Jerome Baldridge - 6 months ago 33

C++ Question

There seems to be some disagreement in another question about whether these two functions have identical logic:

`bool operator<(const screenPoint& left, const screenPoint& right){`

if (left.x < right.x) return true;

else return left.y < right.y;

}

bool operator<(const screenPoint& left, const screenPoint& right){

return left.x < right.x || left.y < right.y;

}

I have stared at these for quite a while and I cannot see how they would behave differently. In both, if

`left.x < right.x`

`true`

`left.y < right.y`

If not, can someone please elaborate.

Also, it was suggested that the first of these is identical to the implementation of lexographical ordering in

`std::tie`

Answer

The two are identical to each other (if you fix the missing parenthesis in the first `if`

), but they do not implement a strict weak ordering, so you probably don't want to use them (it would be invalid to use them in standard ordered containers and algorithms).

Proof: Consider the original relation for a=(1,3) b=(2,2). Then a < b and b < a. (asymmetric property violated)

A correct lexicographical ordering would look like this:

```
bool operator<(const screenPoint& left, const screenPoint& right){
if (left.x < right.x)
return true;
if (left.x > right.x)
return false;
return left.y < right.y;
}
```

If your members have only a `<`

operator and not a `>`

operator, replace `left.x > right.x`

by `!(right.x < left.x)`

. This is how lexicographical comparison is implemented by `std::pair`

and `std::tuple`

(which is returned by `std::tie`

).