Given two positive integer x and y. we have to find the value of y mod 2x. That is remainder when y is divided by 2x.
Input : x = 3, y = 14 Output : 6 Explanation : 14 % 23 = 14 % 8 = 6. Input : x = 4, y = 14 Output : 14 Explanation : 14 % 24 = 14 % 16 = 14.
To solve this question we can use pow() and modulo operator and can easily find the remainder.
But there are some points we should care about:
- For higher value of x such that 2x is greater than long long int range, we can not obtain proper result.
- Whenever y < 2x the remainder will always be y. So, in that case we can restrict ourselves to calculate value of 2x as:
y < 2x log y < x // means if log y is less than x, then // we can print y as remainder.
- The maximum value of 2x for which we can store 2x in a variable is 263. This means for x > 63, y is always going to be smaller than 2x and in that case remainder of y mod 2x is y itself.
keeping in mind the above points we can approach this problem as :
if (log y < x) return y; else if (x < 63) return y; else return (y % (pow(2, x)))
Note: As python is limit free we can directly use mod and pow() function
Time Complexity: O(x)
Auxiliary Space: O(1)
Compute modulus division by a power-of-2-number
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