std::adjacent_difference

Defined in header `<numeric>`
template< class InputIt, class OutputIt > OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first );	(1)	(constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardIt2 adjacent_difference( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );	(2)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOp > OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first, BinaryOp op );	(3)	(constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp > ForwardIt2 adjacent_difference( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp op );	(4)	(since C++17)

Let T be the value type of decltype(first).

1) If [first, last) is empty, does nothing.

Otherwise, performs the following operations in order:

Creates an accumulator acc of type T, and initializes it with *first.
Assigns acc to *d_first.
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++20)val - std::move(acc)(since C++20).

c) Assigns the result to *++d_first.

d) Copy(until C++20)Move(since C++20) assigns from val to acc.

2) If [first, last) is empty, does nothing.

Otherwise, performs the following operations in order:

Assigns *first to *d_first.
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++20)op(val, std::move(acc))(since C++20) 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++20)binary_op(val, std::move(acc))(since C++20) 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++20)

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.
op	-	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); 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

N-1

applications of operator-.

3,4) Exactly

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++20
        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++20
        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
LWG 539	C++98	the type requirements needed for the result evaluations and assignments to be valid were missing	added
LWG 3058	C++17	for overloads (2,4), the result of each invocation of operator- or op was assigned to a temporary object, and that object is assigned to the output range	assign the results to the output range directly

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