Given two numbers n and x, we need to calculate the smallest value of x that is closest to given number n.
Input : n = 9, x = 4 Output : 8 Input : n = 2855, x = 13 Output : 2860 Input : n = 46426171, x = 43 Output : 46426154 Input : n = 1, x = 3 Output : 3
We need to find a k such that x*k is closest to n. If we do k = n/x, we get a value of k that may not lead to maximum. We can get closest by comparing the values floor(n/x) * x and ceil(n/x) * x.
Below is an interesting solution that doesn’t require computations of floor(n/x) and ceil(n/x). The idea is to do following two steps.
n = n + x/2; n = n - (n%x); result = n
Let us consider below example
n = 2855 x = 13 n = 2855 + 13/2 = 2861 n = 2861 - (2861 % 13) = 2861 - 1 = 2860
Below are implementations of above steps.
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