Steven - 6 months ago 28

Java Question

I have code as follows:

``if (a <= 10){`

z = 5;

} else {

z = -1;

}`

I figured out that when

`s(10 - a) = |10 - a| / (10 - a)`

`1`

`a < 10`

`-1`

`a > 10`

Then, I just solve the linear equation

`z = s(10 - a) * m + b`

`5 = 1 * m + b`

`-1 = -1 * m + b`

Which outputs

`b = 2, m = 3`

Then this can be modeled as

`z = 3 * s(10 - a) + 2`

Now the question becomes more tricky. What if I have two variables in nested if statements? Such as:

``if (a <= 10){`

if(b <= 3){

z = 3;

} else {

z = 1;

}

} else {

if(b <= -5){

z = -11;

} else {

z = 4;

}

}`

I tried to solve this using another series of linear equations.

`3 = A * s(10 - a) + B * s(3 - b) + C`

`1 = A * s(10 - a) + B * s(3 - b) + C`

`-11 = A * s(10 - a) + D * s(-5 - b) + C`

`4 = A * s(10 - a) + D * s(-5 - b) + C`

with A, B, C, D as constants. However, this isn't giving me the right answer. What am I doing wrong?

Answer

An if statement can be transformed into a formula by using the following trick: we need to find a formula that's 1 if the `if`

statement is true and 0 otherwise. We can use the signum function for this:

```
f(x, y) = (sign(y - x) + 1) / 2
```

f(x, y) is 1 if x < y and 0 if x > y. The inverse g(x, y) = 1 - f(x, y).

So with those two formulas we can easily put together the whole thing:

```
f(a, 10) * (f(b, 3) * 3 + g(b, 3) * 1) + g(a, 10) * (f(b, -5) * -11 + g(b, -5) * 4)
```