set_symmetric_difference


Category: algorithms	Component type: function

Prototype

Set_symmetric_difference is an overloaded name; there are actually two set_symmetric_difference functions.

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_symmetric_difference(InputIterator1 first1, 
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class StrictWeakOrdering>
OutputIterator set_symmetric_difference(InputIterator1 first1,
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result, 
                                        StrictWeakOrdering comp);

Description

Set_symmetric_difference constructs a sorted range that is the set symmetric difference of the sorted ranges [first1, last1) and [first2, last2). The return value is the end of the output range.

In the simplest case, set_symmetric_difference performs a set theoretic calculation: it constructs the union of the two sets A - B and B - A, where A and B are the two input ranges. That is, the output range contains a copy of every element that is contained in [first1, last1) but not [first2, last2), and a copy of every element that is contained in [first2, last2) but not [first1, last1). The general case is more complicated, because the input ranges may contain duplicate elements. The generalization is that if a value appears m times in [first1, last1) and n times in [first2, last2) (where m or n may be zero), then it appears |m-n| times in the output range. [1] Set_symmetric_difference is stable, meaning that the relative order of elements within each input range is preserved.

The two versions of set_symmetric_difference differ in how they define whether one element is less than another. The first version compares objects using operator<, and the second compares objects using a function object comp.

Definition

Defined in algo.h.

Requirements on types

For the first version:

InputIterator1 is a model of Input Iterator.
InputIterator2 is a model of Input Iterator.
OutputIterator is a model of Output Iterator.
InputIterator1 and InputIterator2 have the same value type.
InputIterator's value type is a model of LessThan Comparable.
The ordering on objects of InputIterator1's value type is a strict weak ordering, as defined in the LessThan Comparable requirements.
InputIterator's value type is convertible to a type in OutputIterator's set of value types.

For the second version:

InputIterator1 is a model of Input Iterator.
InputIterator2 is a model of Input Iterator.
OutputIterator is a model of Output Iterator.
StrictWeakOrdering is a model of Strict Weak Ordering.
InputIterator1 and InputIterator2 have the same value type.
InputIterator1's value type is convertible to StrictWeakOrdering's argument type.
InputIterator's value type is convertible to a type in OutputIterator's set of value types.

Preconditions

For the first version:

[first1, last1) is a valid range.
[first2, last2) is a valid range.
[first1, last1) is ordered in ascending order according to operator<. That is, for every pair of iterators i and j in [first1, last1) such that i precedes j, *j < *i is false.
[first2, last2) is ordered in ascending order according to operator<. That is, for every pair of iterators i and j in [first2, last2) such that i precedes j, *j < *i is false.
There is enough space to hold all of the elements being copied. More formally, the requirement is that [result, result + n) is a valid range, where n is the number of elements in the symmetric difference of the two input ranges.
[first1, last1) and [result, result + n) do not overlap.
[first2, last2) and [result, result + n) do not overlap.

For the second version:

[first1, last1) is a valid range.
[first2, last2) is a valid range.
[first1, last1) is ordered in ascending order according to comp. That is, for every pair of iterators i and j in [first1, last1) such that i precedes j, comp(*j, *i) is false.
[first2, last2) is ordered in ascending order according to comp. That is, for every pair of iterators i and j in [first2, last2) such that i precedes j, comp(*j, *i) is false.
There is enough space to hold all of the elements being copied. More formally, the requirement is that [result, result + n) is a valid range, where n is the number of elements in the symmetric difference of the two input ranges.
[first1, last1) and [result, result + n) do not overlap.
[first2, last2) and [result, result + n) do not overlap.

Complexity

Linear. Zero comparisons if either [first1, last1) or [first2, last2) is empty, otherwise at most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Example

inline bool lt_nocase(char c1, char c2) { return tolower(c1) < tolower(c2); }

int main()
{
  int A1[] = {1, 3, 5, 7, 9, 11};
  int A2[] = {1, 1, 2, 3, 5, 8, 13};  
  char A3[] = {'a', 'b', 'b', 'B', 'B', 'f', 'g', 'h', 'H'};
  char A4[] = {'A', 'B', 'B', 'C', 'D', 'F', 'F', 'H' };

  const int N1 = sizeof(A1) / sizeof(int);
  const int N2 = sizeof(A2) / sizeof(int); 
  const int N3 = sizeof(A3);
  const int N4 = sizeof(A4);

  cout << "Symmetric difference of A1 and A2: ";
  set_symmetric_difference(A1, A1 + N1, A2, A2 + N2,
                           ostream_iterator<int>(cout, " "));
  cout << endl 
       << "Symmetric difference of A3 and A4: ";
  set_symmetric_difference(A3, A3 + N3, A4, A4 + N4, 
                           ostream_iterator<char>(cout, " "),
                           lt_nocase);
  cout << endl;
}

The output is

Symmetric difference of A1 and A2: 1 2 7 8 9 11 13 
Symmetric difference of A3 and A4: B B C D F g H

Notes

[1] Even this is not a completely precise description, because the ordering by which the input ranges are sorted is permitted to be a strict weak ordering that is not a total ordering: there might be values x and y that are equivalent (that is, neither x < y nor y < x) but not equal. See the LessThan Comparable requirements for a more complete discussion. The output range consists of those elements from [first1, last1) for which equivalent elements do not exist in [first2, last2), and those elements from [first2, last2) for which equivalent elements do not exist in [first1, last1). Specifically, suppose that the range [first1, last1) contains m elements that are equivalent to each other and the range [first2, last2) contains n elements from that equivalence class (where either m or n may be zero). If m > n then the output range contains the last m - n of these elements elements from [first1, last1), and if m < n then the output range contains the last n - m of these elements elements from [first2, last2).