The // operator explicitly floors the result. Quoting the Binary arithmetic operations documentation: the result is that of mathematical division with the ‘floor’ function applied to the result. Flooring is not the same thing as rounding to 0; flooring always moves to the lower integer value. See the math.floor() function: Return the floor of x, … Read more
The current answers all focus on decimal digits, when applying the “add all digits and see if that divides by 3”. That trick actually works in hex as well; e.g. 0x12 can be divided by 3 because 0x1 + 0x2 = 0x3. And “converting” to hex is a lot easier than converting to decimal. Pseudo-code: … Read more
The question equals to using 10i mod n (for each i, it can be used at most once) to get a sum m of n. It’s like a knapsack problem or subset sum problem. In this way, dynamic programming will do the task. In dynamic programming the complexity is O(k*n). k is the number of … Read more
In Python 3, number / 10 will try to return a float. However, floating point values can’t be of arbitrarily large size in Python and if number is large an OverflowError will be raised. You can find the maximum that Python floating point values can take on your system using the sys module: >>> import … Read more
They are being divided in integer arithmetics. So dividing integer a by integer b you get how many times b fits into a. Also a % b will give you a remainder of a division. So (a / b ) * b + a % b = a
This is one of those highly-application specific things. It may help in some cases and not in others. (In the vast majority of cases, a straight-forward multiplication is still best.) The “intuitive” way of doing this is just to extract the bits into a 64-bit integer and add the shift value directly into the exponent. … Read more
CPU’s ALU (Arithmetic-Logic Unit) executes algorithms, though they are implemented in hardware. Classic multiplications algorithms includes Wallace tree and Dadda tree. More information is available here. More sophisticated techniques are available in newer processors. Generally, processors strive to parallelize bit-pairs operations in order the minimize the clock cycles required. Multiplication algorithms can be parallelized quite … Read more
There’s a fairly well-known trick for determining whether a number is a multiple of 11, by alternately adding and subtracting its decimal digits. If the number you get at the end is a multiple of 11, then the number you started out with is also a multiple of 11: 47278 4 – 7 + 2 … Read more
The guy who said “leave it to the compiler” was right, but I don’t have the “reputation” to mod him up or comment. I asked gcc to compile int test(int a) { return a / 3; } for an ix86 and then disassembled the output. Just for academic interest, what it’s doing is roughly multiplying … Read more
From the C99 Rationale document: (7.20.6.2 The div, ldiv, and lldiv functions) Because C89 had implementation-defined semantics for division of signed integers when negative operands were involved, div and ldiv, and lldiv in C99, were invented to provide well-specified semantics for signed integer division and remainder operations. The semantics were adopted to be the same … Read more