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Computers usually deal with floating-point numbers rather than with fractions. The main difference is that floating-point numbers have limited accuracy, but are much faster to perform arithmetic with (and are the only type of non-integer numbers supported natively in hardware). Floating-point numbers are stored in "scientific notation" with a fixed ...


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It's quite related to my research work, It would be helpful for me if you post the solution when you get it. But I don't think it can be solved by using pen and paper as the constraints you mentioned is quite huge. Solution 1 : Your problem statement can be re written as , Expressing a Number(P) as sum of kth Power of distinct numbers. Now if you want to ...


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Let me put together the two comments. The function $A$ is Euler's totient function, which is often called $\phi$. The function $B(x)=\sum_{d|n}\phi(d)$ is known to be equal to $B(x)=x$. Now, observe that $D(x)=\sum_{i=1}^{x}C(B(i))=\sum_{i=1}^{x}C(i)=C(x!)$, where the last equation is because $C$ satisfies $C(a)+C(b)=C(ab)$. Now, if $p_1<p_2<\ldots<...


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You're looking to compute the rolling standard deviation (i.e., a streaming/online algorithm for the standard deviation). The standard method is to use Welford's method, or a variation. For the standard deviation, see https://jonisalonen.com/2014/efficient-and-accurate-rolling-standard-deviation/. This is a minor adjustment to Welford's method (which ...


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An employer needs one person who is good at maths. Unless you go deep into scientific software, 90% of all programming jobs rarely require any mathematical skills at all. You will sometimes find problems in programming contests that have clever solutions if you have mathematical skills, but often very similar problems have no such clever solutions.


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If you found Structure and Interpretation of Computer Programs interesting, you might like Functional Differential Geometry (It's from the same authors) . Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with unclear and informal symbol manipulation. To address this problem we use computer programs to communicate ...


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