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Find value of y mod (2 raised to power x) in C++
In this problem, we are given two values x and y. Our task is to find value of y mod (2 raised to power x).
Let's take an example to understand the problem,
Input : x = 2, y = 19 Output : 3
Explanation −
y % 2x = 19 % 22 = 19 % 4 = 3
Solution Approach
A simple solution to the problem is by directly calculating the value of 2x using the pow() function and then finding the value of y % 2x.
Another approach to solve the problem is by using log. For the value of y < 2x, remainder is y. For this case we have
Log2y < x
Also, the maximum value of x can be 63 which will have the value overflow for y. Hence, mod is equal to x.
Taking all these under consideration, we have these three cases −
if(log y < x) -> return y else if(x > 63) -> return y else -> return (y % pow(2, x))
Example
Program to illustrate the working of our solution
#include <bits/stdc++.h>
using namespace std;
long long int findModVal(long long int y, int x){
if (log2(y) < x)
return y;
if (x > 63)
return y;
return (y % (1 << x));
}
int main(){
long long int y = 82829;
int x = 12;
cout<<"The value of y mod 2^x is "<<findModVal(y, x);
return 0;
}Output
The value of y mod 2^x is 909
Updated on: 01-Feb-2022
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