Converting an IF condition to a mathematical equation
I am trying to study about converting algorithms into mathematical equations. For this I just started with a simple random example :
function set_b( int b):int
{ if ( b >= 0) { a = 5 ; } else if ( b < 0 ) { a = -20 }
}By looking at the above algorithm, one can say :
a is dependent upon b. So : a = f(b). Also, the two blocks of Ifs are actually talking about -ve and +ve number lines.
But after this i get stuck, where to start approaching the solution from. Some equation like
a = b + blah blah - blah blah * blah blah etc.
Any clues or hints pls ?
$\endgroup$ 24 Answers
$\begingroup$Try
$$ a = \frac{5}{2}\left( 5 \frac{b}{|b|} - 3 \right) $$
If you just want to shorten your code, I suggest using the ternary operator like (C++ style)
int set_b(int b) { int a = (b<0)?-20:5; return a;
};Hint: try using the function $b / |b|$ (which is $1$ for $b > 0$, -1 for $b< 0$), as a building block, and then applying a couple elementary transforms (vertical dilation and translation) to get what you want.
$\endgroup$ $\begingroup$One way could be:
$$a = f(b) = \begin{cases} 5& b < 0\\-20& b > 0\end{cases}$$
Do you see something that could help this? What about the $b = 0$ case.
Can you see how to also define it using the Heaviside Unit Step function as an alternate solution?
Sorry that I have not yet learned the TeX style to make this look proper.
$\endgroup$ $\begingroup$let $a=f(b)$ ;then code says that for all $b>=0$ ,$a=5$ and for all input $b<0$,$a=-20$,this is if we consider into mathematical term,likely piecewise function
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