^1 + 2^0 =19 Hence y can be represented in the power of x.

Input: x = 3, y = 14
Output: false
Explanation: 14 can be represented as 3^2 + 3^1 + 3^0 + 3^0 but we cannot use one term of power of x twice.

where c0, c1, c2 can be -1, 0, 1, indicating whether to subtract the (-1) term, add the (1) term, Excluding the (0) term −

c0(x^0) + c1(x^1) + c2(x^2) + c3(x^3) + … = y ….(1),

Taking x as a common factor,

c1(x^1) + c2(x^2) + c3(x^3) + … = y - c0,

From equations (1) and (2) we can represent the numbers again, in order for there to be a solution, (y - Ci) should be divisible by x, while Ci can only contain -1, 0 and 1.

So finally we need to check until y>0, whether it satisfies [(y-1) % x == 0] or [(y) % x == 0] or [(y 1) % x = = 0], or if no solution exists.

Example

c1(x^0) + c2(x^1) + c3(x^2) + … = (y - c0)/x ….(2),

Output

#include <bits/stdc++.h>
using namespace std;
int main(){
   int x = 2, y = 19;
   // checking y divisibility till y>0
   while (y>0) {
      // If y-1 is divisible by x.
      if ((y - 1) % x == 0)
         y = (y - 1) / x;
        // If y is divisible by x.
      else if (y % x == 0)
         y = y / x;
         // If y+1 is divisible by x.
      else if ((y + 1) % x == 0)
         y = (y + 1) / x;
         // If no condition satisfies means
         // y cannot be represented in terms of power of x.
      else
         break;
   }
   if(y==0)
      cout<<"y can be represented in terms of the power of x.";
   else
      cout<<"y cannot be represented in terms of the power of x.";
   return 0;
}

Conclusion

In this tutorial, we discussed how to check whether the representation of a number can be expressed in terms of another number Expressed by powers. We discussed a simple way to solve this problem by checking whether the current number, the previous number and the next number are divisible by y.

We also discussed C programs to solve this problem, which we can implement using programming languages ​​​​such as C, Java, and Python. Hope this tutorial is helpful to you.

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