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One lesson I have learned on last Div #3 contest is "avoid using pow() function in C++, it is can lead to Wrong Answer".
I am sharing this with a practical example:
This submission works only if you replace long long p = pow(n1, 3) + pow(mid, 3);
with long long p = n1 * n1 * n1 + mid * mid * mid;
I feel like it is useful to sare it !
Do you know why this happens?
https://en.cppreference.com/w/cpp/numeric/math/pow
Because it shouldn't be used for integers.
I have a blog explaining about why this stuff happens Explanation to weird/strange floating point behaviour in C++.
The explanation is not simply that pow is based on floating point numbers! The real culprit is the weird floating point behaviour of 32 bit g++. For example submitting the code under C++17(64 bit) gets AC 107846368. I can also get AC 107868857 in C++11(32 bit) by turning off most of the weird floating point behaviour with a pragma.
Floating point numbers are a lot more safe than what people give them credit for. To be honest, people just don't know what they are talking about. Fundamentally doubles can be used for exact integer calculations up to
2^53. For example I often use doubles for integer calculations in Python for some extra speed, and I've never gotten WA from it. It is just 32bit g++ that handles floating point numbers in a fucked up way.Beautiful reply from a person from beautiful country!
Canadian duck is cool too!
The following is a fun example of how fucked up floating point numbers are in 32 bit g++ using a small modification of his code. In it I've added the seemingly useless line
calculating
mid3 % 1and not even storing the result. Clearly doing this should have no effect, right?With the "useless" line:
AC 107875701
Without the "useless" line:
WA on TC 1 107875752
It is mainly because pow function returns double and when we convert it to integer , sometimes it gives wrong answer due to ignoring the decimal part. For eg suppose if the returned value is 99.999999 then it will give answer as 99 whereas if the answer is 100.00001 it will be 100.For avoiding this I use this as it always gives correct answer:-
#include <ext/numeric>
using namespace __gnu_cxx;
int ans = power(x , y);
There is the old blog. https://codeforces.net/blog/entry/1521
I never understand why people are amused by this 'problem' so much and even write blogs. It's simple — floating point functions, all of them, like pow and log or literally anything else, are not exact and shouldn't be used in integer tasks. Write your own algorithms like binary exponention or a for loop yourself.
abs() is bad before C++11
How come?
AFAIK std::abs can be used with integers as it seems to be overloaded and I didn't have problems using it. See here.
lol, just realized that there is a function called cbrt() which is short for cubic root.
So I was today years old when I learned that sqrt() has it's funny name because it calculates the square root.
practically you can expect double to precisely store 12 digits