Find the multiple of x which is closest to a^b

Given three integers a, b and x, the task is to get the multiple of x which is closest to ab.

Examples:

Input: a = 5, b = 4, x = 3
Output: 624
54 = 625 and 624 is the multiple of 3 which is closest to 625



Input: a = 349, b = 1, x = 4
Output: 348

Approach:

  • Calculate ab and store it in a variable say num.
  • Then, calculate ⌊num / x⌋ and store it in a variable floor.
  • Now the closest element at the left will be closestLeft = x * floor.
  • And the closest element on the right will be closestRight = x * (floor + 1).
  • Finally, the closest number among them will be min(num – closestLeft, closestRight – num).

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define ll long long int
  
// Function to return the multiple of x 
// which is closest to a^b
ll getClosest(int a, int b, int x)
{
    ll num = pow(a, b);
  
    int floor = num / x;
  
    // Closest element on the left
    ll numOnLeft = x * floor;
  
    // Closest element on the right
    ll numOnRight = x * (floor + 1);
  
    // If numOnLeft is closer than numOnRight
    if ((num - numOnLeft) < (numOnRight - num))
        return numOnLeft;
  
    // If numOnRight is the closest
    else
        return numOnRight;
}
  
// Driver code
int main()
{
    int a = 349, b = 1, x = 4;
    cout << getClosest(a, b, x) << endl;
    return 0;
}

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Output:

348


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Improved By : jit_t