STL pair comparison - first elements

Question

Can someone explain meaning of this paragraph

The great advantage of pairs is that they have built-in operations to compare themselves. Pairs are compared first-to-second element. If the first elements are not equal, the result will be based on the comparison of the first elements only; the second elements will be compared only if the first ones are equal. The array (or vector) of pairs can easily be sorted by STL internal functions.

and hence this

For example, if you want to sort the array of integer points so that they form a polygon, it’s a good idea to put them to the vector< pair<double, pair<int,int> >, where each element of vector is { polar angle, { x, y } }. One call to the STL sorting function will give you the desired order of points.

I have been struggling for an hour to understand this.
Source

score 4 · Answer 1 · answered Jun 06 '15 at 18:33

Consider looking at operator< for pair<A,B>, which is a class that looks something like:

struct pairAB {
    A a;
    B b;
};

You could translate that paragraph directly into code:

bool operator<(const pairAB& lhs, const pairAB& rhs) {
    if (lhs.a != rhs.a) {         // If the first elements are not equal
        return lhs.a < rhs.a;     // the result will be based on 
    }                             // the comparison of the first elements only

    return lhs.b < rhs.b;         // the second elements will be compared
                                  // only if the first ones are equal.
}

Or, thinking more abstractly, this is how lexicographic sort works. Think of how you would order two words. You'd compare their first letters - if they're different, you can stop and see which one is less. If they're the same, then you go onto the second letter.

Ami Tavory · Accepted Answer · 2015-06-06T18:42:29.290

The first paragraph says that pairs have an ordering as follows: if you have (x, y) and (z, w), and you compare them, then it will first check if x is smaller (or larger) than z: if yes, than the first pair is smaller (or larger) than the second. If x = z, however, then it will compare y and w. This makes it very convenient to do stuff like sorting a vector of pairs if the first elements of the pairs are more important to the order than the second elements.

The second paragraph gives an interesting application. Suppose you stand at some point on a plane, and there's a polygon enclosing you. Then each point will have an angle and a distance. But given the points, how do you know in what order should they be to form a polygon (without crisscrossing themselves)? If you store the points in this format (angle, distance), then you'll get the circling direction for free. That's actually rather neat.

score 1 · Answer 3 · answered Jun 06 '15 at 18:35

The STL pair is a container to hold two objects together. Consider this for example,

pair a, b;

The first element can be accessed via a.first and the second via a.second.

The first paragraph is telling us that STL provides built-in operations to compare two pairs. For example, you need to compare 'a' and 'b', then the comparison is first done using a.first and b.first. If both the values are same, then the comparison is done using a.second and b.second. Since this is a built-in functionality, you can easily use it with the internal functions of STL like sort, b_search, etc.

The second paragraph is an example of how this might be used. Consider a situation where you would want to sort the points in a polygon. You would first want to sort them based on their polar angle, then the x co-ordinate and then the y co-ordinate. Thus we make use of the pair {angle, {x,y}}. So any comparison would be first done on the angle, then advanced to the x value and then the y value.

Vlad from Moscow · Answer 4 · 2015-06-06T18:48:21.407

It will be easier to understand if to compare a simple example of pairs of last names and first names.

For example if you have pairs

{ Tomson, Ann }
{ Smith, Tony }
{ Smith, John }

and want to sort them in the ascending order you have to compare the pairs with each other.

If you compare the first two pairs

{ Tomson, Ann }
{ Smith, Tony }

then the last name of the first pair is greater than the last name of the second pair. So there is no need to compare also the first names. It is already clear that pair

{ Smith, Tony }

has to precede pair

{ Tomson, Ann }

On the other hand if you compare pairs

{ Smith, Tony }
{ Smith, John }

then the last names of the pairs are equal. So you need to compare the first names of the pairs. As John is less than Tony then it is clear that pair

{ Smith, John }

will precede pair

{ Smith, Tony }

though the last names (the first elements of the pairs) are equal.

As for this pair { polar angle, { x, y } } then if polar ahgles of two different pairs are equal then there will be compared { x, y } that in turn a pair. So if fird elements ( x ) are equal than there will be compared y(s).

score 0 · Answer 5 · answered Jun 06 '15 at 18:39

It's actually when a you have vector/arrays of pairs you don't have to care about sorting when you use sort() function,You just use sort(v.begin(),v.end())-> it will be automatically sorted on the basis of first element and when first elements are equal they will compared using second element. See code and output in the link,it will be all clear. https://ideone.com/Ad2yVG .see code in link

STL pair comparison - first elements

5 Answers5