std::adjacent_difference(3)

NAME
std::adjacent_difference - std::adjacent_difference

Synopsis
   Defined in header <numeric>
   template< class InputIt, class OutputIt >
   OutputIt adjacent_difference( InputIt first, InputIt (1) (constexpr since C++20)
   last,
                        OutputIt d_first );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2 >
   ForwardIt2 adjacent_difference( ExecutionPolicy&&
   policy, (2) (since C++17)
                        ForwardIt1 first,
   ForwardIt1 last,
                        ForwardIt2 d_first );
   template< class InputIt, class OutputIt, class BinaryOp
   >
   OutputIt adjacent_difference( InputIt first, InputIt (3) (constexpr since C++20)
   last,
                        OutputIt d_first, BinaryOp
   op );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2, class
   BinaryOp >
   ForwardIt2 adjacent_difference( ExecutionPolicy&&
   policy, (4) (since C++17)
                        ForwardIt1 first,
   ForwardIt1 last,
                        ForwardIt2 d_first,
   BinaryOp op );
   1) If [first, last) is empty, does nothing.
   Otherwise, performs the following operations in order:
    1. Creates an accumulator acc of type T, and initializes it with *first.
    2. Assigns acc to *d_first.
    3. For each iterator iter in [++first, last) in order, performs the following
       operations in order:
   a) Creates an object val of type T, and initializes it with *iter.
   b) Computes
   val - acc
   (until C++11)
   val - std::move(acc)
   (since C++11).
   c) Assigns the result to *++d_first.
   d)
   Copy
   (until C++11)
   Move
   (since C++11) assigns from val to acc.
   2) If [first, last) is empty, does nothing.
   Otherwise, performs the following operations in order:
    1. Assigns *first to *d_first.
    2. For each integer i in [1, std::distance(first, last)), performs the following
       operations in order:
   a) Computes curr - prev, where curr is the next i
   th iterator of first, and prev is the next i - 1
   th iterator of first.
   b) Assigns the result to *dest, where dest is the next i
   th iterator of d_first.
   3) Same as (1), but computes
   op(val, acc)
   (until C++11)
   op(val, std::move(acc))
   (since C++11) instead.
   4) Same as (2), but computes op(curr, prev) instead.
   Given binary_op as the actual binary operation:
     * If any of the following conditions is satisfied, the program is ill-formed:
     * For overloads (1,3):
     * T is not constructible from *first.
     * acc is not writable to d_first.
     * The result of
       binary_op(val, acc)
       (until C++11)
       binary_op(val, std::move(acc))
       (since C++11) is not writable to d_first.
     * For overloads (2,4):
     * *first is not writable to d_first.
     * The result of binary_op(*first, *first) is not writable to d_first.
     * Given d_last as the iterator to be returned, if any of the following conditions
       is satisfied, the behavior is undefined:
     * For overloads (1,3), T is not MoveAssignable. (since C++11)
     * For overloads (2,4), [first, last) and [d_first, d_last) overlaps.
     * binary_op modifies any element of [first, last) or [d_first, d_last).
     * binary_op invalidates any iterator or subrange in [first, last] or
       [d_first, d_last].

Parameters
   first, last - the range of elements
   d_first - the beginning of the destination range
   policy - the execution policy to use. See execution policy for details.
                 binary operation function object that will be applied.
                 The signature of the function should be equivalent to the following:
                  Ret fun(const Type1 &a, const Type2 &b);
   op -
                 The signature does not need to have const &.
                 The types Type1 and Type2 must be such that an object of type
                 iterator_traits<InputIt>::value_type can be implicitly converted to
                 both of them. The type Ret must be such that an object of type
                 OutputIt can be dereferenced and assigned a value of type Ret.

Type requirements
   -
   InputIt must meet the requirements of LegacyInputIterator.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.
   -
   ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

Return value
   Iterator to the element past the last element written, or d_first if [first, last)
   is empty.

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last):
   1,2) Exactly \(\scriptsize N-1\)N-1 applications of operator-.
   3,4) Exactly \(\scriptsize N-1\)N-1 applications of the binary function op.

Exceptions
   The overloads with a template parameter named ExecutionPolicy report errors as
   follows:
     * If execution of a function invoked as part of the algorithm throws an exception
       and ExecutionPolicy is one of the standard policies, std::terminate is called.
       For any other ExecutionPolicy, the behavior is implementation-defined.
     * If the algorithm fails to allocate memory, std::bad_alloc is thrown.

Possible implementation
                        adjacent_difference (1)
   template<class InputIt, class OutputIt>
   constexpr // since C++20
   OutputIt adjacent_difference(InputIt first, InputIt last, OutputIt d_first)
   {
       if (first == last)
           return d_first;
       typedef typename std::iterator_traits<InputIt>::value_type value_t;
       value_t acc = *first;
       *d_first = acc;
       while (++first != last)
       {
           value_t val = *first;
           *++d_first = val - std::move(acc); // std::move since C++11
           acc = std::move(val);
       }
       return ++d_first;
   }
                        adjacent_difference (3)
   template<class InputIt, class OutputIt, class BinaryOp>
   constexpr // since C++20
   OutputIt adjacent_difference(InputIt first, InputIt last,
                        OutputIt d_first, BinaryOp op)
   {
       if (first == last)
           return d_first;
       typedef typename std::iterator_traits<InputIt>::value_type value_t;
       value_t acc = *first;
       *d_first = acc;
       while (++first != last)
       {
           value_t val = *first;
           *++d_first = op(val, std::move(acc)); // std::move since C++11
           acc = std::move(val);
       }
       return ++d_first;
   }

Notes
   acc was introduced because of the resolution of LWG issue 539. The reason of using
   acc rather than directly calculating the differences is because the semantic of the
   latter is confusing if the following types mismatch:
     * the value type of InputIt
     * the writable type(s) of OutputIt
     * the types of the parameters of operator- or op
     * the return type of operator- or op
   acc serves as the intermediate object to cache values of the iterated elements:
     * its type is the value type of InputIt
     * the value written to d_first (which is the return value of operator- or op) is
       assigned to it
     * its value is passed to operator- or op
 char i_array[4] = {100, 100, 100, 100};
 int o_array[4];
 // OK: performs conversions when needed
 // 1. creates “acc” of type char (the value type)
 // 2. “acc” is assigned to the first element of “o_array”
 // 3. the char arguments are used for long multiplication (char -> long)
 // 4. the long product is assigned to the output range (long -> int)
 // 5. the next value of “i_array” is assigned to “acc”
 // 6. go back to step 3 to process the remaining elements in the input range
 std::adjacent_difference(i_array, i_array + 4, o_array, std::multiplies<long>{});

Example
// Run this code
 #include <array>
 #include <functional>
 #include <iostream>
 #include <iterator>
 #include <numeric>
 #include <vector>
 void println(auto comment, const auto& sequence)
 {
     std::cout << comment;
     for (const auto& n : sequence)
         std::cout << n << ' ';
     std::cout << '\n';
 };
 int main()
 {
     // Default implementation - the difference between two adjacent items
     std::vector v{4, 6, 9, 13, 18, 19, 19, 15, 10};
     println("Initially, v = ", v);
     std::adjacent_difference(v.begin(), v.end(), v.begin());
     println("Modified v = ", v);
     // Fibonacci
     std::array<int, 10> a {1};
     std::adjacent_difference(std::begin(a), std::prev(std::end(a)),
                        std::next(std::begin(a)), std::plus<>{});
     println("Fibonacci, a = ", a);
 }

Output:
 Initially, v = 4 6 9 13 18 19 19 15 10
 Modified v = 4 2 3 4 5 1 0 -4 -5
 Fibonacci, a = 1 1 2 3 5 8 13 21 34 55
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
      DR Applied to Behavior as published Correct behavior
   LWG 242 C++98 op could not have side effects it cannot modify
                        the ranges involved
                        the type requirements needed for the result
   LWG 539 C++98 evaluations and assignments to be valid added
                        were missing
   LWG 2055 C++11 acc was not moved while being accumulated it is moved
   (P0616R0)
                        for overloads (2,4), the result of each
                        invocation assign the results
   LWG 3058 C++17 of operator- or op was assigned to a to the output
                        temporary range directly
                        object, and that object is assigned to the
                        output range

See also
   partial_sum computes the partial sum of a range of elements
               (function template)
   accumulate sums up or folds a range of elements
               (function template)